Answer:
The expected value of playing the game is $0.75.
Step-by-step explanation:
The expected value of a random variable is the weighted average of the random variable.
The formula to compute the expected value of a random variable <em>X</em> is:
![E(X)=\sum x\cdot P(X=x)](https://tex.z-dn.net/?f=E%28X%29%3D%5Csum%20x%5Ccdot%20P%28X%3Dx%29)
The random variable <em>X</em> in this case can be defined as the amount won in playing the game.
The probability distribution of <em>X</em> is as follows:
Number on spinner: 1 2 3 4 5 6
Amount earned (<em>X</em>): $1 $4 $7 $10 -$8.75 -$8.75
Probability: 1/6 1/6 1/6 1/6 1/6 1/6
Compute the expected value of <em>X</em> as follows:
![E(X)=\sum x\cdot P(X=x)](https://tex.z-dn.net/?f=E%28X%29%3D%5Csum%20x%5Ccdot%20P%28X%3Dx%29)
![=(1\times \frac{1}{6})+(4\times \frac{1}{6})+(7\times \frac{1}{6})+(10\times \frac{1}{6})+(-8.75\times \frac{1}{6})+(-8.75\times \frac{1}{6})](https://tex.z-dn.net/?f=%3D%281%5Ctimes%20%5Cfrac%7B1%7D%7B6%7D%29%2B%284%5Ctimes%20%5Cfrac%7B1%7D%7B6%7D%29%2B%287%5Ctimes%20%5Cfrac%7B1%7D%7B6%7D%29%2B%2810%5Ctimes%20%5Cfrac%7B1%7D%7B6%7D%29%2B%28-8.75%5Ctimes%20%5Cfrac%7B1%7D%7B6%7D%29%2B%28-8.75%5Ctimes%20%5Cfrac%7B1%7D%7B6%7D%29)
![=\frac{1}{6}+\frac{4}{6}+\frac{7}{6}+\frac{10}{6}-\frac{8.75}{6}-\frac{8.75}{6}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B6%7D%2B%5Cfrac%7B4%7D%7B6%7D%2B%5Cfrac%7B7%7D%7B6%7D%2B%5Cfrac%7B10%7D%7B6%7D-%5Cfrac%7B8.75%7D%7B6%7D-%5Cfrac%7B8.75%7D%7B6%7D)
![=\frac{1+4+7+10-8.75-8.75}{6}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%2B4%2B7%2B10-8.75-8.75%7D%7B6%7D)
![=0.75](https://tex.z-dn.net/?f=%3D0.75)
Thus, the expected value of playing the game is $0.75.
Answer:
ok I think the answer is the second one
Answer: t=10
Step-by-step explanation:
FOIL 8(2t-6)= 16t-48
Combine like terms 3t+16t-48=2+14t becomes 19t-48=2+14t
Put all t's on same side 19t-14t=2+48
5t=50 Divide by 5 on each side to have t by self
204/68=3, 207/69=3, 210/10=3, 213/71=3, 216/72=3, 219/73=3
![y = 50x + 100](https://tex.z-dn.net/?f=y%20%3D%2050x%20%2B%20100)
This is the equation for this problem.