Answer:
210 sq in
Step-by-step explanation:
Box dimensions: 5 x 5 x 8
2 faces: 5 x 5 -> 2 * 5 * 5 = 50
4 faces: 5 x 8 -> 4 * 5 * 8 = 160
Total = 50 + 160 = 210 sq in
Let

be the random variable indicating whether the elevator does not stop at floor

, with

Let

be the random variable representing the number of floors at which the elevator does not stop. Then

We want to find

. By definition,
![\mathrm{Var}(Y)=\mathbb E[(Y-\mathbb E[Y])^2]=\mathbb E[Y^2]-\mathbb E[Y]^2](https://tex.z-dn.net/?f=%5Cmathrm%7BVar%7D%28Y%29%3D%5Cmathbb%20E%5B%28Y-%5Cmathbb%20E%5BY%5D%29%5E2%5D%3D%5Cmathbb%20E%5BY%5E2%5D-%5Cmathbb%20E%5BY%5D%5E2)
As stated in the question, there is a

probability that any one person will get off at floor

(here,

refers to any of the

total floors, not just the top floor). Then the probability that a person will not get off at floor

is

. There are

people in the elevator, so the probability that not a single one gets off at floor

is

.
So,

which means
![\mathbb E[Y]=\mathbb E\left[\displaystyle\sum_{i=1}^nX_i\right]=\displaystyle\sum_{i=1}^n\mathbb E[X_i]=\sum_{i=1}^n\left(1\cdot\left(1-\dfrac1n\right)^m+0\cdot\left(1-\left(1-\dfrac1n\right)^m\right)](https://tex.z-dn.net/?f=%5Cmathbb%20E%5BY%5D%3D%5Cmathbb%20E%5Cleft%5B%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5EnX_i%5Cright%5D%3D%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5En%5Cmathbb%20E%5BX_i%5D%3D%5Csum_%7Bi%3D1%7D%5En%5Cleft%281%5Ccdot%5Cleft%281-%5Cdfrac1n%5Cright%29%5Em%2B0%5Ccdot%5Cleft%281-%5Cleft%281-%5Cdfrac1n%5Cright%29%5Em%5Cright%29)
![\implies\mathbb E[Y]=n\left(1-\dfrac1n\right)^m](https://tex.z-dn.net/?f=%5Cimplies%5Cmathbb%20E%5BY%5D%3Dn%5Cleft%281-%5Cdfrac1n%5Cright%29%5Em)
and
![\mathbb E[Y^2]=\mathbb E\left[\left(\displaystyle\sum_{i=1}^n{X_i}\right)^2\right]=\mathbb E\left[\displaystyle\sum_{i=1}^n{X_i}^2+2\sum_{1\le i](https://tex.z-dn.net/?f=%5Cmathbb%20E%5BY%5E2%5D%3D%5Cmathbb%20E%5Cleft%5B%5Cleft%28%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5En%7BX_i%7D%5Cright%29%5E2%5Cright%5D%3D%5Cmathbb%20E%5Cleft%5B%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5En%7BX_i%7D%5E2%2B2%5Csum_%7B1%5Cle%20i%3Cj%7DX_iX_j%5Cright%5D%3D%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5En%5Cmathbb%20E%5B%7BX_i%7D%5E2%5D%2B2%5Csum_%7B1%5Cle%20i%3Cj%7D%5Cmathbb%20E%5BX_iX_j%5D)
Computing
![\mathbb E[{X_i}^2]](https://tex.z-dn.net/?f=%5Cmathbb%20E%5B%7BX_i%7D%5E2%5D)
is trivial since it's the same as
![\mathbb E[X_i]](https://tex.z-dn.net/?f=%5Cmathbb%20E%5BX_i%5D)
. (Do you see why?)
Next, we want to find the expected value of the following random variable, when

:

If

, we don't care; when we compute
![\mathbb E[X_iX_j]](https://tex.z-dn.net/?f=%5Cmathbb%20E%5BX_iX_j%5D)
, the contributing terms will vanish. We only want to see what happens when both floors are not visited.

![\implies\mathbb E[X_iX_j]=\left(1-\dfrac2n\right)^m](https://tex.z-dn.net/?f=%5Cimplies%5Cmathbb%20E%5BX_iX_j%5D%3D%5Cleft%281-%5Cdfrac2n%5Cright%29%5Em)

where we multiply by

because that's how many ways there are of choosing indices

for

such that

.
So,
Answer:
0.80 for 0.5 mile
0.80/0.5 for 1 mile
18.5 × 0.80/0.5 for 18.5 mile
Use calculator and you answer will be 29.6
Here it is!
First, let's multiply the first equation by two. This is because we have to eliminate either x or y by subtraction or addition so that means either both of the x's or both of the y's in the two equations have to be equal. Thus multiplying the first equation by 2 will give 12x+8y=4.
Next, subtract equation two from equation one:
We get a third equation, 2x-0= -28
Thus, x=-28/2. x= -14
In the same way, to find y, we need to eliminate the x's in both equations. This can be done by multiplying the first equation by 5 and the second by 3
Thus : 30x+20y=10 and 30x-24y=96
Subtracting the second equation from the first, we have 0+44y=-86
y=-86/44
y = 1.96 or 43/22
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