Answer:
In the long run, ou expect to lose $4 per game
Step-by-step explanation:
Suppose we play the following game based on tosses of a fair coin. You pay me $10, and I agree to pay you $n^2 if heads comes up first on the nth toss.
Assuming X be the toss on which the first head appears.
then the geometric distribution of X is:
X
geom(p = 1/2)
the probability function P can be computed as:

where
n = 1,2,3 ...
If I agree to pay you $n^2 if heads comes up first on the nth toss.
this implies that , you need to be paid 

![\sum \limits ^{n}_{i=1} n^2 P(X=n) =Var (X) + [E(X)]^2](https://tex.z-dn.net/?f=%5Csum%20%5Climits%20%5E%7Bn%7D_%7Bi%3D1%7D%20n%5E2%20P%28X%3Dn%29%20%3DVar%20%28X%29%20%2B%20%5BE%28X%29%5D%5E2)
∵ X
geom(p = 1/2)








Given that during the game play, You pay me $10 , the calculated expected loss = $10 - $6
= $4
∴
In the long run, you expect to lose $4 per game
Answer:
5/11
Step-by-step explanation:
let x=0.4545...
100x=45.4545...
100x-x = 99x=45.4545... - 0.4545...=45
x=45/99=5/11

We need to solve for x, we need to get x alone

Lets start by removing -5
Add 5 on both sides


Now to isolate x , we need to remove the square from x
To remove square , take square root on both sides

square and square root will get cancelled

So
and 
Answer:
x=-5
Step-by-step explanation:
-2x-41=5x-6
-35=7x
-5=x