Statistics and Excel. Bell curve batting average comparison. Get ready, taking a deep breath, holding it in for 10 seconds, looking forward to a smooth, soothing Excel. Here we are in Excel. First, a word from our sponsor. Yeah, actually we're sponsoring ourselves on this one because apparently the merchandisers, they don't want to be seen with us.  Like our crunching numbers is my cardio product line. Now, I'm not saying that subscribing to this channel, crunching numbers with us, will make you thin, fit and healthy or anything. However, it does seem like it worked for her, just saying. So, subscribe, hit the bell thing and buy some merchandise so you can make the world a better place by sharing your accounting instruction exercise routine. If you would like a commercial free experience, consider subscribing to our website at accountinginstruction.com or accountinginstruction.thinkific.com. Well, if you don't have access to this workbook, that's okay because we'll basically build this from a blank worksheet. But if you do have access, currently five tabs down below, the two example tabs in essence answer keys. The two practice tabs having pre-formatted cells so you can get to the heart of the practice problem. The blank tab, blank worksheet so we can practice formatting cells within Excel as we work through the practice problem. Let's go to the example tabs to get an idea of what we will be doing starting with the data tab where we will be pulling baseball statistics information in from an online resource, building them into a table so that we can sort and filter the table, pulling what we want from the table, in this case batting averages, and putting them into a separate tab so we can focus just on those items that we want. We'll do some of our standard statistical calculations, the mean, the standard deviation, the median, comparing two years of batting average information, probably won't be doing 2020. I think we'll do 2022 and then 1920. And then if it conforms to a bell curve distribution as we expect it would, then we'll do some of our graphing of the bell curves, plotting the relative bell curve information. And since we have two sets of data, this is what's different in part from some practice problems we've done in the past, one being we're taking the data from an online resource and filtering it, and two, that we have this comparative information that we can look at the differences and analyze a comparative information and make some charts from that comparative information. All right, let's go to the blank tab over here and we're going to start by pulling our information in from an online resource. So I just looked up statistics, baseball statistics for 1920, and I found a website which is baseball reference, and I'm going to scroll down and say I don't want the team standard batting. What I want is the player standard batting. So a player standard batting, and then over here it says that we can download this. Where did it go? Ah, here it is. Now I'd like to download it as an Excel worksheet, but it only gives me like 500 lines. So it's going to give me all the data if I convert it to a CSV file, which is often the case we have to convert from a CSV. So I'm going to say give me the CSV file. It looks kind of weird because it's just comma deliminated information as we saw way back when we were just practicing uploading data. What I can do is copy this whole thing though. I can say I'm just going to copy this because all the data is there and then I'm going to convert it from a comma deliminated data set to a table. So I'm going to just copy all of that, control C, and go to my worksheet. I'm going to put that in A1, right click and just paste it. I'll paste it. Can I paste it? Does it matter which way I paste it? I don't think so. Match, keep source, let's match it. And then I'm going to make it a little bit smaller here so we can see what's going on. Now it's separated by commas now. So what I want to do now is go to my data up top. I'm going into the data tab and then we're going into the group of data tools and then we're going to go into text to columns. Well, this notice that only column A is highlighted, even though the data is kind of spilling out over the other, all the data is in column A. So I'm going to select the text to columns and then it's deliminated here, characters such as commas, so that looks correct. So I'm going to say next, and I don't want the tab to be the deliminating factor. I instead want the comma and you can see it changes the data down here to more of a table type format. So I'm going to say, all right, next, that looks good. And I think that's good. So I'm going to say let's finish it, finish it. So there we have it. So now we've got our data broken out here. We've got more than the stuff that we need because we really just want batting averages. I'm going to make the top part of it bold, home tab, font group. Let's embolden it so that the system knows I want to create a table from it. When I insert a table and they can see that that will be the header. Then I'm going to go to the insert. I'm just going to select one cell in here. Be careful with this table though, because there's some blank spots. There's some unfilled areas which can throw off the table. So let's see if I can insert the table. If it'll pick up the entire range, insert tables, group, insert a table. Now let's go all the way down. So does it pick everything up? Is it doing the dancing ants doing the whole lapping the entire place or not? So it looks good. So I'm going to say, OK, table has been inserted. So we're going to mainly just focus on, in this case, the batting averages. So we're going to go over here to the batting averages. But first, let's add another set of data. I'm not going to add the data to the right this time. I'm going to add it below, because I might filter