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
A function assigns the values. The value of (p·p)(x) is x⁴ + 10x³ + 30x² + 25x.
<h3>What is a Function?</h3>
A function assigns the value of each element of one set to the other specific element of another set.
Given p(x)= x²+5x, therefore, the value of (p·p)(x) can be written as,
(p·p)(x) = p(p(x))
= (x²+5x)²+5(x²+5x)
= x⁴ + 25x² + 10x³ + 5x² + 25x
= x⁴ + 10x³ + 30x² + 25x
Hence, the value of (p·p)(x) is x⁴ + 10x³ + 30x² + 25x.
Learn more about Function:
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Answer:
27 28 29
Step-by-step explanation:
Let the first be n , and if they are consecutive then the next two numbers are n+1 and n+2.
n+(n+1)+(n+2)=84.
3n+3=84.
⇒3n=81.
⇒n=27.
Hence numbers are n,n+1,n+2→27,28 and 29
Answer:
$42
Step-by-step explanation:
Given
Principal (P) = $300
rate of interest (R) = 7%
Time (7T) = 2 years
Interest (I) = ?
We know
I = PTR / 100
= 300 * 7 * 2 / 100
= $ 42
Hope it will help :)❤
Answer:
33%
Step-by-step explanation:
350 * 100 = 35,000
35,000 / 550 = 63.4
100 - 63 = 37
If I did this wrong I am very sorry. 37 is close to 33. The closest answer would be the first choice (approximately 33%).
