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

No, table a is not a function. It is not a function because no x coordinates can share the same y coordinates.
Answer:
The y-intercept
Step-by-step explanation:
Y = mx(slope)+b(y-intercept)
mark Brainliest!!
Let x be the original radius. Given that a semicircle will have an arc length of half of a circumference and C=2pr, the arc length will be just pr.
Now the difference of arc is then going to be:
p(6+x)-px
p(6+x-x)
6p inches
So the arc will be 6p inches longer. Or if you wish to approximate...
≈18.85 inches