Answer:
the is c because the answer
Answer:
y = x - 2
General Formulas and Concepts:
<u>Algebra I</u>
Slope-Intercept Form: y = mx + b
Step-by-step explanation:
<u>Step 1: Define</u>
Slope <em>m</em> = 1
y-intercept <em>b</em> = -2
<u>Step 2: Write linear function</u>
y = x - 2
Answer:
4. 23
4. 206
5. 75 ft
7. 6 sections
8. 6 families
Step-by-step explanation:
4. 3x + 5 is the same thing as 3 x 6 + 5 so it equals to 23
4. x to the power of 3 - 10 is equal to 6 to the power of 3 - 10 so it equals to 206
5. Formula for area of triangle = 1/2 x base x height
So, it's 1/2 x 10 x 15 = 75
7. 3/4 ÷ 1/8 = 6 (Trick: When dividing fractions, make sure to flip the fraction for the 2nd one and leave the 1st one as the same. After that, multiply them together)
8. 3 families have 4-5 pets, 2 families have 6-7 pets and 1 family have 8-9 pets. At least 4 pets means 4 pets and above. So 3 + 2 + 1 = 6 families.
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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.
