Answer: ![\bold{y=-\dfrac{1}{3}x-1}](https://tex.z-dn.net/?f=%5Cbold%7By%3D-%5Cdfrac%7B1%7D%7B3%7Dx-1%7D)
<u>Step-by-step explanation:</u>
(4, 1) & (2, -5)
First, find the slope (m) and then the perpendicular (opposite reciprocal) slope:
![m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\\m=\dfrac{-5-1}{2-4} = \dfrac{-6}{-2}=3\quad \rightarrow \quad m_{\perp}=-\dfrac{1}{3}\\](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%5C%5C%5C%5Cm%3D%5Cdfrac%7B-5-1%7D%7B2-4%7D%20%3D%20%5Cdfrac%7B-6%7D%7B-2%7D%3D3%5Cquad%20%5Crightarrow%20%5Cquad%20m_%7B%5Cperp%7D%3D-%5Cdfrac%7B1%7D%7B3%7D%5C%5C)
Next, find the midpoint of (4, 1) and (2, -5):
![Midpoint=\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{4+2}{2},\dfrac{1-5}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{6}{2},\dfrac{-4}{2}\bigg)\\\\\\.\qquad \qquad=(3, -2)](https://tex.z-dn.net/?f=Midpoint%3D%5Cbigg%28%5Cdfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%5Cdfrac%7By_1%2By_2%7D%7B2%7D%5Cbigg%29%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%3D%5Cbigg%28%5Cdfrac%7B4%2B2%7D%7B2%7D%2C%5Cdfrac%7B1-5%7D%7B2%7D%5Cbigg%29%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%3D%5Cbigg%28%5Cdfrac%7B6%7D%7B2%7D%2C%5Cdfrac%7B-4%7D%7B2%7D%5Cbigg%29%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%3D%283%2C%20-2%29)
Lastly, input the perpendicular slope and the midpoint into the Point-Slope formula to find the equation of the line:
![y - y_1 = m_{\perp}(x - x_1)\\\\y - (-2) = -\dfrac{1}{3}(x - 3)\\\\y + 2=-\dfrac{1}{3}x +1\\\\y =-\dfrac{1}{3}x - 1\\](https://tex.z-dn.net/?f=y%20-%20y_1%20%3D%20m_%7B%5Cperp%7D%28x%20-%20x_1%29%5C%5C%5C%5Cy%20-%20%28-2%29%20%3D%20-%5Cdfrac%7B1%7D%7B3%7D%28x%20-%203%29%5C%5C%5C%5Cy%20%2B%202%3D-%5Cdfrac%7B1%7D%7B3%7Dx%20%2B1%5C%5C%5C%5Cy%20%3D-%5Cdfrac%7B1%7D%7B3%7Dx%20-%201%5C%5C)
The converse of a conditional statement switches the hypothesis and conclusion.
Answer:
6
Step-by-step explanation:
5*6=30
7*6=42
7. tails, odd, 4
P(tails) = 1/2
P(odd) = 3/6 = 1/2
P(4) = 1/6
P(tails then odd then 4) = (1/2)×(1/2)×(1/6) = 1/24 ≈ 0.041666
Answer: 1/24, 4.2%
8. tails, 6 or 1, 3
P(6 or 1) = 2/6 = 1/3
P(3) = 1/6
P( tails, 6 or 1, 3) = (1/2)(1/3)(1/6) = 1/36 ≈ 0.027777
Answer: 1/36, 2.8%
9. heads, not 2, even
P(heads) = 1/2
P(not 2) = 5/6
P(even) = 1/2
P(heads, not 2, even) = (1/2)(5/6)(1/2) = 5/24 ≈ 0.208333
Answer: 5/24, 20.8%
Answer: 68%
Step-by-step explanation:
150-48=102/150=.68 x 100=68