the data. Now it might even be better to put the second data on a whole other worksheet. But I'd rather put it, but I want to keep just one other worksheet. So I'm going to put it below instead of next to. So I'm going to say control shift down. Oh, that's not down. Control shift down to get to the bottom of the table. I'm going to put the second data set right here. So I've done a similar search for 2022. Same thing, baseball references. So not the team, but I want by player. So here are the players. So that looks good. The standard batting. Here's the dropdown. I'm going to convert it to CSV files. There they are. And then I'm going to pick up all of this data in the comma deliminated format. All of this great information that we can work with and do comparisons about and talk about who's the best and who's the worst and like who's in between not even worth talking about because they're like in the middle. You've got to be either good or bad. If you want people to be talking about you, maybe it's better not to have people talking about you anyways. I don't know. But I'm going to paste that here and then I'm going to go into the data up top and then we'll go into the data tools and the text to columns and then once again deliminated by the commas. Next. And I want it comma deliminated. Looks good. It looks like it's doing what we want down here. Next. And okay general. Okay. Finish it. Let's make the top bit bold so that we can then hopefully excel. We'll know that that's the header home tab font group bolden. And then I'm going to put my cursor somewhere in the data and go to the insert tab and I'm going to be picking up the table and the table here. So let's insert the table and boom. So now we've got our two data sets for 1920 and 2000. I'm going to insert another one more row above it insert. So I can say this was 2022 data and let's do that up here too just so I can make sure I know which data is which which is which insert. And I'll say this was 1920. Those are the two years we did. Am I right? Am I right? Okay. I think so. Okay. So there's our data. So now what I'd like to do is just get the batting averages over. So I want to pick up the batting. So I'd like to get the player's name as well possibly. So do I need their age or any of this other stuff? No, let's just get the batting average. So I'm going to put my cursor from C and I'm going to scroll over. Now you possibly might do this with pivot tables as well, but I'm just going to do the good old normal table. I'm going to right click and hide. So now we've got our batting averages. Now when we sort the batting averages, I'm going to make column wider so we could see the player's names. Notice that we might have like some outliers with the batting averages. So if I drop it down and go from Z to A, all these zeros and the batting average, when you're looking at the actual data sets, then that might not be applicable. You might not want the zeros and the batting averages because that might be indicating that these people didn't have any at bats or anything like that. So maybe we trim off the zeros and on the high side as well, you could say, well, one or 100% possibly that's because they had a very low at bats. They might not have that many at bats. So these are kind of skewing our data if they had one at bat and they got hit. So oftentimes we might say maybe it would be better for me to trim off the extreme numbers and so I can filter by hitting the dropdown and say maybe I should trim off all of the zeros. Maybe I'll keep everything else and maybe I trim off like the 100s and anything that's a blank that doesn't have anything in it. Then I want to remove those as well. So I'll trim down my data to that thinking that maybe that's a more better representation of the people in the data set. So now notice what happened is it hid some rows because I filtered. I filtered those out so it goes from two to six. That's why I don't want to have anything to the right of my data set because if I have this filtered it's going to squish up all of the stuff I do to the right because it removed these rows. That's why I'd rather copy this information now that it's filtered and paste what I want to deal with in another tab. So I'm going to open up another tab. I'm going to double click on it. I'm going to call it blank two or let's call this one blank data. This is the blank data. It's not blank data but it's the data for our blank worksheet. And then I'm going to copy this. I'll select these two and then I'll say control shift alone. So it goes down to the bottom. I'm going to right click and copy it and then go to my blank worksheet, paste it. I'm going to call control shift and scroll in a little bit and a one. I'm going to place it just 123. All right. So there we have it. And then the top bit. I'm just going to put in boldened home tab font and in boldened and then I'll put a table around this table. After notice I've removed those top bits. Like if I go to the last one, you might think, you might think, hey, maybe it's still pulled in those ones, but it didn't because like if I copy this control C and you look at the dancing ants and I unfilter and I say, remove the filters or select all actually that's not where the filter was. Remove the filters. You can see the dancing ants are not around these ones because we filtered them out. So the filtered ones are not included here.  