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Anelyze tle & raph oF ~aHionqL Cunck'owRk)XEX+Z X8raph 14...

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Anelyze tle & raph oF ~aHionqL Cunck'owRk)XEX+Z X8raph 14

Anelyze tle & raph oF ~aHionqL Cunck'ow Rk) XEX+Z X 8raph 14



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$$ \begin{array}{|c|cccccc|}\hline X & {3} & {7} & {9} & {12} & {14} \\ \hline P(X) & {\frac{4}{13}} & {\frac{1}{13}} & {\frac{3}{13}} & {\frac{1}{13}} & {\frac{2}{13}} \\ \hline\end{array} $$

Okay. Ah, good day. Um, today I am looking at a problem where I have two factors. X y t. And I want to know whether they are literally independent or linearly Deed dependent. Um, okay, so let's how would we solve that? Well, um, there's there's a number of ways to do it. Ah, but maybe the best way is to just look at the ron scam. So this is straightforward. Knew when you buy the ron skin. Um, so if you recall w of tea here, um, this is the Ron skin, and it's equal to the Terminator of Except E, which is just the determinants of this matrix here. And, um, now, the determiner of this guy, of course, is just equal to this. It is, um, this this minus this this times this, um minus. So the diagonals, basically this diagonal minus that diagonal. And, um, then when you do your algebra, you end up with t minus one. Um, you end up with this guy here, and, uh, now from there, a we have to do is find a value of tea that that, um, the ron schemes not zero at, and you'll notice that W zero, of course, is negative one, which is not zero. Um, meeting that Exxon wire linearly independent. And that's really all you had to do for this question. So okay.

So to solve this problem, we're gonna use order of operations. I put that over here. So remember parentheses, exponents, multiplication and division left right edition instruction left to right. Now, this fraction bar means that we're going to do the entire top first and the entire bottom. And once we have an answer on each, then we'll divide. So the top of a scan through in the first and look for his parentheses, and I see them here. So first thing about a perform is seven minus two and seven months to, of course, is five. So I got four times five squared notice. I'm rewriting the entire problem exactly as I see it. Except for the seven minus two on the bottom. I'm also gonna follow pandas at the same time. So first I see parentheses. But there's nothing inside. So the next thing I'm going to do is look for exponents, which I see. So I'm going to do 12 squared, which is 144 about 144 minus eight times three. The top. I'm looking for parentheses, which I have, but there's only one number inside. Five squared is 25 so I've got four times. Five times five is 25 over one on the bottom. I have subtraction and multiplication. And according to Penn Gas, multiplication is gonna come first. So I've got 140 poor minus eight times three, which is 20 snow on the top. I'm going to do four times five because my last step, which is 100 in the bottom I've got 144 minus 1 24 which is going to be 1 20 And now if I simplify that, I'm going to divide. At first I might divide top bottom by 10 which will cut off those zeros something at 22nd and then all divide top and bottom by two, which will get me 5/6. It's also important to know that this fraction answer cannot be converted to a decimal because it would not be exactly equivalent. We have to leave it as 56

So in this problem, we're gonna use order of operations or penned asked to solve it. And because of this fraction bar, that means that I'm gonna treat everything on top as its own problem and everything on bottom as its own problem. So the top the first time the scan for is parentheses. And on the top, I see parentheses 14 minus four. So I'm going to do that. So I'm gonna get 14 minutes for is 10 and I'm going to rewrite the rest of the problem. So 10 squared minus four, cubed over Now on the bottom. I'm gonna also do the same thing and I don't see any parentheses. I don't see any exponents, but I do see multiplication. So four times nine is 36 minus. I can also do three times 11. Since I know this multiplication will happen before this subtraction which is 33 some of the top again. I go 10 times 10 sets exponents which would be 100 minus. And I can also this this exponents since I know this expert will happen for its attraction for to the third power, remember, That means to four times four times four four times for 16 16 times for 64 and in the bottom, I've got 36 minus 33 which is three now. 100 minus 64 or 100 minus 60 is 40 40 minus for is 36 and 36. Divided by three is 12.


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