Hi friends welcome back to my channel and welcome if you're new here. My name is Jen I'm a certified weight loss and nutrition coach and I'm on the WW or the Weight Watchers blue plan It is a monthly favorites video And I am so incredibly excited about all of the favorites that I have to share with you guys there were so many I actually had to save some for next month So what I'm showing you today are all of my January favorite things. We have WW foods Beauty kitchen you name it We have the bases covered and I will make sure that I link everything that you can't pick up at your local grocery store like some of the WW foods down in the description box everything I show you today are my new very very favorite things So if you're excited for today's video, please give it a big huge thumbs up It means a lot to me and lets me know to keep putting out these monthly favorite videos And if you're new or you're not yet subscribed, I'd love to have you join my channel Just hit the little subscribe button and of course the bell next to it So you're notified whenever new videos are uploaded Don't forget to check out the description box where I will link everything I shared with you today As well as my 2021 custom calendar. I'm about sold out. So if you're interested This is your last chance to pick one up for 2021. They're amazing They're a great way to track self-care water fitness and food and of course your life as well There's lots of space for you to track your day to day activities on the calendar as well You'll also find my nutrition coaching where I offer personalized to you macros and calories Highly recommend having this service done. So you know exactly what you should be eating every day to be most successful in your weight loss I also have 30 in 60 minute one-on-one sessions if you just need a little bit of extra One-on-one coaching all of the other links and discount codes to my other favorite things not mentioned in today's video Are also in the description box as well as my facebook group. We'd love to have you come join us over there So we have lots and lots and lots of favorites to go over. So let's jump in Start with my ww food favorites for the month of january First thing I want to share is a frozen item so that I can get it back in the freezer So this is the birds eye veggie made mac and cheese elbows with cheddar cheese sauce Now I used to eat this all the time and I kind of forgot about it And I've recently rediscovered it and myself and my husband are loving this It's a great way to get your kids to eat their vegetables because it's actually made with zucchini and lentils But you would never ever know it. It is super reasonable in calories and points You can eat the entire bag for 440 calories Which is not bad at all popping a little bit of zero point protein and have a one cup serving and you have a really delicious Decadent meal. So highly recommend they have quite a few different veggie made pastas from birds eye We've tried most of them and they're all really good. You truly can't go wrong with any of them Next up is my new favorite sparkling water. I have been raving about this not only on my facebook group Instagram and even here on youtube. These are the aura borah waters So this is a brand new start-up company. They actually were just featured on shark tank and struck a deal So congratulations aura borah, but I discovered these from the thrive market The thrive market is the least expensive place to purchase the waters and I have a membership So I just went ahead and ordered a whole bunch of their waters because not only do they taste Incredible they are made with clean ingredients I've always talked about spin drift and how that is the only sparkling water on the market that doesn't have natural flavors Until aura borah came into my life. It is made with the essence of flowers herbs and fruits So no natural flavors nothing artificial It is perfection when it comes to ingredients and the flavor just shines through I have to say that my favorite flavors are the peppermint watermelon The basil berry and then the lemongrass cucumber. I also love the cactus rose and the lavender They're all absolutely incredible. So I recommend picking these up off the thrive market Right now thrive is offering you 25 off your first order when you join the thrive market Plus they send you a free gift. So you can pick up the aura borah waters at the cheapest price with an extra 25 off So I'll link thrive down below for you. I have also seen the aura borah water at walmart But I only saw one flavor in my area and that was the basil berry And then you can also buy it on the aura borah website, but it's much more expensive than picking it up off of thrive So highly recommend thrive for your aura borah water next up are these tuna packets And I picked these up at costco because they were on a really good coupon 899 for eight of the pouches each one of these pouches is 26 grams of protein 110 calories It is the best tasting tuna. It is a safe catch tuna. It is 100 wild yellow fin I don't know what it is, but the tuna fish is superb I've been mixing it with a little bit of mayo and wrapping it up in some lettuce I also made a really good tuna pickle lettuce wrap in my last what I eat in a day video So I've been loving having these because you can't beat 26 grams of protein for 110 calories So if you struggle to get your protein in these ahi tuna packets are a great way to up your protein game Also at costco, I found these everything but the bagel parmesan crisps These are so good and they're nice clean ingredients. It's literally parmesan cheese I've been loving these as a snack So it's a good way to get in some fat as well as some protein But what I really like to do with these is pop a few of these on a salad in place of croutons They are so delicious. They're about the size of a quarter. They're really really good They're pretty pricey at the grocery store, but they were on sale at costco And this big bag I think was less than seven dollars Which is a great price for nine and a half ounces of parm crisps Also at costco. I found the reyos italian wedding soup and it was such an excellent price I had stopped by my local natural grocers Which is like our whole foods or sprouts in my area and paid $5 for one jar of the reyos soup I found the three pack at costco for $7.99. This soup is so delicious Not only does it have excellent flavor it again has nice clean ingredients You can have a one cup serving or the entire jar the entire jar is eight smart points And in my what I eat in a week video that I put out recently I had this for dinner one night filling delicious satisfying and clean you can't beat it So if you have a costco or possibly a sam's club in your area That is the best price to pick up really any of the reyos products the marinara and especially their jars of soup Pistachios are my very favorite nut But I can overeat pistachios or really any nut very very easily So i'm a big proponent on buying things that you tend to overeat in individual serving size packs So when I was at walmart, I saw these pistachios both in the shell and out of the shell In individual serving packets nine bags for about seven dollars Which is a really good deal that's less than a dollar per package And I decided to go ahead and go with the ones in the shell So that number one I would eat them slower and enjoy them and I actually had to work for the pistachio They are only four smart points per package and 130 calories Nuts are a great source of healthy fat and they give you a little bit of protein as well So I've really been liking having these as a go-to snack I have them in my car my purse since they don't need refrigerated. They're really truly a great Really easy go-to snack and last but not least for ww foods is this boom chicken pop and cheddar and caramel corn So i'm not the biggest fan of boom chicken pop a lot of the other flavors But I decided to give this one a try. I actually ordered this from imperfect foods You guys know I get their box every couple of weeks and they do rotate in and out the products that they carry And the last time I ordered they had this cheddar and caramel corn. Oh my gosh, it is so good It is that pub style popcorn. It's amazing I will always always repurchase this as long as I can find it either in my grocery store Which I've never seen or on imperfect foods I'll also make sure imperfect foods is linked down below for you guys with ten dollars worth of free groceries But this popcorn is delicious. It's dangerous So I make sure that I weighed out on my food scale one serving and I take that to watch tv instead of the entire bag because Next thing I know the whole bag would be gone. Now. Let's move into my beauty favorites I actually have quite a few new things this month that I've really truly fallen in love with Starting with some lashes now you guys know I'm a big proponent of the toribelle magnetic lashes But I'm a little bit bored to be honest of the variety of lashes that they have If you know me, you know that I really like the more dramatic lash versus the more natural looking lash And toribelle does have some dramatic lashes, but they have a lot of very natural looking lashes as well So a company by the name of majosi reached out to me and offered to send me some glue on press on nails And I declined just simply because I have Nails from the salon, but I didn't realize on their website that they also sold lashes So I did a little peeking around and I came up with some lashes that I fell in love with And I wanted to share those with you guys because I've been wearing the majosi lashes a lot now Don't get me wrong. I still really like the toribelle. They serve their purpose But majosi just has a wider variety of styles very natural very short to very long and very dramatic So I went ahead and actually picked out six different styles of lashes and majosi sent those over to me So thank you majosi for sponsoring this portion of my favorites video because the lashes are definitely most definitely My favorite now I buy my glue the duo glue off of amazon It's the most affordable So I'll make sure that I link the glue as well as all of the different lashes I picked And the majosi website so that you can see what other types of lashes they have because like I mentioned They have everything from very natural to very bold and very full long lashes as well So I think that the packaging of the lashes is absolutely stunning. It is a magnetic closed pink box plastic That's very easy to pull out of the box So that you can peel the lashes off and apply them I find them to be very very easy to apply I just put a very thin line of glue on the lash Press them on and then I just use this little eyelash tool to press them down and make sure that they're firmly attached to my I don't notice that I'm wearing them. They're very lightweight. They're very natural feeling But they definitely give you a fuller lash look whether you're going for dramatic or much more natural I'll go ahead and show you all the different lashes that I picked out I'll pop the price and the name of the lash here on the screen so that you can see some of the different lashes That I selected so you'll see that I picked some that are very dramatic very bold very dark I also picked some that are a little bit less long But a little darker and bolder just so that it gives you that fuller eyelash look I also went ahead and selected some like the ones that I'm wearing today that are very long and dramatic That are very very long and dramatic. They also have a great selection of wispy lashes So these are a great dupe for the ardell wispies and they're less expensive and higher quality I picked quite a few of the dark long and bold eyelashes just because that is much more my style than the natural But you can see that I went with a natural looking lash a wispy lash And then several of the really bold styles down in the description box I'll link a video that majosi put together on how to apply the lashes even though I showed you how I put mine on for today I will also make sure that I link that video down below for a little bit more in-depth application process I am loving majosi. I definitely will be using these as my go-to gluon lashes So definitely check out their website see all the different varieties that they have and thank you again to majosi For sponsoring this portion of today's video My next beauty favorite is this kodi airspun original formula loose face powder Now to be honest this reminds me a lot of my grandma and I don't know if I remember seeing this packaging Or if just the the packaging style reminds me of her But this is not your grandma's powder. This is an amazing amazing powder. Now. It is a translucent loose face powder So what I do is I apply this After I have applied my foundation and my concealer in place of a pressed powder You know I'll bake my under eye and then I'll apply that kodi loose translucent powder before I apply bronzer blush highlighter I love it.  