And then batting average. This is for 1920. Let's say. So there we have it names a little bit larger. Let's do the same thing for the 2022 control shift down. And so now I want to pick up the 2022. There's my batting averages. I'll do the same thing. I don't want these blank numbers and I don't want the zeros and I don't want the hundreds because those are probably skewed stats possibly because of the number of bats or whatever it. So here's like this one even has a 0.04. That's, you know, pretty low. You know, maybe we remove the 0.04 and the 0.05. And I'll keep the ones after that. And then I'll go down to the bottom and this one goes up to 0.75. Let's get rid of the blanks 0.75 is pretty out there. It's probably probably probably one person that didn't have that many at bats, but I'll keep it and we'll say, okay. So then I'm going to copy these two. Control shift down and then control C copy. I'm going to put this on the blank tab and we'll put it up here in D one. Right click and pasted just one, two, three. Select in the top bit. Home tab font group data or bold. And then I'm going to put my cursor somewhere in the table and go into the insert tables and put a table around it. The dancing ants doing their table dance. It's not like a not like a table dance. It's a dance that makes a table. They're not like dancing on the table. The table like makes rain. It's not like, you know what I'm talking about. The table dance. But in any case, this is going to be batting average for 2022. I think it was right now. Note that you can see these data sets are in a decimal format. You can put them in a percent format. But sometimes when we do our norm.dist, it's useful to see them as whole numbers. So I'm going to multiply these times. I'm going to insert a tab here. Insert. I'm going to multiply these times a hundred. So this is going to be, I'll say it's the same thing. Batting average. Batting average. B. A. 1920 again. Batting average. 1920. But I'll say multiply times a hundred. This equals this times 100. And then let's add a decimal. Home tab. Number group. Actually, do I need to add decimals? No, I keep it like that. I'll put an H after it for whole numbers. Okay. And then, and the reason it won't let me do a decimal is because it's in general format. So let's actually select these cells. Let's select the entire worksheet. Actually, I'm going to select the entire worksheet. Right-click. Format the cells. And I'm going to make them currency. Negative numbers. Bracketed. No dollar sign. And let's add the two decimals. So now I'm going to say, okay. So now we can see them a little bit more uniform numbers. Let's do the same thing over here. I'm going to call this BA 2022 H for whole numbers. That's what I was thinking. Or I'm not even sure that's a W. But it's going to be this times 100. Okay. So now we've now we're representing it. Not at 0.25 or 25%. But rather 24.6, which represents the same thing. 24.6%. Okay. So we can compare the data now this way. I can look and sit and look at the look at the data comparisons for the two. I can try to sort them and whatnot and look at them this way and compare them. But it might be useful to then build some tables with it. Now, another thing I could do is make a histogram with my data thus far. So I can select this data set. And so notice one data set is longer than the other. That also causes some difficulties. But that's what statistics is kind of forward to kind of help to deal with these kind of difficulties. I'm going to say control back to get back to the top. Let's insert charts and make a histogram. So I'll say this is the histogram for the 1920. So 1920. And you can see we have some outliers. This one we maybe could have trimmed off possibly. But you can see that it's hovering around the 22. So we'll say, okay, it looks like it's somewhat symmetrical. So I'm going to say that probably could lend itself to a bell curve that we'll generate. And then this data over here, let's do it for this one. 2022 control shift down control backspace back up to the top insert charts histogram boom. And so we have that one. And this one has all of these buckets out here because we had some more kind of outliers on the high end. Let's see if I sorted this from Z to A. Yeah, we had these. So probably should have trimmed off maybe the 75 out there. But in any case, you could see it's somewhat still kind of a bell shaped type of curve. So we're going to try to use our analysis of the bell curve to analyze these data sets. Because that'll help us to give us uniform things like the Z scores and whatnot that we can make comparisons with. So 2000, let's say this is going to be 2022. So I'm going to say, all right, so now we'll see if we can start to build some stats with this stuff and our tables. So if I'm going to go back on over, I'm going to say, all right, let's do, let's make a skinny H. And we're going to do our calculations for like, let's say this is going to be our data and we're going to have 1920 and 2022. I'm going to make this general formatting so I don't have a number format. Home tab numbers, drop down general and then selecting the top bit because I want it to be a header, home tab, font group, black, white. I'll center just these two maybe, home tab, alignment and center. So we're going to do the mean, we'll do that standard deviation, the median, possibly the mode. I don't know if that will be helpful, but let's try it. We'll say this is the mean equals the average for the 1920s. I'm going to say average of this information, control shift down and enter. So now we've got 2417. Let's put a difference in here, difference just for the fun of it. We're going to say home tab, font group, black, white, center it. So then we'll do the average here, average for 2022, which is this data, control shift down, enter. And then the difference, here's the difference. So we're going to have an average, a little bit different average standard deviation, standard deviation. We're going to say for the population and I'll pick up this data set, control shift down and enter. So there we have that. Let's do it again. This standard deviation for the population, this data set, control shift down, holding control backspace. There's our calculation and enter. The difference equals this minus this. Okay. And then we've got the median, middle