F(x) = -x + 4
Substitute x = -2 to the equation:
f(-2) = -(-2) + 4 = 2 + 4 = 6
Answer: A) 6
Answer: GCF of 40 and 42 is 2
Answer:
r=3
Step-by-step explanation:
simplify each side
4r+17=6r+11
Subtract 4r from both sides.
17=2r+11
Subtract 11 from both sides
6=2r
divide both sides by 2
3=r
Answer:
![-\sqrt{3} /2](https://tex.z-dn.net/?f=-%5Csqrt%7B3%7D%20%2F2)
Step-by-step explanation:
300 degrees is in the fourth quadrant (it's between 270 and 360); sine is negative in the fourth quadrant.
Given we're in the fourth quadrant, the reference angle is 360 - 300 = 60 degrees
sin(60°) =
And since sine is negative, this value turns negative:
sin(300°) = ![-\sqrt{3} /2](https://tex.z-dn.net/?f=-%5Csqrt%7B3%7D%20%2F2)
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)