Let's be honest We're staying home a lot. We're not going out and about very much So it's very unlikely that we're going to put on a full face of makeup every single day So I love that not only does this serve as my moisturizer in the morning It's also my very natural looking foundation now. It's not full coverage I would say that it's very much a light coverage But it's just what you need to add a little tint to your skin and to just cover up any small blemishes that you may have So i'm loving this I wear this more than I do traditional foundation And I especially love that my moisturizer is part of the foundation If you didn't know beauty counter is a cruelty free completely clean brand of skincare and makeup If you watch my videos, you know, I use a lot of their skincare and their makeup as well But highly recommend next is this matte and I know that it looks a little bit lackluster But this matte has been a game changer for me As you know, we recently remodeled our bathroom and we have granite countertops And I was afraid that my hot curling iron or flat iron would crack or damage my countertop So I went on to amazon and ordered this little mat and what I do is I just put this on the countertop And place my hot tool on top of the mat until it is cooled That way I don't have to worry about it cracking my countertop It was so cheap less than 10 dollars and I just throw it in the drawer and when I'm done doing my hair I put it on my counter and put my hot tool on it. So I love it I'm really excited that I picked it up and it is so small that you could even take it with you If you were to travel my next beauty favorite is the jackal and hill by morphe eyeshadow palette I have recently gotten back into wearing eyeshadow I usually would just wear a liner and then a bolder lip But I've been loving experimenting a little bit more with eyeshadow. I'm a little bit of an eyeshadow snob I definitely don't want one that has a lot of fallout because I don't want to have to clean it off of my face So I've heard rave reviews about this jackal and hill morphe palette So I went ahead and ordered it and you guys I am obsessed with it There is a total of 35 shades from neutral to really bold You can create any eye look with this palette and this palette is super super affordable A lot of you have complimented on my eyeshadow lately. So thank you. I've been using this palette I ordered this off of the morphe website But I'll do a little peeking around online to see where I can find it for the least expensive And I'll definitely link it down below for you guys. I just ordered another one of the jackal and hill palettes So if I love it as much, I'll share it in a future video But if you're looking for a very versatile neutral and glamorous eyeshadow palette Definitely pick up the jackal and hill and my last beauty favorite actually comes from a company called madame glam And this is an at home gel polish company I am not about to purchase a hundred or two hundred dollar UV light to do gel polish at home So I was looking for something that was a more affordable alternative Now as you know, I do get my nails done at the salon, but I do like to in the winter paint my toenails I'm not someone that gets a pedicure in the winter. I usually reserve my pedicures for the summer I feel better spending the money on those during the summer when my toes are exposed not in the dead of winter When I'm wearing snow boots, but I still wanted my toes to be pretty So I went ahead and ordered a few polishes from the madame glam website I ordered their soak off base coat and their soak off top coat and then you know my love for glitter So I went ahead and ordered a glitter polish. It is a nude, but it has a nice pretty gold glitter It is called casual friday So I'm loving this if I'm wanting just a little bit more Nude or even to put over the top of the other color that I ordered and that is drama queen And this is a red and it also has a little bit of glitter. I'm a sucker for glitter So sometimes I'll put the casual friday over the drama queen Sometimes I'll just use this one or this one But I was able to pick up the base coat the top coat in two different colors And a UV light. Are you ready for this? This is the box that the UV light came in It's very very small, but it is very very affordable and it is very very effective So this here is my UV light. It is usb charge So I just charge it in a usb outlet You can see on the bottom here that it has the little feet That pop out so that you can put your hands or your toes right underneath it has a very bright UV light And like I said, it's extremely effective and extremely extremely affordable They have tons and tons of polished colors on their website And to be honest with you quality and wear these are the best gel polishes I've ever used and for the price you can't go wrong I just was happy that I didn't have to spend a hundred or two hundred dollars on the UV light. This is small It's compact.  I'll link them down below for you guys with 30 off Thank you, madam glam for offering a discount for my subscribers It really means a lot to me the link for the 30 off down below for you So if you're like me and you're looking for an affordable gel polish system at home Highly recommend madam glam and my last two favorites. I guess you could consider to be health and home First are my probiotics, but before I jump into those I need to take them for today Several weeks ago, I ordered a gut health kit test from a company called thrive So what they did is they sent me the test kit. I sent them a sample They sent me back my gut health results and then they customized a probiotic for me that is custom Just to me I was deficient in five good bacteria in my gut and all five of those good bacteria are part of my daily probiotic I take two of these every day. There are soft gel capsules. So they're very very easy to take I just take them with a couple of swigs of water after a meal breakfast lunch Whenever you remember to take them you can order them by the one month or three months supply But let me just tell you like I've mentioned before in several other videos These have been a complete game changer for me. My gut health has never been better My sleep my weight loss my skin has never been better Like I said, I was deficient in five good bacterias All of those correlated with sleep skin and weight loss maintenance and weight gain So since I've been taking this I've noticed all three of those areas have dramatically improved I'm a lifer for the thrive probiotics once you take the gut health test You can order your probiotics again in a one month or three month supply And what's really exciting is sitting right here in my hot little hands is my husband's gut health test So when he saw the results from my gut health test and how much better I felt After taking the probiotics, we ordered him a test and I'm dropping this bad boy in the mail today for him So that we can check his gut health and get him his personalized probiotics So when it comes back, I'll be sharing it with you guys on a future video And we'll compare his gut health to mine and the areas in his gut health that need improvement compared to mine So I am going to link the thrive gut health test down below with a 50 off discount for you Thrive was so nice to offer a link for 50 off just for you guys So I'll link that down below if you struggle with your gut health or you feel like that may play a part in why you're not losing weight Definitely definitely check out thrive figure out where your gut health is And how you can improve that to just have a better overall quality of life And last but not least is the cup that i'm currently drinking out of so this was an instagram ad that got me I'm really bad about that facebook instagram. They get me every time But this cup is actually called a brew mate. So this is a yeti dupe It's much more affordable. I think it's adorable with the black leopard print on it It keeps your beverage so cold or so hot The other day I got sidetracked for about an hour came back and my water was just as cold So it's an excellent excellent yeti dupe because it's much more affordable I love the lid because it's spill-proof and there's a spot big enough to put a straw in And I always like to drink my water out of a straw. This is the imperial pint in the onyx leopard pattern There's tons and tons of different colors and patterns and different products. So this is the 20 ounce tumbler They actually have these that go around energy drink cans beer cans or pop cans beer bottles or pop bottles wine glasses They have pretty much everything and I love that my water stays cold all day long I pour it in and no matter how long it takes me to finish this tumbler My water's cold till the end. So I will definitely link brewmates website down below for you guys I just clicked on the instagram ad and here we are. Those are my january favorites I hope you enjoyed seeing all of my ww food favorites beauty health and home Don't forget. I will link everything down in the description box for you And if I'm able to find a discount or a coupon code or even the lowest price That is what I will make sure is linked down below for you down in the comments Let me know which of these items you pick up so that we can talk about it and compare our experiences With the products that I shared in today's video If you enjoyed this video, please give it a big huge thumbs up And of course if you're new or not yet subscribed, I'd love to have you make sure you hit the little subscribe button And of course the bell next to it. So you're notified whenever I upload I do a favorites video every month. So you definitely don't want to miss out Don't forget to check out the description box for all of these products My calendar nutrition coaching links and discount codes to my other favorite things and my facebook group Head on over and join us there. We'd love to have you Thank you guys again so much for hanging out with me. Happy february, and I'll see you all in my next video. Bye


Surprising everyone on the upside. Notwithstanding this progress, the target of 4 percent CPI is yet to be reached and we have to stay the course. Headline inflation continues to be volatile due to multiple supply side shocks which have become more frequent and intense. The trajectory of food inflation needs to be closely monitored. Recent vegetable price shocks could once again push up the headline inflation in November and as I said possibly December. While monetary policy would look through such one of shocks, monetary policy has to stay alert to the risk of such shocks becoming generalized and derailing the ongoing disinflation process. In the midst of these uncertainties, monetary policy has to remain actively disinflationary to ensure a durable alignment of headline inflation to the target rate of 4 percent while supporting growth. I would now like to focus on the liquidity and financial market conditions. Like most of the central banks, the Reserve Bank had injected additional liquidity into the system to counter the COVID-related onslaught on our economy. Consequently, the size of the Reserve Bank's balance sheet had expanded significantly. Persistence of such expanded balance sheet far too long could have created macroeconomic and financial instability. It is worth noting that the Reserve Bank has successfully reduced its balance sheet size well in time. Illustratively, the size of Reserve Bank's balance sheet swelled to 28.6 percent of GDP in 2020-21. With modulation in liquidity in the post-COVID period, the balance sheet size moderated to 23.3 percent of GDP in 2022-23 and further to 21.6 percent in the current financial year up to December 1. We consider this as a significant achievement. System liquidity as measured by net position under the liquidity adjustment facility that is LAF turned into deficit mode for the first time in September this year after a gap of nearly four and a half years since May 2019. Deposit liquidity conditions persisted during October and November, prompting large records to marginal standing facility that is MSF by the banks. In parallel, utilization of standing deposit facility that is SDF has also been high. The overall tightening of liquidity conditions is attributed mainly to higher currency leakage during the festive season, government cash balances, and Reserve Bank's market operations.