point equals the median. And we're going to say this data from here, control shift down, control backspace back up and enter. And it's pretty close to the mean. That's an indication that the bell curve might give us, might be a good tool to use. And then we're going to say the median on this one is going to be this data set, control shift down, control backspace and enter. Pretty close to the mean, which is usually an indication that the bell curve is something we can use. There's the difference between the two and the mode equals the mode, single mode. And from here on down, we got 25, which again is pretty close to the mean. Another indication that the bell curve might be useful mode, single mode here, control shift down, backspace, enter. So again, that is close to a little bit further off, but still relatively close to the mean. So it's an indication that the bell curve might be a tool to use. And the difference between those two is zero. All right. So then I could say, okay, let's start with our data for for 1920 and start to build our bell curve. So we'll build our table to create our bell curve. So I'm going to make a small M skinny M. I'm going to see I need my X's and my P of X's. And then these tables are getting in the way again. You need to get way out of here. Get out of here. You're in my way. Like it's like a pet little Chihuahua under my feet all the time. It's like I'm trying to walk.  This thing's trying to kill me. Keeps on walking under my foot. And then they anyways. Home tab font group black, white, let's center it. Now we need to know the starting point. So where should I start the X's at? You might say, well, if we're talking about averages, which we're representing in whole numbers, I could just go from zero to 100. Because you would think that would be the entire spectrum. But let's do our thing where it's usually the four standard deviations. So I'm going to say, let's do the number of standard deviations. Let's take it for standard deviations out for both data sets, because that will encompass the vast majority of the data. So the lower X and then the upper X would then be what? The lower X for 1920 would be the mean times the standard deviation, or I'm sorry, plus the standard deviation times four. So standard deviation times four minus the mean. The mean minus the standard deviation times four, four of the standard deviation below. Alright, enter. Notice it goes below zero, which in reality isn't going to happen, because you can't have a negative batting average. But I'm going to keep it because once we graph the curve, it'll show all of our data points, which gives us that kind of double check that we have all of our data in there. So I'll keep it there. And then we're going to say the upper is going to be equal to the mean plus the standard deviation times four. Enter. Boom. And then let's do on this one. This is going to be for 2020 the mean minus the standard deviation times four. And this is going to be equal to the mean plus the standard deviation times four. So there's our upper and lower X's. So let's go down to the lowest X because I want it and then up to the highest. So for both of these. I'm going to go from five to 50 to 53 so that we have X's that will line up under both data sets. So I'm going to say the X is going to be at negative, let's say negative five. We're not going to have negative batting averages, but I'm going to start it there so that we cover the whole data set. And then I'm going to go from to negative four, negative three. I'm going to select that group. I'm going to bring it down to 54. So I'm going to put my cursor on the fill handle. Take it on down till we get to 54, 50, 54 right there. Boom. I don't need the decimals on this one. Let's go to the home tab number group. Remove the decimals. Get out of here decimals. You're not needed or welcome in this on these cells. And then we can do our P of X. So this is going to be equal to the norm dot dist tab. The X is going to be this comma the mean we're looking at the 1920s. So we're picking up this one and not not the that's the mean. And then f four to make it absolute dollar sign before the J and the two so I can copy it down comma the standard deviation. We want this one f four dollar sign before the J and the three comma. Do we want it to be cumulative? No, false or zero. Therefore closing it up enter putting my cursor on it. And we're going to just double click to let's make it a percent home tab number percent if I adding some decimals. And then I'll put my cursor on the fill handle and double click copying it down. So notice all of this data is now selected and adds up to 100% because we went, you know, all the information is kind of within the four standard deviations. That's what's kind of nice about picking that up even the negatives because then you get that full kind of curve or pretty much the full curve the full data. Okay, so I'm going to stop it here and we'll continue on with this next time building our curve and then doing the same for 2022 and then looking at the differences between them.


For over 10 years, I have been leading communities and individuals, predominantly adolescents, to stop and breathe. And when asked why I value mindfulness practices in my ministry settings, I am quick to admit that it's a selfish invitation. I invite you to stop and breathe because I know that I desperately need it. You see, I'm in Enneagram 7. I have more ideas than I know what to do with and potentially enough energy to try them all out. My mind doesn't have an off switch, just a button for fast and another one for faster. This is why I need mindfulness to counteract what could become manic. It's easy for me to do, it can be hard for me to be. So let's all take a moment right now to stop and breathe. And if you don't want to do it for you, well, then do it for me.


