Option D:
The equation of a line in point-slope form is y = 3x – 7.
Solution:
Take any two points on the line given in the graph.
Let the points be (–4, 4) and (2, 2).
![x_1=-4, y_1=4, x_2=2, y_2=2](https://tex.z-dn.net/?f=x_1%3D-4%2C%20y_1%3D4%2C%20x_2%3D2%2C%20y_2%3D2)
Slope of the given line:
![m_1=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![m_1=\frac{2-4}{2-(-4)}](https://tex.z-dn.net/?f=m_1%3D%5Cfrac%7B2-4%7D%7B2-%28-4%29%7D)
![m_1=\frac{-2}{6}](https://tex.z-dn.net/?f=m_1%3D%5Cfrac%7B-2%7D%7B6%7D)
![m_1=\frac{-1}{3}](https://tex.z-dn.net/?f=m_1%3D%5Cfrac%7B-1%7D%7B3%7D)
<em>If two lines are perpendicular, then the product of their slopes are –1.</em>
![\Rightarrow m_1\times m_2=-1](https://tex.z-dn.net/?f=%5CRightarrow%20m_1%5Ctimes%20m_2%3D-1)
![\Rightarrow \frac{-1}{3} \times m_2=-1](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B-1%7D%7B3%7D%20%5Ctimes%20m_2%3D-1)
Multiply by 3 on both sides of the equation.
![\Rightarrow- m_2=-3](https://tex.z-dn.net/?f=%5CRightarrow-%20m_2%3D-3)
Multiply by –1 on both sides of the equation.
⇒
Perpendicular line passes through the point (2, –1).
Here,
.
Using point-slope form:
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
![y-(-1)=3(x-2)](https://tex.z-dn.net/?f=y-%28-1%29%3D3%28x-2%29)
![y+1=3x-6](https://tex.z-dn.net/?f=y%2B1%3D3x-6)
Subtract 1 on both sides of the equation.
![y=3x-7](https://tex.z-dn.net/?f=y%3D3x-7)
The equation of a line in point-slope form is y = 3x – 7.
Therefore option D is the correct answer.
The mean time it takes to walk to the bus stop is 8 minutes (with a standard deviation of 2 minutes) and the mean time it takes for the bus to get to school is 20 minutes (with a standard deviation of 4 minutes). The distributions are normal.
a. How long will it take (in minutes), on average, to get to school?
b. What is the standard deviation of the trip to school?
c. What is the probability that it will take longer than 30 minutes to get to school?
Due to a miscalculation, you realize it actually takes an average of 10 minutes to walk to the bus stop.
d. How long will it take (in minutes), on average, to get to school?
e. What is the standard deviation of the trip to school?
f. What is the probability that it will take longer than 30 minutes to get to school?
The only ones I need help with is C and F. I have the answer for the rest of them. Can someone please help me with parts C and F??
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Answer:85
Step-by-step explanation:
Use PEMDAS (Parentheses Expinents Multiplication Divison Addition Subtraction) in that order to solve in the correct order