Let
denote the value on the
-th drawn ball. We want to find the expectation of
, which by linearity of expectation is
![E[S]=E\left[\displaystyle\sum_{i=1}^5B_i\right]=\sum_{i=1}^5E[B_i]](https://tex.z-dn.net/?f=E%5BS%5D%3DE%5Cleft%5B%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5E5B_i%5Cright%5D%3D%5Csum_%7Bi%3D1%7D%5E5E%5BB_i%5D)
(which is true regardless of whether the
are independent!)
At any point, the value on any drawn ball is uniformly distributed between the integers from 1 to 10, so that each value has a 1/10 probability of getting drawn, i.e.

and so
![E[X_i]=\displaystyle\sum_{i=1}^{10}x\,P(X_i=x)=\frac1{10}\frac{10(10+1)}2=5.5](https://tex.z-dn.net/?f=E%5BX_i%5D%3D%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5E%7B10%7Dx%5C%2CP%28X_i%3Dx%29%3D%5Cfrac1%7B10%7D%5Cfrac%7B10%2810%2B1%29%7D2%3D5.5)
Then the expected value of the total is
![E[S]=5(5.5)=\boxed{27.5}](https://tex.z-dn.net/?f=E%5BS%5D%3D5%285.5%29%3D%5Cboxed%7B27.5%7D)
Answer:
its alot to explain but i will try to make it as simple as possible
Step-by-step explanation:
your first goal is to make each problem into the form ax^2+bx+c=0
number 1, 2, 7 and 8 is already done for you
now all you have to do is plug in each number in the standard form into the quadtratic formula.
basically at this point you can just use your calculator to do the rest of the work. dont forget parentheses so it doesnt get confused...
or you can perform the algebraic work.. its all just a matter of plugging in the right numbers into the quadratic formula...
cant really do the work for you since im on my phone. but yeah all you need to do step one is transform each problem into ax^2+bx+c=0 form
then step 2, plug in each number in to the quadtratic formula. from there calculate using basic algebraic rules
Answer:
Equation: 3x - 11 = 85
Solution: x = 32
Step-by-step explanation:
3x - 11 = 85
You will have to do the opposite to the equation shown on the screen.
3x = 96 (85 + 11)
x = 32 (96 / 3)
Answer:
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Step-by-step explanation:
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Order everything, negative to the left side and positive to the right side
<u><em>Negative numbers:</em></u>
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<u><em>Positive numbers:</em></u>
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<em><u>Now order it on a number line:</u></em>
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