Hi there, I'm Sandy Alnok and it is once again time for an Ellen Hudson release and we've got a really cool lemon or lime tree to make today. These are the colors I'm going to be using for my Copic marker coloring and I'm making mine a lemon tree but you can also turn it into a lime tree if you'd prefer. And the stamps don't come as a tree like this. They come individually so I stamped them at different angles. I have some leaves to go in different ways. I kind of had in my head a direction that the branch would go and then I just took a pen and started drawing the branch in.  And I'm just going to add some extra leaves. I could have stamped them but look at all that masking I would have to do. And with these leaves, since I have some stamped already, I can kind of follow along with the leaves that are there and get some general shapes to follow. And as long as some of them looked really good because they were stamped ones, it didn't matter if my leaves didn't look as good as those. I just wanted to have them kind of connected and have them have the branch, that thick dark branch that I drew in look like it's all coming down cascading from one area so that it looks like it's all connected instead of having sort of disjointed branches, if that makes sense. And then the coloring can begin. So I was just looking for one more leaf that I could drop in there. You could also drop the leaves in after you get the coloring done and see which areas might need that. And I might still decide to do some alterations before I finish this. But instead of drawing them in in the first place, you can draw them in a marker and then go over that with a black pen as an outline when you're done. If you're not really ready to decide right away where you want to have each one of those leaves. Because sometimes it will be easier to see once the coloring is there. So I'm going to use some Y17 for a shadow color. But if you know me, you know that Y17 is a really bright orange for this. So guess what I'm going to do? I'm going to jump in with a blue violet color. And you can see the difference between the kind of shadow that blue violet makes on yellow versus that orangey color. And then when I go over the orangey color with the blue violet, it also dulls it down. It just kind of brings it down a little bit and makes it a little less garish. Because with lemons, they're not going to have quite that much garish color. Lemons are lemon yellow. I'm not sure why I had to say that, but in order to hear it, I guess myself. But they're not a really warm, sunny yellow. So I'm going to blend my colors then with a Y08 to just soften those edges just a little bit. You can even use a Y06, but stay in that Y0 for your lemons. If you're going to use limes, Google some pictures of limes and see what kind of colors are going to work to make this a lime tree instead. There are some really funny sentiments in this that you can use with limes. So just I'll leave it to you to go look up the stamp set and see them because they're pretty funny. You know, it's a it's a Julie stamp set. And that's the way Julie rolls. She's always hilarious with the stuff she comes up with. So once I got the blending done, I'm going to add a few dots on here. And that's going to give me some texture that's going to match for my lemons. And if I use this light BV, it's going to add just a little bit of texture in the shadow areas without being that really bright or or kind of garish color. It's just going to be really subtle and make them feel like lemons. So now here's all of the leaves. And this is the point where if you hadn't drawn the leaves in, you could draw them just with your marker. And that way you can sort of adjust them and see where they belong. Are they connected to each other? Are they pointing and hanging in the right direction?  You get to make them with your green marker, which can often be a lot easier than making them with a big black pen. Now, I decided this was all way too bright. So I darkened them. I picked a G99, which is really dark. But boy, look how bright those lemons start to look and those flowers when I've got that's really rich color on here. If we get too afraid of having contrast, we can end up with a really weak looking picture. But if you're bold in your choices, sometimes even if you look at it like I did when I first went, oh, my goodness, why did I pick a G99? But once I started seeing how that contrast worked against those bright lemons, I thought, yeah, that's what I want to do. So then I took a G94, which is just one step down from the G99 and started going into the leaves that I wanted to be in the background and started pushing those backwards with the green marker because anything that's going to be darker is going to look like it's deeper underneath that branch. And then I'm only leaving a few of those light green colored leaves in the foreground, and they're going to look like they're catching sunlight. So I'm just kind of slowly starting to knock those back one at a time that you could knock them all back and get rid of all of that bright color. But it seemed like it was going to work best if I could just do some of those leaves and allow a little bit of that bright green to come forward. Now, here's where I started just seeing if I could add a little bit more green in between some of these. I wanted to leave some white spaces so they felt like there was some air going through. But I just added a few extra leaves to complement the ones that I had already drawn in there. And I could have done this entirely instead of doing any of the black line work at the beginning, and sometimes that's a little easier, a little less scary. So I'll put a little bit of BG in my flowers because these are white flowers with little yellow centers, so it's really not much color in them. And now I'll take that black pen and go around the outside edges of my extra leaves that I added to just add that finishing touch on my card and there we go. Just added it onto a yellow card base and kept it really simple. Otherwise, squeeze the day is hilarious. I'm often saying seize the day and telling myself to go out there and tackle it, especially when it's a Monday. That's a great saying for a Monday morning. But I also want to show you some cards that I made with the other stamp sets. This one has lots of things we say to ourselves in our little heads. And there's also a set of dies that have these speech bubbles in it. They're going to be fun to use and keeping it wheel. This is this is a hilarious little set that has a bunch of different stamps that you can put together. And I put the dog together on the bike because I thought that would be funny with the balloons. So you can see all of that over on the blog. There's also links in the doobly-doo to the new release and all the stuff used to make my card today. And I will see you guys again next time. Have a great day. Bye bye.


