Answer:
b, 5=3
Step-by-step explanation:
Answer:
The age of the horse, in human years, when Alex was born can be determined by simply deducting the Current age of Alex from the Current age of the horse in human years.
Therefore, the age of the horse, in human years, when Alex was born was 42 years.
Step-by-step explanation:
Current age of Alex = 8
Current age of the horse in human years = 50
Since the age of the horse is already stated in human years, it implies there is no need to convert the age of the horse again.
Therefore, since Alex is a human who was born 8 years ago, the age of the horse, in human years, when Alex was born can be determined by simply deducting the Current age of Alex from the Current age of the horse in human years as follows:
The age of the horse, in human years, when Alex was born = 50 - 8 = 42
Therefore, the age of the horse, in human years, when Alex was born was 42 years.
This can be presented in a table as follows:
Age of Alex Age of the Horse (in human years)
Eight years ago 0 42
Current age 8 50
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:
40
Step-by-step explanation:
Ok, so basically let's start with a proportion.
x/32 = 11.25/9
Cross multiply:
x * 9 = 32 * 11.25
9x = 32 * 11.25
9x = 360
Solving for variable 'x'.
Divide each side by '9'.
x = 40
I don't know if this is the correct answer, but it was based on my math. I hope this helps!
13000-5600=7400...that's about it, just multiply then subtract