Hey there!!
Equation given :
A = h ( a + b ) / 2
Multiply by 2 on both sides
2A = h ( a + b )
Divide by h on both sides
2A / h = a + b
Subtract by b on both sides
2A / h - ( b ) = a
Hence, the option ( a ) is the correct answer
Hope my answer helps!
Answer:
The worth of one bill is $20 and the worth of the other bill is $1
Step-by-step explanation:
Let
x----> the worth of one bill
y ---> the worth of the other bill
I assume x > y
we know that
x+y=21 ----> equation A
x=y+19 ---> equation B
Solve the system by elimination
Multiply equation B by -1 both sides
-x=-y-19 ----> equation C
Adds equation A and equation C
x+y=21
-x=-y-19
------------
y=21-y-19
2y=2
y=1
Find the value of x
x=y+19 -----> x=1+19=20
therefore
The worth of one bill is $20 and the worth of the other bill is $1
It should be 51 miles over 3 gallons.
Answer: 70º
Step-by-step explanation:there are two angles with the same measurement on the vertices, therefore with the same angle. A triangle has a sum of 180º in the inside angles. 55º+55º=110º, and 180º-110=70º
Answer:
a) 
b) 0.0620
Step-by-step explanation:
We are given the following in the question:
Population mean, 
= 6
Variance, 
= 12
a) Value of 
We know that
Dividing the two equations, we get,
b) probability that on any given day the daily power consumption will exceed 12 million kilowatt hours.
We can write the probability density function as:
We have to evaluate:
![P(x >12)\\\\= \dfrac{1}{16}\displaystyle\int^{\infty}_{12}f(x)dx\\\\=\dfrac{1}{16}\bigg[-2x^2e^{-\frac{x}{2}}-2\displaystyle\int xe^{-\frac{x}{2}}dx}\bigg]^{\infty}_{12}\\\\=\dfrac{1}{8}\bigg[x^2e^{-\frac{x}{2}}+4xe^{-\frac{x}{2}}+8e^{-\frac{x}{2}}\bigg]^{\infty}_{12}\\\\=\dfrac{1}{8}\bigg[(\infty)^2e^{-\frac{\infty}{2}}+4(\infty)e^{-\frac{\infty}{2}}+8e^{-\frac{\infty}{2}} -( (12)^2e^{-\frac{12}{2}}+4(12)e^{-\frac{12}{2}}+8e^{-\frac{12}{2}})\bigg]\\\\=0.0620](https://tex.z-dn.net/?f=P%28x%20%3E12%29%5C%5C%5C%5C%3D%20%5Cdfrac%7B1%7D%7B16%7D%5Cdisplaystyle%5Cint%5E%7B%5Cinfty%7D_%7B12%7Df%28x%29dx%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B16%7D%5Cbigg%5B-2x%5E2e%5E%7B-%5Cfrac%7Bx%7D%7B2%7D%7D-2%5Cdisplaystyle%5Cint%20xe%5E%7B-%5Cfrac%7Bx%7D%7B2%7D%7Ddx%7D%5Cbigg%5D%5E%7B%5Cinfty%7D_%7B12%7D%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B8%7D%5Cbigg%5Bx%5E2e%5E%7B-%5Cfrac%7Bx%7D%7B2%7D%7D%2B4xe%5E%7B-%5Cfrac%7Bx%7D%7B2%7D%7D%2B8e%5E%7B-%5Cfrac%7Bx%7D%7B2%7D%7D%5Cbigg%5D%5E%7B%5Cinfty%7D_%7B12%7D%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B8%7D%5Cbigg%5B%28%5Cinfty%29%5E2e%5E%7B-%5Cfrac%7B%5Cinfty%7D%7B2%7D%7D%2B4%28%5Cinfty%29e%5E%7B-%5Cfrac%7B%5Cinfty%7D%7B2%7D%7D%2B8e%5E%7B-%5Cfrac%7B%5Cinfty%7D%7B2%7D%7D%20-%28%20%2812%29%5E2e%5E%7B-%5Cfrac%7B12%7D%7B2%7D%7D%2B4%2812%29e%5E%7B-%5Cfrac%7B12%7D%7B2%7D%7D%2B8e%5E%7B-%5Cfrac%7B12%7D%7B2%7D%7D%29%5Cbigg%5D%5C%5C%5C%5C%3D0.0620)
0.0620 is the required probability that on any given day the daily power consumption will exceed 12 million kilowatt hours.