Hey, this is Brett, and this 2022 Chevy Tahoe RST, or Rally Sport Truck Package, is stock number 23J139A. I am here at Summit Automotive in Fond du Lac, Wisconsin. You're new and used SUV headquarters. This 2022 Chevrolet Tahoe RST has the 5.3 liter V8 gas engine. It's paired up with the 10-speed automatic transmission. This vehicle has been fully safety and inspected by our service shop, has a fresh oil and filter change. All the fluids have been checked and topped off, and it is 100% ready to go. I'm going to go all the way around in this video, inside, underneath, start it up, and take a look under the hood. Go over all the options on the interior to give you the most accurate representation of the vehicle possible. Summit white is the color, and I shoot all my videos in 4K, so if you have HD capabilities, turn them on out, because it is your best way to check out the quality condition options and cleanliness of the vehicle before seeing it in person. If you like the video, you can subscribe to my YouTube channel, which is youtube.com slash summonado. Click the bell notifications, and you'll get updates on the videos I do each and every day, as well as having access to one of the largest catalogs of vehicle walkarounds on YouTube. This one comes with the 22-inch painted and polished aluminum wheels, part of that RST package. It has Bridgestone Alenza tires. These are 27550R22s. I would say they have right around 50 to 60% of the tread left on them. Front fender is absolutely perfect. This one has the LED headlamps, the LED running lights, and we're going to turn all those on at the end of the video, so stick around for that. Front bumper is very nice and clean. You get the front bumper parking sensors. I didn't see any major dents or scruffs or scrapes on there. The hood is in very nice condition as well. The passenger side front fender is in great shape too. Passengers side front wheel, no major scuffs or scrapes on there. Looks really good. As you go down this side of this 2022 Chevrolet Tahoe RST, take note of how clean that body is, how reflective and mirror-like that paint is. I take these HD videos, so if you are far away or even if you're close by, you just cannot make the trip down, but you're still interested in purchasing the vehicle. You can see the vehicle, hear the vehicle, and have confidence in what you're looking at before you even get here. So when you do get here, there's absolutely no surprises, and you can make a smart and informed buying decision from wherever you're at. If this video helps you make that buying decision, definitely let your salesmen know that you saw the video. It was helpful and that Brett sent you, and then I can keep doing these videos each and every day here at Summit Automotive. Back tires have just as much tried as the front tires. You get the kind of felt wheel well wire, which keeps your frame and underbody looking good, and this one's in excellent shape. And you get the nice factory running boards on here as well. Rear quarter looks really good. I didn't see any denser dings on there. Coming around to the back of the vehicle, rear bumper is in great shape. You do get the backup parking sensors. This one does have the full towing package, which includes a receiver hitch, four pin and seven pin wiring. There's your spare tire as well. The rear gate is in really nice condition too. Didn't see any denser dings on there. It is a power lift gate. I got one thing that's really cool to show you in just a second. There's your receiver hitch cover. We do keep those inside so they don't go missing on the lot. And you can power fold down these seats. Watch how fast these things go down. Just with these buttons right here. Then they come up just as, almost as fast. Very nice storage area under there. And to get this gate down, just got to press that button right there. Does have the flipper glass so you can get to the back area in case you have a hitch or a trailer or a boat on your hitch. You can still get that open and get back there. And the other cool thing about this vehicle, and if I got the keys on me here, which I think I do, one sec. Okay, so you see there's that spot on the floor. Looks like a, I don't even know what it looks like. Just lit up there. If you put your foot there when you have the key in your pocket, that's where you put your foot to get that door open. So it is the spot to wave your foot for the hands-free door. So you can wave it again, and then it'll come on down. So that's pretty sweet as well. You can see that closes nicely too. Going down the driver's side just as clean as that passenger's side. No dents or dings on the rear quarter. And for full disclosure, this back wheel is in fantastic condition as well. This has the capitalist feel-fill, which is a really nice feature, never get gas on your hands again. And as you go down the driver's side here, no dents, no dings on the doors, very nice and clean. One of the nicest Tahoe's we've ever had on our lot. Has the heated mirrors, blind spot monitoring, built-in directional signals, 360 cam.  Very clean inside this vehicle. I don't think it's ever been smoked in. Power driver's seat, of course, and power passenger's seat. All-weather floor mats, push-button full-wheel drive, auto headlamps, power tilt, and telescopic steering wheel. Audio controls in the back of the steering wheel. There's for your PowerPoint, your start-stop capabilities, 360 camera, parking sensors, lane departure warning, stability control, power windows, locks and mirrors, memory driver's seat. Over-folding mirrors, I always like showing both sides so that you know that both sides are working properly. And they are. And of course, it does have the Bose sound system. Got this kind of, I don't know how you would call it, mesh-looking finish on the door trim there. Second row bucket seats or quads, you get the latch child safety system for any child car seats you may have. Both of these seats in back are heated. All-weather floor mats back here as well. These seats do slide like that. They go down nice and flat like that, or you can pull them up like so to get to that third row. Third row seats are in fantastic condition, no rips or tears on them, and once again smells very clean. The headliner is in great shape. This one does have the panoramic vista roof there. You also get rear air controls and two USB-C points back here, as well as a charging point, I'm guessing that's a 120-volt, 150-watt plug-in. Child safety locks on the back doors and the inside and bottoms of the doors are all in fantastic condition. Hop inside, check out the Myles radio, then we'll start it up. Take a look under