Hi there. So my talk today is not so super notes. How well does the US dollar note prevent counterfeiting? And introduce myself. My name is Matthew Duggan. I'm a member of technical staff at VMware and I've been a software engineer for almost ten years. I hold a bachelor's and master's degree in computer science. What interests me about security is I just, in working with systems, I like testing the limits of them and seeing how they react to adverse input. I'm also an amateur lock picker and beer brewer. So what this talk today is, is the security of US dollar notes. What the security is, how it's implemented, and how good a job it does at deterring counterfeiting. And so specifically what we're going to analyze is exactly what, um, how well it stands up against counterfeiting. And through information that I've read through publicly available sources, I'm not affiliated with the US Treasury nor have any affiliation with counterfeiters nor have attempted counterfeiting and nor intend to. So the reason why this is important is because despite the fact that a great deal of financial transactions are done electronically, the US dollar note is still widely used both nationally and internationally. And the value of the US dollar note or any other note for that matter is directly dependent upon its security, among other things. Counterfeiting attacks against currency at a low level lead to financial losses to the victim of the attack. But at a medium level can devalue the currency and at a large scale can actually constitute as an attack of economic warfare. And this has been done in the past and war is including World War II, the Civil War and the Revolutionary War. Now for this talk, I'm only going to be talking about US dollar notes. And as far as counterfeiting, I'm only going to talk about counterfeiting attacks in regards to the analysis of the features on US currency. So this will not be a how to, to happen with as far as counterfeiting. And I'm not going to be talking about coins or any other currencies. Now before I continue, I'm sure you all know, but I just like to say for the record, that counterfeiting is a very serious crime. And by counterfeiting I simply mean the creation of counterfeit notes. If you actually try and use a counterfeit note in a financial transaction, this is an even worse crime, which is known as passing a note. To give you an idea of the level of severity of it, it's actually defined directly in the Constitution alongside treason and piracy, not software piracy. And the, the Secret Service who investigates and arrests counterfeiters does so in a way that they try and maximize the conviction rate. And they boast a conviction rate of over 90%. And they also heavily emphasize investigations of amateur counterfeiters. So as far as the, the dollar design has been concerned, prior to the major redesign that was done in the 1996 series of bills, the US dollar note enjoyed a fairly long history with little change. The, that particular design was first issued in 1928. The reason why the design started changing and starting in the, starting with a major design in the 1996 series is due to the, due to research that was initiated by the US government about the emerging threat model of high quality scanning and inexpensive home color printing equipment, as well as the increasing incidents that were seen counterfeits. This was done in 1993 and additional studies were commissioned in 2006 and 2007. These studies were done by the national academies who assembled a panel of experts from the following institutions. What they found was is that the, the dollar note needed to be redesigned in order to better deter against counterfeiting threats. And this has led to two major redesigns, one being the 1996 series for denominations 5, 10, 20, 50 and 100. And the 2004, 2006 redesign of 5, 10, 20 and 50. And the unveiled but yet to be released 2009 redesign of the $100 bill. You have an idea, here's the $100 bill for the last 90 years. Anyone tell me it was on the 1922 bill? I heard someone say Benton, that's correct. So the US government that's in charge of designing the US dollars and also printing them is the Bureau of Engraving and Printing which is part of the US Treasury. I'm sorry, Department of the Treasury. They operate two printing plants, one in Washington D.C. and one in Fort Worth, Texas. The paper that's used for printing bills is made by a small family owned company in Dalton, Massachusetts known as Crane and Company. They are the sole supplier for secure paper for the US government and they also provide paper for passports and print currency for several small countries. Prior to the, prior to the 1996 major redesign and also the minor redesign of 1992, the original security bills are these three main features. First, the secure paper made by Crane and Company, it's a 75% cotton, 25% flax based paper, which makes it very durable and is created in a very painstaking process to give it a readily identifiable feel. Second is the Intaglio method of printing. Intaglio is where you take, you engrave an image onto a metal die and within the press, you fill ink into the recesses, wipe the top of it clean, and then press it into the paper at very high pressure. This gives the image that is printed a raised feel to it that is also readily identifiable. And lastly, are red and blue silk fibers that are distributed throughout the paper substrate to further, to further complicate the counterfeiting of bills. By the way, feel free to take out a bill and follow along with me in these features. So current security has added the following features to bills. First is the micro printing, which you can see from the first image, is a zoom in of the color of Benjamin Franklin, where they have United States of America is written in very fine print. This was added to thwart scanning and printing, which could not, for ones that were incapable of doing such a resolution. Second was the multicolor background, which was added to complicate the overall design of bills. Next is the watermark, which is visible in transmitted light, which is to say light transmitted through the bill, but not reflected light, which is light reflecting off the bill. This is a feature that can't be duplicated through scanning and printing. Also, there was the fairly high tech optically varying ink that was added to the bill. This is an ink that varies between one of two different colors that is generally was originally for the 1996 series was on denominations 20 and above. On later designs, it was on denominations 10 and above. This ink changes color depending upon the angle of incidence of light. So in holding up the bill, you'll be able to see a color change as you move it back and forth. This is accomplished by having microscopic particles that do this light changing effect suspended within the ink. Next is the security strip. This was added back in the minor 1992 redesign. This is a strip of polyester that's woven into the substrate of the bill, which is only visible in transmitted light. The security strip is has the denomination printed on it to defend against attacks where someone would try to change the denomination of an existing bill. It also glows a specific color by denomination under a black light, which also aids in defense against this kind of attack and is placed in a different position by denomination. The last two features, the magnetic ink and the infrared ink, are invisible to the naked eye, but were added to aid in machine recognition of bills. So to analyze how good a job all these features do together, I looked at each feature to determine one of two things. First, could it be replicated? And this is within the scope of a small scale operation. So say small group of people with money probably ranging in anywhere from like hundreds to probably tens of thousands of dollars. And whether it could be replicated, which is to say creating the same feature using the same processes or imitated, creating a facsimile of the feature which was suitable to pass. So, and let me just also add that the feasibility of the replication and the effectiveness of the imitation are justified by research that I have done for millions of dollars of counterfeits that have since been successfully created and passed. So the paper is by far the most difficult and complicated feature of the bill. Like I said before, it is 75 percent cotton, 25 percent flat-space paper made by Crane and Company. Now any paper making operation is a very difficult undertaking. It's very expensive, very complicated, requires very large equipment in order to make and expertise. Secure paper making is an even more difficult process. To add in difficulty of this, that particular paper that's used for the dollar is the only secure paper of its kind and it's only made by Crane and Company. So expertise in making that is very limited. Crane and Company also manufactures their paper using a different process than any other secure paper company in the world. They use a fordrenier machine whereas the others use a cylinder mold machine to form the paper. So expertise in that and secure paper making is also very limited. Added on top of that, a expert within the secure printing industry was quoted as saying to recreate the secure paper making operation Crane and Company would cost on the order about a hundred million dollars. So this is infeasible for any small scale operation. So for imitation we have to be concerned with two major features, two major tests of the paper. First, the counterfeit pen and second is the feel of the paper. So the way the counterfeit pen works is that this draws a yellow on genuine currency and draws black on fake currency. It's very inexpensive, very easy to be used by any cashier. So this is obviously a test that would have to pass. Now the way in which it works is that the secure paper used for it is a starch free paper as opposed to most other papers that are made. Most other papers, other starch free papers such as newsprint that are also made without starch would also mark as genuine currency. So if we use something like that we could pass the counterfeit pen. So the question then remains, if we used a starch free paper as our base for printing, for a counterfeiter to print their bills, would the feel of it, the lack of the readily identifiable feel be recognizable by an average person? Turns out from millions of counterfeits they're not. Oh yeah, in addition, as far as replication, in not being able to replicate the paper, the other features such as the red and blue fibers in the watermark would also not be replicable because those are required to be made during the paper manufacturing process. So as it turns out, from millions of counterfeits that have been passed, newsprint is not identifiable as fake by an average person taking a bill in a financial transaction. It's also very cheap. I estimated this cost by looking at a roll of newsprint on Amazon and defining the area by the effective number of bills and then dividing the cost by that. So second, we have to come up with a solution for the Intalio printing. So Intalio is the de facto standard for secure printing in the entire world, which is because of the fact that the metal dies that are used to make the bills are extremely difficult to reproduce. The machines are extremely expensive and access to them is limited. And the feel of it that's put into the paper by the Intalio is infeasible to create using any non-Intalio process. So the Intalio, secure Intalio presses are only made by three companies in the world and they're only sold to countries and private printers, private secure printers that is, which is a very difficult club to get into. And it's also one that's very visible to the secure printing industry who greatly frowns upon counterfeiting. So the, and the cost of one of these presses, if you had access to them, it's unknown because of the fact that secure, the secure industry generally uses non-disclosure agreements in the sale of any of their materials. And so the finding that is difficult. However, I did find an expert who said, who stated that the cost of a single secure press would be over fifty million dollars. So this would be infeasible for a small-scale operation. So if we wanted to imitate it, we would need to make sure