Answer:
-$7
Step-by-step explanation:
20 - 15 = 5
5 + 5 = 10
10 - 10 = 0
0 - 7 = -7
I'm assuming
is the shape parameter and
is the scale parameter. Then the PDF is

a. The expectation is
![E[X]=\displaystyle\int_{-\infty}^\infty xf_X(x)\,\mathrm dx=\frac29\int_0^\infty x^2e^{-x^2/9}\,\mathrm dx](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%5Cfrac29%5Cint_0%5E%5Cinfty%20x%5E2e%5E%7B-x%5E2%2F9%7D%5C%2C%5Cmathrm%20dx)
To compute this integral, recall the definition of the Gamma function,

For this particular integral, first integrate by parts, taking


![E[X]=\displaystyle-xe^{-x^2/9}\bigg|_0^\infty+\int_0^\infty e^{-x^2/9}\,\mathrm x](https://tex.z-dn.net/?f=E%5BX%5D%3D%5Cdisplaystyle-xe%5E%7B-x%5E2%2F9%7D%5Cbigg%7C_0%5E%5Cinfty%2B%5Cint_0%5E%5Cinfty%20e%5E%7B-x%5E2%2F9%7D%5C%2C%5Cmathrm%20x)
![E[X]=\displaystyle\int_0^\infty e^{-x^2/9}\,\mathrm dx](https://tex.z-dn.net/?f=E%5BX%5D%3D%5Cdisplaystyle%5Cint_0%5E%5Cinfty%20e%5E%7B-x%5E2%2F9%7D%5C%2C%5Cmathrm%20dx)
Substitute
, so that
:
![E[X]=\displaystyle\frac32\int_0^\infty y^{-1/2}e^{-y}\,\mathrm dy](https://tex.z-dn.net/?f=E%5BX%5D%3D%5Cdisplaystyle%5Cfrac32%5Cint_0%5E%5Cinfty%20y%5E%7B-1%2F2%7De%5E%7B-y%7D%5C%2C%5Cmathrm%20dy)
![\boxed{E[X]=\dfrac32\Gamma\left(\dfrac12\right)=\dfrac{3\sqrt\pi}2\approx2.659}](https://tex.z-dn.net/?f=%5Cboxed%7BE%5BX%5D%3D%5Cdfrac32%5CGamma%5Cleft%28%5Cdfrac12%5Cright%29%3D%5Cdfrac%7B3%5Csqrt%5Cpi%7D2%5Capprox2.659%7D)
The variance is
![\mathrm{Var}[X]=E[(X-E[X])^2]=E[X^2-2XE[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%5E2-2XE%5BX%5D%2BE%5BX%5D%5E2%5D%3DE%5BX%5E2%5D-E%5BX%5D%5E2)
The second moment is
![E[X^2]=\displaystyle\int_{-\infty}^\infty x^2f_X(x)\,\mathrm dx=\frac29\int_0^\infty x^3e^{-x^2/9}\,\mathrm dx](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%5Cfrac29%5Cint_0%5E%5Cinfty%20x%5E3e%5E%7B-x%5E2%2F9%7D%5C%2C%5Cmathrm%20dx)
Integrate by parts, taking


![E[X^2]=\displaystyle-x^2e^{-x^2/9}\bigg|_0^\infty+2\int_0^\infty xe^{-x^2/9}\,\mathrm dx](https://tex.z-dn.net/?f=E%5BX%5E2%5D%3D%5Cdisplaystyle-x%5E2e%5E%7B-x%5E2%2F9%7D%5Cbigg%7C_0%5E%5Cinfty%2B2%5Cint_0%5E%5Cinfty%20xe%5E%7B-x%5E2%2F9%7D%5C%2C%5Cmathrm%20dx)
![E[X^2]=\displaystyle2\int_0^\infty xe^{-x^2/9}\,\mathrm dx](https://tex.z-dn.net/?f=E%5BX%5E2%5D%3D%5Cdisplaystyle2%5Cint_0%5E%5Cinfty%20xe%5E%7B-x%5E2%2F9%7D%5C%2C%5Cmathrm%20dx)
Substitute
again to get
![E[X^2]=\displaystyle9\int_0^\infty e^{-y}\,\mathrm dy=9](https://tex.z-dn.net/?f=E%5BX%5E2%5D%3D%5Cdisplaystyle9%5Cint_0%5E%5Cinfty%20e%5E%7B-y%7D%5C%2C%5Cmathrm%20dy%3D9)
Then the variance is
![\mathrm{Var}[X]=9-E[X]^2](https://tex.z-dn.net/?f=%5Cmathrm%7BVar%7D%5BX%5D%3D9-E%5BX%5D%5E2)
![\boxed{\mathrm{Var}[X]=9-\dfrac94\pi\approx1.931}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cmathrm%7BVar%7D%5BX%5D%3D9-%5Cdfrac94%5Cpi%5Capprox1.931%7D)
b. The probability that
is

which can be handled with the same substitution used in part (a). We get

c. Same procedure as in (b). We have

and

Then

Answer: a) 2092278989 b) 576, c) 
Step-by-step explanation:
Since we have given that
Number of students = 16
Number of desks = 16
a) How many days must pass before the class must repeat a seating arrangement?

If the number of rows = 4
b) How many seating arrangements are there that put Larry, Moe, Curly, and Shemp in the front seats?

c) How many seating arrangements are there that put Larry, Moe, Curly, and Shemp in the front seats?

Hence, a) 2092278989 b) 576, c) 
Answer:
The answer should be 120.
Step-by-step explanation:
30% of 400 = 120 cats
Answers:
1. V=triangle area × length
V=1/2×8×12×20
V=960in³
2. triangle area × length
Area of the triangle=1/2×4×11
A=22ft²
V=22×6
V=132ft³
3. b, volume always have cubic power (³)
4. d, same reason of question 3