the hood and check out all those LED lights in the front. So you can see that this one has 29,009 miles. You do get a compass display, digital speedometer, nice full digital dash, comes with the leather wrapped steering wheel, Bluetooth and information center controls on the right, cruise controls, and I'm sure that's adaptive cruise controls on the left, as well as forward collision warning. This one has the nice big screen on it. You do need a data plan to use the maps with this vehicle. On this infotainment system, you have the phone to connect to your Bluetooth. This one does have AM, FM, and Sirius XM radio capabilities on here. You also have the different cameras on here. If we can get those to show up, maybe the mission's got to be on or it has to be started. But we'll get to that in a second. It tends to be to automatic transmission controls, dual climate controls, heated seat buttons, USB, USB-C, and your wireless cell phone charge pad. Keyless entry with remote start, power lift gate and power lift glass, or I suppose it doesn't power lift up, but it releases. Passengers side, all weather format and seat are in fantastic condition. Once again, this vehicle's never been smoked in, smells very clean inside. You get that second row fixed glass and the power sunroof in front. Appears your home link buttons, map lights, on-star and SOS buttons, sunshade controls, and power sunroof controls, rear gate controls. You can put the headrest down on there as well. Let's start it up. Take a look under the hood. Check out all those LED lights in the front. Starts right up. No check engine lights or anything like that. And that is the adaptive cruise right there so you can adjust your gap between you and the car in front of you. So that's pretty sweet. I would personally like to thank you for checking out the video today. And hopefully from this HD video you've been able to verify the quality, condition options, and of course, cleanliness of this Tahoe all the way around. Really really nice condition. I like the dark chrome look to the grill there. And under the hood we have the 5.3 liter V8 gas engine, 355 horsepower engine base. Very clean runs, very smooth. Once again, this Tahoe has been fully safe and inspected by our service shop. It has a fresh oil and filter change, all the fluids have been checked and topped off. There is the emissions sticker. And I wonder if this has the trailering information on it. It does, so I wanted to show that real quick as well. Of course your tire and loading information sticker, and then of course your VIN sticker. Alright. But yeah, this Tahoe is 100% ready to go. Like I said, it's been through our shop. Everything's been checked out on it.  And I would highly recommend this one from a quality and condition standpoint. I don't think you'll find too many 2022s with almost 30,000 miles on it that are this nice. And to see more pictures of this Tahoe, or one of our other 550 new and used cars, trucks, SUVs, minivans, Wranglers, halftones, three quarter tons, one tons, you name it, we got to go to that website right there, summitauto.com. Full pictures and descriptions of every single vehicle, all at summitauto.com. And if you'd like to check out more HD videos, you can go to youtube.com slash summitauto. Click the bell notifications, you'll get updates on the videos I do each and every day, as well as access to one of the largest catalogs of vehicle walk-arounds on YouTube. In fact, in a second, you will see a link to subscribe to my YouTube channel on the upper left, a link to more Tahoe videos I've done in the upper right, a link to this vehicle on our website on the lower left, and a link to one of our latest YouTube videos on the lower right. Click those, check us out. We're super excited to help you with this Ultra Clean 2022 Chevrolet Tahoe RST in Summit White Clear Coat. Thanks again for checking out the video. Remember to like, subscribe, and share on the YouTube channel. I really appreciate it. Thanks again.


This video is called solve trinomials by factoring two, so we know that we have to factor it and then set everything equal to zero so I can see where this polynomial, which is a parabola, see where it crosses the x-axis on a graph. Before I start factoring though I recognize I can take out a GCF. I can pull out a two. So I have an x squared plus 3x minus four left. So now that I'm ready to factor, I've just made it a lot easier and simpler on myself to see what multiplies to give me negative four and adds to give me positive three. Well four is a four and one or a two and two. I think a positive four and a negative one can add to give me a positive three and a positive four times a negative one can multiply to give me negative four. So, oops, I continue on with my two parentheses. Don't forget to bring down the two and the equals zero. I'll split up my x. I'll put the plus four in one parentheses, the minus one in the other and now I remember I've got three terms to set equal to zero. Two equals zero, x plus four equals zero, x minus one equals zero. Well two will never equal zero, so I can get rid of that choice or that option. Here, when I subtract four from both sides, I get x equals negative four and when I add one, I get x equals one. So those are my answers, but just to make sure you understand what's going on, remember if you were going to put these on a graph, at one and negative four is where this parabola would cross the x-axis. So we'd have a sketch like that. The second problem for this video, again, we want to solve trinomials by factoring, but I notice this is not in the right format to solve. I need to get all my terms on the left-hand side of the equal sign. So I'm going to add 24 to both sides. So I get x squared minus 25x plus 24 equals zero. Can I take out a GCF? No, because I don't have an x in all three terms and I don't have a number bigger than one in all three terms that I can factor out. So we'll start by thinking about what multiplies to give us a positive 24 and adds to give us a negative 25. Well, product, or factors of 24 are 24 and 1, 12 and 2, 8 and 3, 6 and 4. Which set will multiply to give me a positive 24 and add to give me a negative 25? Well, a negative 24 plus a negative 1. So I make my two parentheses. I don't forget to bring down my equals zero. I've got x minus 24 and x minus 1. So it looks like I have two different terms. I've got to split it up and set them equal to zero. So I'm going to add 24. So I have x equals 24 and I'm going to add 1. So I have x equals 1. So if I were going to graph this, I would know that my problem, my u-shape would cross the x-axis way out at 24 and at 1.