that we had an image that was suitable for a person to be able to, that would look like the bill, which would include the precision of the micro printing as well as all the other subtle features of it. And it also might have to replicate the feel of Intalia. So if we use the low-cost, low tech approach, meaning we use a retail scanner and printer, we can easily replicate the precision of the images on the bills. So the question here is that, I mean, a secure, a professional money handler could definitely tell the lack of the feature of the Intalia type of printing. But the question is, could an average person do it? If the bill looked close enough to a genuine one? And turns out, they're not good at it. This cost is also very cheap and also gives us the ability to imitate the red and blue fibers, allows us to replicate the micro printing, I'm sorry, imitate the red and blue fibers, and also to imitate the multi-car background. Cost for this I found by taking the expected yield of Epson printer cartridges, taking the effective number of bills and dividing it by the cost of them. This also includes the red and blue fibers and the micro printing. Now the multicolor background is an imitation by the inkjet because of the fact that it's generally done by an offset printer. But counterfeits are shown that some counterfeits are made with a offset print press, some are not, and the ones that are not using inkjet, so it's suitable to pass. So that's also, so it's both infeasible because it's already expensive and the expertise is rather high and the fact that it is unnecessary. So next we get to the watermark which is a little more difficult. So the reason why, this is generally made by varying densities throughout the paper substrate. So during the paper making process when they form it, they have a three dimensional cutout on the wire mesh that the slurry is put upon, such that more would collect along the darker portions of the image, which is then pressed out to the same width. So unfortunately this is actually easily imitatable by a very low cost attack, where you simply print out an image of the watermark and you put it between two ply bills. Really all it takes is effort to do that. So that is, the imitation of that is certainly feasible and very cheap as well. So the OVI, like I'd say before, is very technically sophisticated. It was, this is an ink that was an adaptation of a technology that was created for the space shuttle. It is made by, like I said, it's suspending these microscopic particles within the ink to do the color changing effect. So, and this is made in a lab, it's very high tech, it's definitely infeasible for small scale operation. Unfortunately for us, unfortunately for the counterfeiters, the company that sells this ink to the Bureau of Engraving and Printing also makes color changing automotive paint. And they of course won't give you the same color combinations that are printed in any currency, but when analyzing whether or not it's the color changing effect or the colors themselves, the effect is sufficient. And this one's a little more expensive. The security strip, very simple. All we really have to do is we have a polyester sheet. We have to be able to print the denomination on it. Although we have to make it go in the dark, but you can get ultraviolet ink and in cartridge form. And just basically print that all out, you cut it out, you place it in the right place, and we're making two ply bills so inserting it in the bill is no problem. That's feasible and very cheap. And these eight features by themselves would give us a passable bill for any person that's receiving it since a person can't check the last two. But in analyzing those as well, the magnetic ink and infrared ink are also available in cartridge form. So if one were to take the time to figure out how to scan the image and be able to buy one of the machines which are fairly cheap in order to test, they'd be able to work out and ensure that they were, once they created and were able to tweak a solution for this, they'd be able to replicate it with high precision. So these are also both very feasible and not too much more expensive. So in the end, if we use this particular method of creating it, we can manufacture bills for less than $3 a bill after the initial cost of the setup and the expertise that we put into it. And really, there's nothing about this expertise that is limited to anyone of any training or anything like that. This is something that could probably be done within weeks or months by any determined attacker. So really what we can assess from this is that the efforts of the Secret Service are pretty good in keeping counterfeit dollar bills off the street since the dollar bill is the currency of choice to counterfeit. So two successful counterfeiters that I'd like to mention, Arthur Williams and Albert Tallton, who were independent of each other, they counterfeited modern currency, meaning the 1996 and the series and on, and they were independent of each other and they were both self-taught. And in addition to that, they also used the method of counterfeiting the bills, which was almost exactly the recipe that I just stated to you. Both of these guys were very successful and also convicted and were able to pass millions of dollars of counterfeit money. The interesting case with Albert Tallton is he was able to get all his supplies from staples. Lastly, I'd just like to touch upon the Supernote, which is what inspired this talk to begin with. The Supernote is different than the type of counterfeit that I described in this proposed attack in that it replicates all major features of the bills. So this includes the paper, the intaglio printing, the OVI, everything. And it does so with very high precision. Called the Supernote because in the opinions of some people, they say in some cases it looks better than the genuine bill. This was first discovered in 1989 by a professional money handler. The way in which they said they detected it was that the feel of the paper was a little off. And this is still around today. It's unknown who makes them. Although North Korea has been formally accused and then that accusation has been somewhat rescinded due to the fact that their diplomatic personnel keep getting caught trafficking large amounts of these. So the reason why it's doubted that they're making them is because secure industry experts have doubted that they would possess the technical sophistication to create the bills given the materials that they would need to create them. I'd love to tell you more about this bill, but unfortunately information is very limited and often conflicting. But if I can find, you know, a sufficient amount of stuff I'll certainly put together another talk on that. If you'd like to read more about the stuff, I recommend the following sources which I used to put together this presentation. First being the book Money Makers, which got here by Klaus Bender, who's a financial journalist. He put together this book which is a very good overview of the international secure printing industry. The next one, the art of making money is a very nice biography on one of those counterfeiters I mentioned, Art Williams, who was caught, went out of jail, then was caught again. It's currently in jail. But it's a very interesting tale as to how he came about becoming a counterfeiter and how he taught himself. And lastly are three publications that were made by the National Academies. These were commissioned by the Bureau of Engraving and Printing to study the current state of counterfeiting, counterfeit deterrent features and the current state of US dollars as to how well they would hold up. It's a very interesting and thorough analysis if you have any interest of this. I mean all the ideas you might think of like using plastic substrates, holograms, or like any other ideas, they generally go over and analyze to give the pros and the cons. And it's also interesting to see why some things might make the design some might not. And that's it. And I think I've got a few minutes left. So are there any questions? Yes. So the question is, is whether or not it would still be illegal to make bills if you did so for artistic or otherwise purposes. The answer is a definite yes, which is why I thoroughly emphasized the thing in the beginning. One of the additional things I'd like to emphasize in that, in these publications made by the Bureau of Engraving and Printing, when they talk about the, they break down the types of counterfeiters they're looking for being from low level all the way up to state sponsored. And the one that they're most concerned about is the amateur. And even ones doing it just to see if they can do it because they see that as a very big threat of someone who's proved to himself that he can make the bill, then we'll think of doing it later in the future. And they're very, they're very specific in saying they want to find these people and ensure that they stop them before they catch them and stop them before they become low level because any distributed attack would be very difficult to to find and take down. So the question is, is whether or not to take a $1 bill and turn it into a $100 bill? Yes, this is a valid attack. There are features and it's one that the US dollar is vulnerable to as opposed to other currencies because all the bills are made the same size. That's one of the reasons in addition to assisting blind people and being able to tell their money in other countries they make bills different size to prevent such an attack. And features such as a security strip that have the denomination in addition to the watermark prevent these types of attacks. Do the same laws apply to making all I see to making counterfeit foreign currency and then exchanging that for American currency. That would most likely fall under the the jurisdiction of the country whose currency you're counterfeiting. And I'm guessing at a money changing station they probably actually would have the machine recognition and and or professional money handlers to direct we go against this. That's so I would imagine that would be a very difficult attack factor. So the question is that the modern designs would be difficult to replicate wouldn't it wouldn't attack or try and and replicate a previous design bill. Yes they could. The the issue with that is is obviously if any large number of counterfeits or any prevalence of counterfeits were to start occurring in those types of bills people would simply stop accepting them as has been shown to give an example of things that I can be done despite the fact there is legal currency. People can still decide not to accept it depending upon the security of the bill which is why I mentioned that as as it pertains to its value. To give you an example in Canada back around 2000 they had a large problem with counterfeits of their hundred dollar bill to a point that about 10% with a it was estimated by the Bank of Canada that when the number of counterfeits reached 300 per million by the way the American is estimated about five per million back in 2002 that about 10% of vendors stopped accepting hundred dollar bills. So that would certainly be a way to which that you would stop having those bills be effective. And I believe that's all the time I have.


The city of Garrison may be dealing with a Grinch. The Garrison Concourse, which normally this time of year is decorated with large illuminated decorations, was vandalized sometime after 9 o'clock Friday night. The Crow Wing County Sheriff's Office reported that a truck went off Highway 169, crashed into the decorations and then went back onto the highway. The Sheriff's Office is looking for a Ford truck with heavy damage to its front passenger side and the bumper that hit the decorations. An estimated $8,000 to $10,000 in damage was done to the display. The Garrison Commerce Club owns the light display. The Christmas decorations had LED lighting that included a large train held into the ground by rebar. The incident remains under investigation, but the Sheriff's Office reported the crash as a possible accident. Anyone with information on the incident is asked to call the Sheriff's Office at<PHONE_NUMBER>. If you've enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland Public Television.


