Answer:
Step-by-step explanation:
One is given the following function (
). The given problem asks one to find the output of the function when the input is (10). Keep in mind, a general rule for dealing with functions is that, when present, the variable (x) represents the input. Whereas the variable (y) represents the output. Thus, if one were to substitute (10) in place of (x), and simplify: the result one would get is the output. Apply this idea to the given scenario:
Answer:
<em>Part A </em>C = (10,5)<em> Part B </em>C. D'(0,10)
Step-by-step explanation:
<em>Part A</em>
Since c is at the point (2,1) in relation to the origin, we can multiply those distances by our scale factor of 5
(2,1) * 5 = (10,5)
The new point C is going to be (10,5)
<em>Part B</em>
If you dilate with a factor of 5 -- relative to the origin -- you have to multiply the distance from <em>the origin</em> by 5.
In this case, point D is already on the y axis, so it's x value wouldn't be affected. Point D is currently 2 units away from (0,0), so we can multiply 2*5 to get 10 -- our ending point is (0,10)
Answer:
169
Step-by-step explanation:
You need to use a Z-table for this.
There are different tables, in this table i searched for the probability of 97% because that equivalent to the top 3%.
for 0.97, Z = 1.88
The formula of Z is:
Solving x:
Answer:
one side is 40 other is 50
Step-by-step explanation:
perimeter=180cm
let one side=length=x
Acc. to condition:
other side=width=x+10 (one side exceed other by 10)
perimeter= 2(length+width)
subtitue all values given above:
180=2(x+x+10)
180=2(2x+10)
2x+10=180/2
2x+10=90
2x=90-10
2x=80
x=40
now
lenght=x=40cm
width=x+10=40+10
width=50cm
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