The security of quantum key distribution, QKD, relies on the Heisenberg uncertainty principle and bit flip errors in sifted keys. But a recent protocol proposed by Sasaki et al does not rely on the bit error rate and can tolerate channel error rates close to 50% within a typical experiment setting. This article was authored by Zhen Zhong, Xiao Yuang, Zhu Cao and others.


Good afternoon everyone. I am Dr. Sneha Santoshrati. My topic for paper presentation is prenatal ultrasound evaluation of retrology of phallid. Ames. We emphasize the ultrasound findings of retrology of phallid, early detection of retrology of phallid, evaluation of other associated pathologies and congenital defects in fetus by ultrasound. Introduction. Toph is a congenital heart defect classically described like a four anatomical heart abnormalities. It is most frequent cyanotic heart defect and the most common cause of blue baby syndrome due to right to left shunt. Retrology of phallid has four classic features, VSD and overriding outer, pulmonary artery stenosis and right ventricular hypertrophy. The VSD associated with retrology of phallid is usually sub-outic and is due to overriding of outer. Toph is caused by unequal division of the conness resulting from anterior displacement of the trunco-conal system. Prevalence of retrology of phallid is 3 to 7% of congenital heart defects. The main reason for suspecting Toph is failure to demonstrate the normal crossing of great vessels at the base of the heart. Methods. Retrospective study was conducted at ANCOPD in our mother and child care hospital within a span of 6 months. Out of 15 cases suspected for congenital cardiac anomalies, 10 cases of Toph were recognized by ultrasound between 20 to 28 weeks of gestation. GE logic P5 ultrasound machine was used. Strict adherence to PCP&T guidelines and proper written consent was ensured. In each case, a four chamber view to assess abnormalities of atria and ventricles and a base view to demonstrate crossing of great vessels were performed. Results. Out of 15 cases suspected for congenital cardiac anomalies, 10 cases of tetralogy of phallid were recognized by ultrasound between 20 to 28 weeks of gestation. Based on the small series, prenatal sonographic findings suggested of Toph may be summarized as follows. A large autic root which is the most common prenatal sonographic finding. A small pulmonary artery or stenosis of the right ventricular outflow tract. A ventricular septal defect in the outlet portion of the septum. An overriding outer which is best seen in the long axis view and a right ventricular hypertrophy. The most common characteristic were ventricular septal defect and a large autic root. Other associated findings like hydropsvitalis and polyhydromoids were also detected in three cases. Discussion. Toph is due to an embryological development of the heart in which an unequal conotrunkal division results in a small pulmonary artery and a great autic artery. The incomplete embryologic rotational process of the conotrunkal septum explains a lack of alignment of the septum with the interventricular septum and tetralogy of phallid. The incomplete rotational process of the autic artery explains its extra position, its overriding location above the interventricular septum and its relationship with the right ventricular. The pulmonary artery remains in an anterior position in relation to the outer. Now this differentiates Toph from complete transposition of the great vessels where the position of the pulmonary and autic arteries is inverted. Under normal circumstances, one septum is continuous with the other. The abnormal alignment process produces a defect of tissue between the septum causing the interventricular communication. On ultrasound examination, a perimembranous VSD is noted. Myelistinotic right ventricular outflow tract is noted. Right ventricular hypertrophy is not noted in the mid-second trimester but it develops after birth. Inverse relationship between the size of the ascending outer and pulmonary artery. A large autic root is an important diagnostic clue. Colour Doppler may demonstrate a reverse flow in the ductus arteriosus to the main pulmonary artery. In pulmonary stenosis and atresia, high velocity and turbulence is noted. Doppler studies demonstrate increased peak velocities in the pulmonary artery due to the right ventricular outflow tract obstruction. It may also demonstrate no flow in the pulmonary artery if complete atresia is present. The overhiding of outer with blood entering from both ventricles into the outer is visible in the form of a five-shape image in colour Doppler during systolic phase. Other findings such as hydropsvitalis or polyhydromneus may also be helpful especially in the case of this plastic pulmonary valves. In the following images, in the first image, there is a VSD with a large autic root. In the second and third image, there is mildly synotic right ventricular outflow tract with high velocity and turbulence noted. In the fourth image, there is a VSD with overhiding of outer. And in the fifth image, in the three-vessel view, only two vessels are seen. Narrow pulmonary artery is noted. Conclusion. The top is the most common congenital synotic heart disease. The antenatal diagnosis can be to look for other associated abnormalities or chromosomal aberrations and allow us to determine a therapeutic strategy. Thank you.