is the sizes. That's what they were created for. So if the woman was very small and the man was much bigger, there are a bunch of positions where the woman's legs are kept as wide apart as possible. If it was the other way around that the woman was very big and the man is much smaller, then there are all these positions where the woman is actually curled up or where her legs are as tightly put together. So either on her side or where you link the thighs and you will actually be able to pulse at the same time so that it contracted the size of the vulva. If of course the vulva was very big and the man was very small, then you resorted to the little armor I was telling you about, the dildos that you had to learn how to make. So what was interesting is that now there's lots of different positions and over time these positions have been changed a little bit. They morphed because you have to remember that furniture morphed. So in yeah, two thousand years ago if I said there was a sitting position it was more than likely you were sitting on a mattress on the floor or a cushion on the floor. Five hundred years later maybe there's a bench. Another five hundred years later you have a chair. So the positions have changed slightly because of the change in furniture. But it's not just the positions, he actually doesn't just give you the structure, the architecture of the positions. It's also about the emotions behind it. So suppose you have according to the Kamsutra again let me tell you this is a really really unusual idea and most people are like no. The best lover is your longest standing lover. That's the best sex. So he doesn't say that you should change lovers and move on etc. He says that the best sex you can have is with the person that you have had in your life for the longest time. And I say this to various people sometimes you know who are about my kind of age and I'm pretty old I'm 57 now and you think I've been married for like 35 years and people are like are you kidding me there's nothing left there. That's the whole point. When there's the least amount of excitement it takes so much longer to arouse yourself to that point that you actually feel all the little steps of arousal. When you see somebody that you fancy that pants off you're up there that quickly and you're finished with it that quickly. It doesn't fit in with his agenda or pleasure because the idea is that every little bit has to come alive and make you feel like you're tingling. You have to be able to feel the little bits because that's where the pleasure actually lies. So the idea is that suppose you're married to somebody who is okay you've had the person in your life for a long time. Let's say okay let's start with this one. He's very good looking, he's very nice, he's very kind, he's very cultured, he's all of those things and he's very good at foreplay.  So there is a position for that. It's called the cobra. I will go into this one position and I won't bother with the others but I haven't actually included the positions in the book because I found that that needed a much deeper study. It's not something you can do in one short chapter. This book has a lot of very short chapters. So in the cobra the idea is that the woman gets herself addressed. She gets it. So again this was something that they believed in that when you were going to have sex it wasn't okay to turn the lights off or wash my makeup off you know let me get back into bed now and no you got dressed for it and there were 16 different things ornaments and makeup and hair and perfume that you actually put on because you acknowledge this is something very special that you were going to do. So she gets herself all dressed up.  According to the Kamsutra the meal has to be had afterwards.  It won't go for the other thing. So yeah so she gets him all. She gets herself all dressed up. She feeds him with just the right amount of stuff. She does all the right things and then because you know she starts to actually pleasure him. She starts to kiss him. She starts to do all the right things and then when she feels that his excitement is getting over there and very likely to finish very quickly she retreats. So that retreat is called the cobra. She retreats and curls herself up in the pillows and does not allow him any access to her vulva and apparently that pulling back at that point instead of letting it come to its natural conclusion and sort of dying away it actually makes the energy go up a little bit. Now I haven't tried it personally but I would imagine that it would work. Either way this was the idea behind it that there was a certain emotion behind it. There were places, there were opportunities, there were times, there were things that would happen. It even goes so far as to say that there was, do you know that we had something called therapeutic sex where you could use certain sexual positions to cure chronic illnesses? Yeah, now you're all here. Including things like gastric wind. So you can actually get rid of wind. So this is again something that doesn't get practiced in India anymore. It's still very big in China or in some parts China. I actually had to go up into the hills to find a couple who treat people with therapeutic sex.  So the couples that come they actually treat them with therapeutic sex. There are different positions. My favorite one is actually where it's, I think they talk about stress relief and the reason I'm talking about the stress relief one is because it just explains certain things. So in the stress relief one they say that the woman, her stress collects over here. So when a woman is stressed and the stress builds up it is a lot of pain in this region and lower backache. For a man the stress seems to collect in the neck and shoulders. That's where they will have the pain. So this is okay. Therapeutic sex depends on thrusting. It's an art. Thrusting is an art. You have to practice the art of thrusting. Get it absolutely right and flow it. We have a chapter in thrusting you can practice. It's very good actually to understand how to do that. And therapeutic sex depends on how long you can hold a position. Okay because it's very very slow. And for stress busting one you have the woman lying flat on her back and the man has to kneel. Okay and sorry and she has a rectangular cushion under her bottom. So the different shapes of cushion will change the angle at which the energy will flow into you.  That's how therapeutic sex works.  That's what the basis of it. So in this one you have your rectangular cushion under your bottom then you have the man kneeling in front of her on the floor which is why the bed had to be a certain height. You know I said to you the first part of the book was all about how to decorate your house and what all to do. So there are eight different types of cushions and so on and so forth. Anyway because the man has to be as straight as possible because that's when his energy will flow up and down. The woman has to be as flat as possible because that's when her energy will flow up and down up here and I don't remember how many thrusts there are but at some stage you read that up and I told that it's very very useful and very good for you. So yes so positions actually had a huge amount of importance but not for the reasons that we think it is. There are a couple of them that I don't understand how. I mean all of this sounds very good and it sounds very good of like yeah it makes a lot of sense but there are a couple of positions that I truly don't understand. There's one in particular where the man lies flat on his back. The woman sits on top of him she penetrates and then she goes round and round. I have no idea why. It's been it's been a 10 long years of studying this. There are a lot of things I still haven't discovered what they mean. There's another one which is I've never known anybody who's been able to do this. So you have the sitting positions. The man is sitting. The woman sits on his lap, penetrates and then he somehow manages to flip around so that she's facing the other way but they have not broken contact. That has to take a lot of doing. A lot of yoga. And then if you're really really really good at what you're doing then the man also flips around. I think in this case he's on the he's on his all fours on the ground and she's on top of him. I don't know I've been trying to work this out.


Hey everybody! Super exciting lecture today because we finally get to talk about something that is alive. Before we start our lecture talking about the cell, I want to take you through a little slideshow of some different kinds of cells. Inside humans, now if you haven't figured it out already, I definitely have a human bias. I find human anatomy and physiology super interesting and I definitely know more about humans than any other critters out there, but this class as a general biology class, we have to prepare you with content to get you into anatomy and physiology but we also have to take some time to appreciate all life and the diversity of life. That's one of the coolest things about this class. So let's just start with a little survey of some cool-looking cells. This first slide has two different kinds of cells. They have a lot in common, these two cells, but if you look at them, you're like, dude, what are these even? Both cells, and they are. The one on the left is a protist. It's a animal-like single-celled organism. One single cell, that's its whole being, and we'll spend some time talking about protists. They're kind of a weird group of critters. The cell next to it is a neuron. That's like a brain cell in humans or in lots of animals have neurons. It's kind of an advanced nervous system cell that plays a role in communication. You can see how that cell has the central cell body, like we will see all cells have, but then it has these really long extensions of basically of cell guts, like cell membrane reaches way out and it has all the cytoplasm and cell guts that reach way out and communicate with other cells. One of the things that we will see is that cells really specialize for their needs. So different kinds of cells look the way they do. They have the structures that they have because those structures enable various functions. This is a single-celled fungus. It's a yeast. Yeast, I mean, anywhere we go, we got to appreciate our yeast. Yeast are provided gases to make rising breads. So if you like bread, then yeast are your friends and of course yeast pee is alcohol. So in the absence of oxygen yeast make alcohol and lots of humans like to ingest yeast pee and have a good time. We'll talk more about that at a later date for sure. Here are some red blood cells. These are one of the smallest cells in human bodies. They look kind of like little doughnuts and they fill our bloodstream. They carry oxygen and carbon dioxide around oxygen to your cells.  Garbage, that's why we breathe it out. Thank you, red blood cells. White blood cells. They don't carry oxygen around. They use the oxygen. They produce carbon dioxide, but they are our immune system. So you've probably been hearing a lot about white blood cells and T cells and different immune cells in our bodies. And this is one of them. The other thing that I think is really cool is to look at this. You might look at this and be like, dude, what is that white blood cell sitting on? It looks to me. I'm like, oh my gosh, it's a parasite worm that it's sitting on and it isn't. It's sitting on the fibers that form blood clots.  