2m = 4mi that means (12m)
2m × 6 = 4mi × 6 that is 24mi.
Hope this helps.

a. The mean of
is
![E[X]=\displaystyle\int_{-\infty}^\infty xf_X(x)\,\mathrm dx=\frac12\int_0^\pi x\sin x\,\mathrm dx=\frac\pi2](https://tex.z-dn.net/?f=E%5BX%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20xf_X%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cfrac12%5Cint_0%5E%5Cpi%20x%5Csin%20x%5C%2C%5Cmathrm%20dx%3D%5Cfrac%5Cpi2)
Recall that the variance of a random variable
is
![\mathrm{Var}[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2](https://tex.z-dn.net/?f=%5Cmathrm%7BVar%7D%5BX%5D%3DE%5B%28X-E%5BX%5D%29%5E2%5D%3DE%5BX%5E2%5D-E%5BX%5D%5E2)
We have
![E[X^2]=\displaystyle\int_{-\infty}^\infty x^2f_X(x)\,\mathrm dx=\frac12\int_0^\pi x^2\sin x\,\mathrm dx=\frac{\pi^2-4}2](https://tex.z-dn.net/?f=E%5BX%5E2%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20x%5E2f_X%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cfrac12%5Cint_0%5E%5Cpi%20x%5E2%5Csin%20x%5C%2C%5Cmathrm%20dx%3D%5Cfrac%7B%5Cpi%5E2-4%7D2)
so that
![\mathrm{Var}[X]=\dfrac{\pi^2-4}2-\dfrac{\pi^2}4=\dfrac{\pi^2-8}4](https://tex.z-dn.net/?f=%5Cmathrm%7BVar%7D%5BX%5D%3D%5Cdfrac%7B%5Cpi%5E2-4%7D2-%5Cdfrac%7B%5Cpi%5E2%7D4%3D%5Cdfrac%7B%5Cpi%5E2-8%7D4)
and the standard deviation is
![\sqrt{\mathrm{Var}[X]}=\dfrac{\sqrt{\pi^2-8}}2](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cmathrm%7BVar%7D%5BX%5D%7D%3D%5Cdfrac%7B%5Csqrt%7B%5Cpi%5E2-8%7D%7D2)
b.


Answer:
(0, 2)
Step-by-step explanation:
for x . -2 + 2 = 0
for y 2 x 1 = 2
Q: Reflect B (2,7) over the y-axis
Answer:
(-2,7)
Hope this helps! Feel free to comment on this reply if you have any questions. :)
Answer: the vertex is (12,−144)
Step-by-step explanation: