add 6a and 5a and get 11a
then:
11a=-11
a=-1
Answer:
.20
Step-by-step explanation:
75/500 = .15
35-15=20
Answer:
c) 2
d) 0.96
Step-by-step explanation:
We are given the following in the question:

a) probability density function.
![\displaystyle\int^{\infty}_{\infty}f(x) dx = 1\\\\\displaystyle\int^{\infty}_{-\infty}2x^{-3}dx = 1\\\\\displaystyle\int^{\infty}_{1}2x^{-3}dx\\\\\Rightarrow \big[-x^{-2}\big]^{\infty}_1\\\\\Rightarrow -(0-1) = 1](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5E%7B%5Cinfty%7D_%7B%5Cinfty%7Df%28x%29%20dx%20%3D%201%5C%5C%5C%5C%5Cdisplaystyle%5Cint%5E%7B%5Cinfty%7D_%7B-%5Cinfty%7D2x%5E%7B-3%7Ddx%20%3D%201%5C%5C%5C%5C%5Cdisplaystyle%5Cint%5E%7B%5Cinfty%7D_%7B1%7D2x%5E%7B-3%7Ddx%5C%5C%5C%5C%5CRightarrow%20%5Cbig%5B-x%5E%7B-2%7D%5Cbig%5D%5E%7B%5Cinfty%7D_1%5C%5C%5C%5C%5CRightarrow%20-%280-1%29%20%3D%201)
Thus, it is a probability density function.
b) cumulative distribution function.

c) mean of the distribution

d) probability that the size of random particle will be less than 5 micrometers

Answer:
y = -4
Step-by-step explanation:
3y - 2(5y - 7) = -9y + 6 (Given)
3y - 10y + 14 = -9y + 6 (Distribute)
-7y + 14 = -9y + 6 (Add like terms)
2y + 14 = 6 (Add 9y on both sides)
2y = -8 (Subtract 14 on both sides)
y = -4 (Divide 2 on both sides)
You can check by substituting the solution for y:
3(-4) - 2(5(-4) - 7) = -9(-4) + 6
-12 - 2(-20 - 7) = 36 + 6
-12 - 2(-27) = 42
-12 + 54 = 42
42 = 42