Here is a bacterium. Now this type of bacteria, if you look really closely, each one, they're like these little rod-shaped cells. Bacteria are much smaller than all the other cells that we've looked at so far and we'll talk about those guys. But I just think, I don't know, I got a little enchanted with the person who went through and colored all these micrographs because they are super pretty. But they just kind of, again, show you the diversity of what we can see out there. We've seen Henrietta Lacks's cells before. Remember these came from her cervix when they were diagnosing her with cervical cancer, took her cells, didn't ask, and continue still, are using her cells. And I don't think they've even yet, maybe they finally have compensated her family. But you can see some of the qualities of cells that are common to all these guys. You can see that big red nucleus and we'll talk about that guy at length. I could spend all day looking at these guys. Here's another protist, a single-celled organism, and these guys have stalks. And I learned when I was finding that picture going, oh my god, that's so cool. I learned that they have a that little stalk has the fastest muscle proteins. I don't know. I'm sure they don't call the muscle, but mover, mechanical movement proteins known that we know of. And there's a video, I'll try to link it somewhere so that you guys can check this out, but there's a video that they took of this guy where just all of a sudden like one of them will like contract and like run away. And then they, their little stalks come back up again, and then they'll contract really really fast. And you can see how how fast it happens, but that's one-cell. That's one-cell with some sort of cellular appendage that has this phenomenal function. I don't know if you can see it down here in this corner.  This is a filamentous green algae. So this is a multi-cellular organism, but I just was again enchanted by the colors and how like organized and nicely structured these cells are. Each one of these boxes is a cell and it's filled with all the cell parts that we have seen and we will see in this whole lecture. Here are a couple more protists. This is a really interesting series here because these protists, you can see that fur that's all over them.  So that's how these guys move around. And I believe the guy with the two strings of cool hair, I think that guy is about to eat the furry one with all the hair. So there's actually a really cool series of pictures where you can see the one cell ingesting the other one. We'll talk a lot about energy and why everything needs to eat. So of course, of course, there are white guys involved in our conversation and I need to say this out loud. We're gonna talk about the cell theory and I'm gonna give you some facts about the cell theory. These guys came up with cell theory in the 1800s. I believe they're both German fellows. They were friends. I think they were botanists, whatever. We see a lot in any time I go and try to look up some history of science because it is interesting to think about the humans who discovered these things and think about them working together and the process of science. It is really interesting.  And those were the two rules to participate in science. Now those were the rules to participate in science, the science that we know in our society. And I think it's really important to keep in mind that that's where our information is coming from and that's who got to participate. I would like to think that we must change that. We must have diverse minds. We must have diverse perspectives. When learning, especially now, like the stakes are kind of high, we have lots to learn. But when I show you some of these historical humans, I definitely want to be sure you know that it was a very exclusive time in science. And I would argue an exclusive time in history as well. So the historical information that we get is determined by people who had penises and white skin. Okay, so let's talk a little bit about the concepts, the ideas that these guys came up with. And just take a second to think about they had access to microscopes, but they like this was kind of amazing for them to figure out that basically everything is made out of cells. Okay, so let's go. Let's see. I'm gonna close that down. I'm gonna go here. We want to do this. Come on now. Hold, give me a second. Okay. It's, I hate it when this does this. Okay, did that work? Okay, I'm gonna push pause and I'll be right back. Well, I think that worked. I paused it for a really long time and you didn't know, except that now I told you which why would I tell you? Okay, let's make a list of the cell theory tenets. There's three that the fellows we just looked at came up with and three more that got added after over some time. I would never ask you about their names or even the timing, like the historical information is not something that I'm gonna hang on to. I just think it's really interesting to have context and perspective. Okay, so cell theory. This is what the fellows came up with. Number one, I already said this, the cell is the fundamental unit of life. Do you feel like, dude, yes, we already know that. Okay, we don't need to spend any more time on that. We've labeled that and named that all along in the class. All, and this is interesting. This is kind of a chicken egg thing. All critters, all living things are made of one or more cells. Okay, this is where we have a virus debate in our future because the case is made that viruses do not have a cell membrane. Therefore, aren't cellular. So in order to be alive, you have to have a cell and then these guys, though the fellows came up with all cells come from other cells. This was kind of a shocking revelation that cells didn't just spontaneously arise out of like rat heaps or garbage dumps or anything like that. They actually had to come from existing cells. Those were our original tenants and then we added some more and I'll go ahead and throw these in a different color. They are basically all cells. I'm gonna not write all cells because I'm gonna run out of room here. All cells have the same chemical composition and dude, this is the part that I think is so cool. We're all, we're made of the same stuff. We've learned the building blocks. Those building blocks make up all cells. All cells have, use energy through metabolic processes and the metabolic processes are conserved. We see the same general processes in all critters using energy and producing waste products. And then the last one we have is that all cells have DNA and they pass it on to their daughter cells. In a world where the penis was sort of required to get in, it's interesting to me that we talk about daughter cells during cellular reproduction. We produce daughter cells and that's like, I don't know how, that's a common way that we talk about the cell, baby cells they get produced from other cells. So the DNA in the cell when we divide and make new cells, because we learned that all cells come from other existing cells, they get all the DNA which we will spend a lot of time talking about. Okay, that's your introduction to the cell. In the next section we're going to look at the two main categories. Now I showed you a whole pile of diverse cells. In the next section we're going to divide those into just two types and look at what those are.


Hi, I'm Zor. Welcome to Unizor Education. I would like to talk about linear functions today. It seems to be like a relatively simple topic, however. There are many nuances which you probably should know, and they're quite interesting actually, even from a historical perspective. Well, what can be simpler than linear functions, something like this, right? Well, obviously. It is a simple function. However, I would like to point out certain peculiarities and properties of these functions, graphical representation, etc. So let me start from certain definitions. Well, there is a certain duality in the concept of what linear function actually is. There is an abstract, more, I would say, purely mathematical aspect of linearity. It means basically the following. We can consider function to be linear in this abstract sense. Let's say you have a function f of x. Now, let's assume x is just a number, let's say a real number. So the concept of linearity in its abstract sense says the following. That the function is supposed to be considered linear if the following is true. So these are just numbers. So u and v are numbers where the function is defined. Now, if you will multiply u by some factor and v by some factor and combine them together in this expression, then the function, if it behaves this way, then it can be called a linear function. Now, for example, obviously, e is something like this.   So this property of linearity, abstract linearity, is preserved in this particular function. Now, how about a different function which we also used to call linear, at least in high school, something like this. Is this function linear in this abstract sense? Well, let's just calculate. 2 times a u plus v v plus 1, right? Now, that's on the left. On the right, you have 2 times the function of u, which is, the function of u is 2 x plus 1 plus b, sorry, it's not x, it's u, plus b 2 v plus 1. Now, are these two equal to each other? Well, let's consider this is, let's open the parenthesis, b v plus 1.  Obviously, it's not exactly the same as this one. So this function in this abstract sense is not linear. What I would like to say right now is the following. Usually, this type of function is considered to be linear in high school and in some other places. And I will talk about why. The abstract linearity concept. Well, you just probably should remember it if you want to, but usually we will not be talking about linearity in this more strict sense. We will be talking about linearity in this sense, which basically means that this is some kind of a polynomial and the x, the highest degree of the polynomial is 1. And then quadratic functions will be those polynomial functions where the highest degree of the argument will be 2. So, to get about abstract linearity quality, and let's concentrate on this step. So now I can define a linear function in this, I would say more elementary if you wish sense. I don't know how else to qualify this particular thing. But basically what I would like to say is that the function of type A x plus B where A is not equal to 0. This is a mandatory requirement. A is not equal to 0. It's also called linear function. Now, a little later I will talk about why A should not be equal to 0. But basically understand that the function is not really the same if A is equal to 0, which means it doesn't really depend on argument, it's constant B. So, it's still a function from the strict definition of the function, but it's not an interesting function to research or to analyze. It doesn't have many properties with which this function where A is not equal to 0 does actually have. And we will talk about these properties. Now, if B is equal to 0, by the way, let me just for one second return back to abstract linearity concept. If B is equal to 0, then function A is equal to A x is linear in this abstract sense.  