Answer:
1/4
Step-by-step explanation:
6.25 because 2.5+2.5= 5 and then half of 2.5 is 1.25 so 6.25
The answer is B, f(x) = 4x + 4.
If you substitute 2 for x, the resulting answer will be 12, therefore it is correct.
Answer:
![E(X_n)=\frac{2(n-1)}{27}](https://tex.z-dn.net/?f=E%28X_n%29%3D%5Cfrac%7B2%28n-1%29%7D%7B27%7D)
![E(y)=\frac{14}{9}](https://tex.z-dn.net/?f=E%28y%29%3D%5Cfrac%7B14%7D%7B9%7D)
Step-by-step explanation:
From the question we are told that:
Sample size n=9
Number of Green ![g=4](https://tex.z-dn.net/?f=g%3D4)
Number of yellow ![y=4](https://tex.z-dn.net/?f=y%3D4)
Number of white ![w=4](https://tex.z-dn.net/?f=w%3D4)
Probability of Green Followed by yellow P(GY) ball
![P(GY)=\frac{4}{9}*\frac{3}{9}](https://tex.z-dn.net/?f=P%28GY%29%3D%5Cfrac%7B4%7D%7B9%7D%2A%5Cfrac%7B3%7D%7B9%7D)
![P(GY)=\frac{4}{27}](https://tex.z-dn.net/?f=P%28GY%29%3D%5Cfrac%7B4%7D%7B27%7D)
Generally the equations for when n is even is mathematically given by
![Probability of success P(S)=\frac{4}{27}](https://tex.z-dn.net/?f=Probability%20of%20success%20P%28S%29%3D%5Cfrac%7B4%7D%7B27%7D)
![Probability of Failure P(F)=\frac{27-4}{27}](https://tex.z-dn.net/?f=Probability%20of%20Failure%20P%28F%29%3D%5Cfrac%7B27-4%7D%7B27%7D)
![Probability of Failure P(F)=\frac{23}{27}](https://tex.z-dn.net/?f=Probability%20of%20Failure%20P%28F%29%3D%5Cfrac%7B23%7D%7B27%7D)
Therefore
![E(X_n)=\frac{n}{2}*P](https://tex.z-dn.net/?f=E%28X_n%29%3D%5Cfrac%7Bn%7D%7B2%7D%2AP)
![E(X_n)=\frac{n}{2}*\frac{4}{27}](https://tex.z-dn.net/?f=E%28X_n%29%3D%5Cfrac%7Bn%7D%7B2%7D%2A%5Cfrac%7B4%7D%7B27%7D)
![E(X_n)=\frac{2n}{27}](https://tex.z-dn.net/?f=E%28X_n%29%3D%5Cfrac%7B2n%7D%7B27%7D)
Generally the equations for when n is odd is mathematically given by
![\frac{n-1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bn-1%7D%7B2%7D)
![E(X_n)=\frac{n-1}{2}*\frac{4}{27}](https://tex.z-dn.net/?f=E%28X_n%29%3D%5Cfrac%7Bn-1%7D%7B2%7D%2A%5Cfrac%7B4%7D%7B27%7D)
![E(X_n)=\frac{2(n-1)}{27}](https://tex.z-dn.net/?f=E%28X_n%29%3D%5Cfrac%7B2%28n-1%29%7D%7B27%7D)
b)
Probability of drawing white ball
![P(w)=\frac{2}{9}](https://tex.z-dn.net/?f=P%28w%29%3D%5Cfrac%7B2%7D%7B9%7D)
Therefore
![E(w)=\frac{1}{p}](https://tex.z-dn.net/?f=E%28w%29%3D%5Cfrac%7B1%7D%7Bp%7D)
![E(w)=\frac{1}{\frac{2}{9}}](https://tex.z-dn.net/?f=E%28w%29%3D%5Cfrac%7B1%7D%7B%5Cfrac%7B2%7D%7B9%7D%7D)
![E(w)=\frac{9}{2}](https://tex.z-dn.net/?f=E%28w%29%3D%5Cfrac%7B9%7D%7B2%7D)
Therefore
![E(y)=[E(w)-1]\frac{4}{9}](https://tex.z-dn.net/?f=E%28y%29%3D%5BE%28w%29-1%5D%5Cfrac%7B4%7D%7B9%7D)
![E(y)=[\frac{9}{2}-1]\frac{4}{9}](https://tex.z-dn.net/?f=E%28y%29%3D%5B%5Cfrac%7B9%7D%7B2%7D-1%5D%5Cfrac%7B4%7D%7B9%7D)
![E(y)=\frac{14}{9}](https://tex.z-dn.net/?f=E%28y%29%3D%5Cfrac%7B14%7D%7B9%7D)
Ok, so here, we need to use the slope formula which is:
(y2 - y1)/(x2-x1)
y2 = 9
y1 = 5
x2 = x
x1 = 10
So:
(9-5)/(x-10) = -2
Now, we just solve for x,
9-5 = -2(x-10)
4 = -2x+20
2x = 16
x = 8