Answer:
Step-by-step explanation:
Hello,
a. The area of region P is the area of the rectangle 1 * e minus the
![\displaystyle \int\limits^0_1 {e^x} \, dx=[e^x]^{1}_{0}=e-1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5E0_1%20%7Be%5Ex%7D%20%5C%2C%20dx%3D%5Be%5Ex%5D%5E%7B1%7D_%7B0%7D%3De-1)
So this is e - (e-1) = e - e + 1 = 1
b. The area of region P is the area of the rectangle 1 * e minus P and minus the
![\displaystyle \int\limits^0_1 {e^{-x}} \, dx=[-e^{-x}]^{1}_{0}=-e^{-1}+1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5E0_1%20%7Be%5E%7B-x%7D%7D%20%5C%2C%20dx%3D%5B-e%5E%7B-x%7D%5D%5E%7B1%7D_%7B0%7D%3D-e%5E%7B-1%7D%2B1)
So this is

This is around 1.08616127...
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:

Step-by-step explanation:
The Pythagorean Theorem states that if you square the two legs and take the square root of the two legs, then you get the hypotenuse.
9^2+4^2
=81+16
=97
= 
Hope it helped!
Answer:
The percentile rank of someone who earns $75,000 per year is the 85th percentile.
Step-by-step explanation:
Meaning of percentile:
When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.
In this question:
Working population of 10,500
8,925 people earn less than $75,000 per year.
8925/10500 = 0.85
0.85*100 = 85
The percentile rank of someone who earns $75,000 per year is the 85th percentile.
Answer:
coordinates of its image
A' = ( -4, -1)
B' =( -3, -3)
C' = ( 0, 2)
Step-by-step explanation:
Reflect in y-axis means mirror it's points in the y -axis.
This means that the x coordinate of each point, changes only. Any mirrored point in the y-axis, will change only, by multiplying the x-coordinate by -1.
(Remember, zero multiplied by -1 remains 0).
Given are these points A, B, and C.
A = (4, -1)
B = (3,-3)
C = (0, 2)
After mirroring in the y- axis you get:
A' = ( -4, -1)
B' =( -3, -3)
C' = ( 0, 2)
To graph the equation of the line, find the x-intercept and the y-intercept of the function
we have

we know that
The x-intercept is the value of x when the value of y is equal to zero
The y-intercept is the value of y when the value of x is equal to zero
Step 1
<u>Find the x-intercept</u>
For 



the x-intercept is the point 
Step 2
<u>Find the y-intercept</u>
For


the y-intercept is the point 
Step 3
Graph the points and draw the line
see the attached figure
therefore
the answer in the attached figure