So, these are exactly, if you remember, f of the function f of u and f of v. So, basically, we can open these parenthesis and put it outside of the function, and that actually means that the function Y equals A times x is linear in this abstract definition. However, again, let's forget about abstract. I always promise to forget about this for a while and then I'll return to it, right? All right, so anyway, this is the functions which we will be considering. A can be anything which is not equal to 0, B is anything. Now, anything means what?  Now, traditionally, and that's exactly what we will be considering. I will consider A, x and B to be real numbers, real, not integer, not rational, real. It can be complex, I mean, in theory there is nothing to prohibit us from this, but this is not what we will be dealing with. We will be dealing with real functions. So, real linear function or just plain linear function as I probably would, you know, skip the word real means that argument is any real number and coefficients, A and B are any real numbers except A is not equal to 0. That's so much about definition. Now, so domain of this particular function with any real A and B, A not equal to 0, obviously domain can be any real, all real numbers because all real numbers can be multiplied by some real number and added another real number which means the function is defined on all real numbers. Now, that's the definition of the function. That's the domain where it is defined. How about the range? How about the codomain? Well, obviously the codomain in general is also all real numbers, but are we reaching every real number using this function? So, what we do is for any real number we can have an argument which would be converted into this real number with this function. Well, let's just think about this way. Let's take any real number R and let's assume that X is equal to R minus B divided by A. By the way, this is one of the reasons why A should not be equal to 0 because otherwise I cannot really construct this. Now, let's take this particular X and substitute it into the function. So, what do we see? Y is equal to A times this X which is R minus B divided by A plus B. What is it equal to? Well, obviously A and A are reduced so it will be R minus B plus B which is B and B reduced which is R. So, if X is equal to this where R is any number, any real number and A and B, they define our function then the function will take the value R which means we can reach using this function any real number. So, if these are real numbers and these are real numbers first the full function can be defined for any one of those. That's obvious, right? What also I'm saying is that for any real number R I can find the prototype. It's this one. So, any real number can be reached which means that the range of this function all the values of this function they cover entire space of real numbers. So, the main is entire space of real numbers and the co-domain is entire space of real numbers and the range of the function is entire space of real numbers which means every number can be reached using this function from some kind of a prototype. So, that's important. Now, let's talk about a little bit more interesting property of this which is very much related. What we are saying right now is that if this and this are sets of all real numbers then the function AX plus B with A not equal to zero now this function is defined for every number here and its values cover an entire space of real numbers Question is, is it a one-to-one correspondence? Can we establish one-to-one correspondence between this set of real numbers and this same set of real numbers using this particular function? I mean, we know that from here you can get there and from any there we can get some prototype argument here but is it one-to-one correspondence? Well, since we can always define these we can say that any number from here corresponds to some number here. All we have to do right now to establish one-to-one correspondence is to prove that this is impossible. We cannot take two different numbers from the set of real numbers using this function arrive to the same value. If I will prove that we cannot arrive to the same value it means all of these guys are different. Whenever these are different these are different and since I already know that they cover an entire space and for every one of them there is a prototype that would prove that this is a one-to-one correspondence. So all I have to do is I have to prove that I cannot take two different real numbers apply my linear function and get the same value. Well, let's prove it. Let's assume there is a pair of real numbers u and v which substituting them into this function where a is not equal to zero obviously would result in the same number. a u plus b equals to a v plus b. Is it possible if u and v are different? Well, let's just think about it. Now, these are equals, right? So from equal if we subtract equal we will get equal. Remember this, right? So let's subtract minus b from both sides. What I will have is a u is equal to a v. Now, if equal values divide by the same not equal to zero value we will get equal. So let's divide by a and I will get u is equal to v. But I have assumed that these are different. Now I've got it equal. So it's a contradiction which means we cannot get into the same value from two different arguments. Which means we have established a one-to-one correspondence between sets of real numbers and itself, the same set of real numbers using this function. For every real number argument there is one and only one value. For every value there is one and only one argument which can be used as an argument to this function to get that value. This is a one-to-one correspondence. Okay, that's fine. Next, have this plan on the left. What's left? One-to-one correspondence. Ah, monotonic. Another property of linear function is that it is monotonic. I'm sure you understand what it means. Basically what it means let me just repeat it. It's always increasing or always decreasing, basically. More precisely. First, case a greater than zero.  So, the value of the function would be greater if the value of argument is greater. Well, how can we prove it? Well, it's basically very easy. Let's think about it. If u is less than v and then you multiply a smaller number by some positive number, then the result will be smaller, which means a u will be less than a b. Now, if you have two numbers, one is less than another, and both are, two both are adding the same number b, well, obviously the result would also be smaller. So, starting from the smaller argument than another, we multiply by a positive real number a, the result also would be smaller, and then we add some number, it doesn't really matter by the way, positive or negative. If one number is smaller than another, we add the same value to both of them, the result will go so smaller than this one. Now, what does it mean? It means that if a is greater than zero, function is monotonically increasing its value. As the argument is increasing, the function is increasing. The argument is increasing, the function is increasing. Now, very, very similar. Let's consider a is less than zero. Well, from this, we multiply both sides of this inequality by a negative number, and that actually changes the sign of inequality. If you have a smaller number and a bigger number, but then you multiply, let's say, by minus one, then this number becomes bigger and this number becomes smaller. They are positioned on a different size of the axis, of the numeric axis. Then again, you add the same number to both sides.  What's important here is that if a is negative, then the inequality is flipped whenever we multiply it by the same number a. Now, in this case, function is also monotonic, but it's not monotonically increasing. In this case, it's monotonically decreasing, which means the greater argument corresponds to a smaller function. So, arguments are increasing, but the function is decreasing. The only thing which I actually wanted to talk about is why we so adamantly insist on a is not equal to zero. And I gave you already a couple of examples of the properties which are important for linear function. For instance, the linear function establishes one correspondence between the real numbers and itself. Monotonic property, like when argument is increasing, the function is either increasing or decreasing. Now, there is one more, again, more abstract consideration. Mathematicians are introducing sometimes new concepts, new types of functions, etc. So, one type of a function is a polynomial. A polynomial function is the function which is expressed as a polynomial. y is equal to a0 x to the n degree, a1 x to the n minus 1, etc., plus a n minus 1 x to the first degree, plus a n. Now, a0, a1, etc., a n are coefficients. This x is an argument. Now, what is this polynomial degree? Well, it's n, right, in this particular case. But to really be the polynomial function of the nth degree means that a0 should not be equal to zero, right? Because if it's equal to zero, then it would be probably n minus first degree, etc. So, if we want to really qualify a polynomial function as the function of certain degree, then the maximum degree x is raised into should have a nonzero coefficient. Otherwise, we can't really say that this is nth degree polynomial function. Well, from this perspective, linear functions are polynomial functions of the first degree. These coefficients are equal to zero, but this one should not be equal to zero. Now, what is the function if a is equal to zero? Well, it's just the constant. From this perspective, all these are zeros, and only a n actually is left, which is x to the zero's degree, if you wish, right? So, whenever you have a function which is equal to constant always for any argument, we can actually talk about this function as a polynomial function of the zero's degree, not the first zero's degree. So, that's another difference. So, from the polynomial function's specification, our linear functions should not have the coefficient a equal to zero, because then it would be just a different type of polynomial function. This is just yet another consideration. The consideration before, like, for instance, that we have established this one-to-one correspondence, are probably more important. And then, obviously, whenever you're talking about certain equations which we have solved this particular equation, we chose the number r as a result, a real number we would like to get if we will have to find whatever the argument is. Now, I basically told you that x supposed to be equal to r minus b divided by a, right? How did I get? Well, I've solved this equation, obviously. So, whenever we will be talking about equations, obviously, again, this coefficient should not be equal to zero. So, there are all these considerations and that's why let's just assume that whenever we're talking about linear functions, a is not equal to, in this expression for linear function, a is not equal to zero. Well, that's it for today. This lecture is just some kind of an introduction to linear functions. I will be talking about graphs and some other properties, but that will be in the next lecture. Thank you.


Going on everyone Sam here with late sports cards renew the recap for 30 case break 23 Bowman draft choice and jumbo random player style We're gonna start off with the first 15 cases before the re-roll so if you go back you were in the break look at the first half See what player you had and that'll correlate to this So go ahead and do the recap gonna start off with our greens to 99 new entry Vargas Elijah green Hans Montero Jacob Gonzalez Brock Rainerberg Jacob ham CJ K fish Jackson shurio Jake DeLeo you entry Vargas a milanios 125 Sam there's that Clevenson tie Floyd Zonatello Kemp Alderman Jason Woodward Chris Clark Spencer Jones Jacob Wilson Jonah Cox Cam Collier You're swayed the call out of 75 Gabriel Gonzalez Brandon winnaker Hunter Haas Geron Watts Brown Alfredo. Do you know Joe Redfields Andrew Muth Jace young hi for Lord Wyatt Crowell Jason Savakul Jota Cox to 50 Brian Acuna Jace young Cole Carrick tie Floyd Cam Collier Kemp Fisher to 25 Jacob Gravey 54 is Colson Montgomery to 25 as well Alex Clemmy to 10 Jason shurio Maui Ahuna young keel and to five Marcella Meyer Start off with the basin refractor autos. So either they'll be base or a fractor Justin Reimer Alberto Rios Cam Fisher Bryce Eldridge Brock Friedenberg Jacob Gonzalez saving Savaios Jackson bowmeister Jovatrono Alberto Rios Jack Hurley Dylan head Mike Bovee Max Anderson Travis Honeyman Jake DeLeo Jackson Wiggins Luke Keschel Zach Levinson Alex Clemmy Zander Muth Justin Reimer Drew Hackenberg Bryce Eldridge Elberto Rios Marcus Brown Next up we've got Charlie Soto Jay Cunningham Enrique Bradfield Jovatrono Maui Ahuna Cam Fisher Colton Ledbetter Jacob Wilson Paul Schienes Ralphie Velazquez Grayson hit Homer Bush Jacob Gonzalez Alex Clemmy Noble Meyer Ty Pete Luke Keschel Zach Levinson Matt Shaw Jonah Cox Alex Clemmy Luke Keschel Marcus Brown Charlie Soto Travis Honeyman Tommy Troy Luke Keschel Alex Clemmy Teddy McGraw Paul Schienes Travis Honeyman AJ Ewing Braden Taylor Jack Mahoney Alberto Rios Jake DeLeo Jacob Wilson Adrian Santana Joe Whitman Ethan O'Donnell Carson Rocca Forte Jay Bashir's Quinn McDaniel Hunter Haas Charlie Soto Zach Thornton Jacob Wilson That is Michael Carrico Keb Alderman Dylan Campbell Tayshon Walton Landon Maraudis Quinn McDaniel Noah Nolan McLean Jackson bowmeister Ty Pete Luke Schlager and Jace Barofin Next up we've got Cole Carrick Brandon winnaker Landon Maraudis Paul Schienes Alberto Rios Christian Campbell Michael Carrico Christian Napsick Matt Shaw Luke Schlager Austin Tresser Kendall George Kendall George Jackson Wiggins Adrian Santana Zach Thornton Zonatello Brock Rodden Hunter Holland Kendall George Maui Ahuna Sean Sullivan Jake DeLeo Teddy McGraw Jake Cunningham Jonah Cox Garrett Forrester Kent Alderman Brock Vraidenberg Max Anderson Cole Miller Colin Hauke EJ Ewing Colin Hauke Ty Floyd Cole Foster Christian Napsick Matt Shaw Homer Bush Max Anderson Paul Wilson Jake Cunningham Last of the Basin refractors. We had Cole Foster Christian Campbell Paul Schienes Austin Tresser Cole Miller Hunter Holland twice Landon Maraudis Jackson bowmeister Max Anderson Seth Keener great Garrett Forrester Cole Carrick Joe Redfield Austin Tresser Noble Meyer Christian Napsick Jacob Wilson Spencer Nivens Brandon winnaker Nolan McLean Zach Thornton Ethan O'Donnell Landon Maraudis Jace Barofin Tommy Hawk Wyatt Langford Keppa Alderman Calvin Harris Jack Mahoney Ethan O'Donnell Zach Levinson Cole Miller Teddy McGraw Andrew Hackenberg On to some of our numbered stuff gonna start with the out of 199s Grayson hit Mike Bovee Maui Ahuna Zach Thornton Jacob Gonzalez The 250 LA and Soto Ty Pete Adrian Santana Michael Carrico Devin Saltibon Tommy Hawk twice Johnny Farmello Rhett Louder Cooper Engel Colton Ledbetter Ty Pete to 199 again here a Wyatt Seth Keener to 150 The blues and the choice exclusives Brandon winnaker Mike Bovee Ethan O'Donnell Jake DeLeo Zach Levinson Brock Rodden Kate Culler Nolan McLean Cole Foster Jackson Wiggins Dylan head Tayshawn Walton Ralphie Velazquez Cole Miller Zander Muth Travis Honeyman Jake DeLeo Luke Keschel Sean Sullivan hero Wyatt Teddy McGraw Nolan McLean Landon Maraudis Eric Watansi Joe Petrano Blake Mitchell Charlie Soto Ty Floyd Cole Emerson Johnny Farmello Travis Honeyman more to 199 Cole Miller or 150 Tommy Hawk Cole Emerson Kendall George Michael Carrico Quinn McDaniel Nazan Zanatello Brock Bradenberg Johnny Farmello Jay Vashiers Charlie Soto Mac Horvath Hunter Haas Sean Sullivan Braden Taylor Alex Clemmey Cole Carrick Steven Sabios Noble Meyer tonight and on Chase Davis Grayson hit Ellie on Soto Tommy Hawk Sean Sullivan Carson Rocca Forte Landon Maraudis Sean Sullivan hero Wyatt Jack Hurley Seth Keener Tayshawn Walton Devin Saltibon Matt Shaw 271 is Jackson Bowmeester Chase Davis awesome Tressor Zach Thornton Grayson hit Enrique Bradfield, Jr Nazan Zanatello Spencer Nivens Cole Emerson Braden Taylor Colin Hauke and Dylan Campbell 250 on the golds Cam Fisher Tayshawn Walton Kate Denton to 25 Jack Mahoney Rhett Louder Dylan Campbell Jackson Wiggins Hunter Haas Kendall George Homer Bush Calvin Harris Rhett Louder Devin Saltibon Dylan Campbell plate to 75 Cole Miller Jake Cunningham Colton Ledbetter 71 is Garrett Forrester 250 Jake DeLeo Saban Sabios Blake Mitchell and orange Cam Fisher First stack of mags we had one two three Wyatt Langford actually four Wyatt Langford's base autos Congrats on that max Clark refractor That is Jacob Wilson to at 199 to 150 Bryce Eldridge to 150 Paul Skeens Ralphie Velasquez to 150 Colt Emerson to 150 299 is Colt Emerson Ty Pete to at 99 Matt Shaw to 99 that is a max Clark to 50 on the gold shimmer Rhett Louder and Ty Floyd Duelotto That is a Paul Skeens gold to 50 Blake Mitchell to 50 Colt Emerson to 50 Enrique Bradfield junior to 50 Enrique Bradfield junior to 25 true orange red of Cole Miller To five Kemp Alderman to five in Brady house red lava five So that is it for the first half. Yes What's gonna do in the same video too, so I Stacked up all of the mags of the same player So I'll give you this I would say that would be the sig pile right there is for those four would be the same Everything else. I think you could fad Yeah All right, so on to the next one. This is now cases 16 through 30 so this is the second half after the re-roll so go on to the results if you were in the break Go to the second half 16 through 30 So 299 got Jonah Cox Gabriel Gonzalez Coleman Picard at Noble Meyer Wyatt cutable Ethan solace Jacob Wilson Cam Fisher drew Hackenberg Ty Floyd drew Jones To 75 is Mike Bovey Conor O'Halloran Luke Schleiger Ludwig Espinosa Colin Hauke Marcella Meyer That was Roman Anthony. Yeah for all four. Okay. Yeah, you're sure beautiful Austin Tresser Travis Honeyman to 50 Yasser Mercedes Matt Shaw Jacob Gonzalez Kinder Delgado Carlson Reed to 25 Samuel Bassio Cole Young to 10 Elijah Green to five Samar Johnson one-on-one printing plate Dylan head Jack Hurley Wyatt beautiful and a Garrett bowman All right stack of base orders. That's new. Yeah, this stuff's all right We got stack of base autos Noble Meyer Austin Tresser Ty Floyd Zach Thorin Blake Mitchell Elyon Soto Garrett Forrester Cole Miller Brock Rodden Cooper Engel Devon salt Yvonne Tommy Hawk Johnny Farmello Tommy Troy Ty Floyd Dylan Campbell Justin Reimer. What is that? Fever Ty Pete camp Fisher Seth Keener Ty Pete Jackson Wiggins Joe Vatrano Matt Shaw Jackson bowmeister Ty Pete Christian Napsick Blake Mitchell Jacob Gonzalez Johnny Farmello Tommy Troy Ty Floyd Cole Miller Michael Caraco Austin Tresser Kevin Sim Marcus Brown Dylan Campbell and Braden Taylor Paul Skeens Cole Foster Kate Denton Seth Keener Quinn McDaniel Hunter Holland Jonah Cox Noble Meyer Jackson bowmeister twice Adrian Santana Ty Floyd Teddy McGrath Marcus Brown Michael Caraco Tommy Troy Zach Thorin Jota Cox Jack Mahoney Brandon Winnaker Joe Redfield Maui Ahuna Enrique Bradfield Kate Culler Teddy McGrath Ethan O'Donnell Zach Levinson Jacob Wilson Paul Skeens Grayson Hitt Christian Napsick Cole Carrick Seth Keener Blake Mitchell Jacob Gonzalez Cole Carrick Colton Ledbetter Teddy McGrath Joe Vatrano Grayson Hitt camp Fisher Hunter Holland Brandon Winnaker Spencer Nivens Paul Skeens Enrique Bradfield Tom Tommy Hawk Jake Cunningham Dylan Head More bass autos of Zach Levinson Ty Floyd Ty Pete Cole Carrick Alberto Rios Joe Vatrano Kemp Alderman Cole Foster Jack Mahoney Dylan Campbell AJ Ewing Mizzan Zonatello Tommy Troy Jonah Cox Noble Meyer Brock Rodden Hunter Holland Homer Bush Jacob Gonzalez Sean Sullivan Teddy McGrath Paul Skeens Jake Cunningham Eleon Soto Zander Muth Cooper Engle Jake DeLeo Zach Thorin Herson Waldrip Devin Saltibon Travis Honeyman Zach Levinson Michael Carricko AJ Ewing Teddy McGrath Andrew Pinkney Nolan McClain Eleon Soto Zach Thorin Refractors to 499 Colton Ledbetter Austin Tresser Drew Hakenburg Max Anderson Matt Shaw Hunter Holland Nolan McClain Quinn McDaniel Hunter Holland Zander Muth Ty Floyd Jake Cunningham Enrique Bradfield Ethan Salas Andrew Pinkney Zander Muth Cooper Engle Matt Shaw Jackson Bowmeister Ty Pete Ralphie Velazquez Colton Ledbetter Rhett Louder Seth Keener Noble Meyer Jackson Wiggins Hunter Holland the 250 on the purples Austin Tresser Connor Burns Dylan Campbell Cole Miller Seth Keener Colton Ledbetter Nolan McClain Mac Horvath Nolan McClain Mac Horvath Brock Vraidenberg to 199 Ty Floyd Carson Rocca Forte Jack Hurley Zander Muth Mortal 199 is going to be Luke Schleiger Colton Ledbetter Seth Keener Braden Taylor to 150 Chase Davis Cooper Engle Jack Mahoney Maui Ahuna Seth Keener Ty Floyd Kevin Sim Joe Whitman Grant Taylor Carson Rocca Forte Mizan Zanatello Elyon Soto Jack Mahoney Nolan McClain Braden Taylor Joe Vatrano Alex Clemmie CJ Kephus Mike Bovee Andrew Pinkney Mizan Zanatello Jack Hurley Ty Pete Tommy Troy Sean Sullivan and Colson Ledbetter We've got a Spencer Nevins Brock Vraidenberg Brandon Winnaker Teddy McGraw Cole Emerson Dylan ahead Nolan McClain Brock Regio Kade Coller Grayson hit Joe Whitman Garrett Forrester Joe Redfield Zander Muth Cooper Engle AJ Ewing Cole Miller Grant Taylor Tayshawn Walton Alberto Alberto Rios Nizan Zanatello Zach Levinson Justin Reimer Devin Saltibon Calvin Harris Jake Cunningham or yeah Jake Cunningham Now it's you 99. We've got greens of Grayson hits Travis Honeyman Tayshawn Walton Jack Hurley Dylan head Brock Rodden Jack No, Jace Barofin Thank you Cole Miller Carson Rocca Forte Jack Mahoney Elyon Soto Jacob Gonzalez Kate Deighton Kevin Sim Charlie Soto Joe Vatrano Blake Mitchell Cole Miller Tommy Troy Jonah Cox Mike Bovee Alex Clemmie Cole Miller Quinn McDaniel Garrett Forrester Adrian Santana Cole Kerrig Ethan O'Donnell kid color Luke Kescheld Colin Hauke Luke Keschel Noble Meyer Devin Saltibon 275 Max Anderson Joe Vatrano to 71 Drew Hakenberg to 50 Andrew Pinkney Sabin Sabio Sean Sullivan Braden Taylor Kemp Alderman Marcus Brown Elyon Soto Hurston Waldrop Teddy McGraw Hurston Waldrop Jake Cunningham Landon Maraudis Cole Miller Maui Ahuna Teddy McGraw to 25 Eric Paton T Alberto Rios hero Wyatt Tommy Hawk 254 is Drew Jones Rainer Arias 101 printing plate auto Brock Rodden That was the Tommy Troy we just magged that one Base autos of Wyatt Langford one two and the class of 23 Four so that's four Wyatt Langford Tom Brady base. Hey, there we go. We hit one of them. Thank God Jesus another Wyatt Langford, so that's fine Max Clark refractor Purple Bryce Eldridge to 250 to 199 Colt Emerson We got a max Clark to 150 Jackson Churio to 99 Ralphie Velasquez green to 99 Take Sean Walton to 75 Matt Shaw to 50 Paul Skeens to 50 Orange true orange Braden Taylor and then a red wave of Sean Sullivan So that will do it for the entirety of the break. Thank you all. Thank you Jesus appreciate it as it Is