Answer:
The coordinates of the other end is ![(16,2)](https://tex.z-dn.net/?f=%2816%2C2%29)
Step-by-step explanation:
Given
![End 1: (-6,2)](https://tex.z-dn.net/?f=End%201%3A%20%28-6%2C2%29)
![Midpoint: (5,2)](https://tex.z-dn.net/?f=Midpoint%3A%20%285%2C2%29)
Required
Find the coordinates of the other end
Let Midpoint be represented by (x,y);
(x,y) = (5,2) is calculated as thus
![(x,y) = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%28%5Cfrac%7Bx_1%20%2B%20x_2%7D%7B2%7D%2C%5Cfrac%7By_1%20%2B%20y_2%7D%7B2%7D%29)
So
and ![y = \frac{y_1 + y_2}{2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7By_1%20%2B%20y_2%7D%7B2%7D)
Where
and ![(x,y) = (5,2)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%285%2C2%29)
So, we're solving for ![(x_2,y_2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29)
Solving for ![x_2](https://tex.z-dn.net/?f=x_2)
Substitute 5 for x and -6 for x₁
![5 = \frac{-6 + x_2}{2}](https://tex.z-dn.net/?f=5%20%3D%20%5Cfrac%7B-6%20%2B%20x_2%7D%7B2%7D)
Multiply both sides by 2
![2 * 5 = \frac{-6 + x_2}{2} * 2](https://tex.z-dn.net/?f=2%20%2A%205%20%3D%20%5Cfrac%7B-6%20%2B%20x_2%7D%7B2%7D%20%2A%202)
![10 = -6 + x_2](https://tex.z-dn.net/?f=10%20%3D%20-6%20%2B%20x_2)
Add 6 to both sides
![6 + 10 = -6 +6 + x_2](https://tex.z-dn.net/?f=6%20%2B%2010%20%3D%20-6%20%2B6%20%2B%20%20x_2)
![x_2 = 16](https://tex.z-dn.net/?f=x_2%20%3D%2016)
Solving for ![y_2](https://tex.z-dn.net/?f=y_2)
![y = \frac{y_1 + y_2}{2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7By_1%20%2B%20y_2%7D%7B2%7D)
Substitute 2 for y and 2 for y₁
![2 = \frac{2 + y_2}{2}](https://tex.z-dn.net/?f=2%20%3D%20%5Cfrac%7B2%20%2B%20y_2%7D%7B2%7D)
Multiply both sides by 2
![2 * 2 = \frac{2 + y_2}{2} * 2](https://tex.z-dn.net/?f=2%20%2A%202%20%3D%20%5Cfrac%7B2%20%2B%20y_2%7D%7B2%7D%20%2A%202)
![4 = 2 + y_2](https://tex.z-dn.net/?f=4%20%3D%202%20%2B%20y_2)
Subtract 2 from both sides
![4 - 2 = 2 - 2 + y_2](https://tex.z-dn.net/?f=4%20-%202%20%3D%202%20-%202%20%2B%20y_2)
![y_2 = 2](https://tex.z-dn.net/?f=y_2%20%3D%202)
![(x_2,y_2) = (16,2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%2816%2C2%29)
Hence, the coordinates of the other end is ![(16,2)](https://tex.z-dn.net/?f=%2816%2C2%29)
Answer: Hence, the probability that he will get at least one lemon is 0.70.
Step-by-step explanation:
Since we have given that
Number of cars = 30
Number of lemon cars = 10
Number of other than lemon cars = 30-10 = 20
According to question, he bought 3 cars,
we need to find the probability that you will get at least one lemon.
So, P(X≤1)=1-P(X=0)=1-P(no lemon)
Here, P(no lemon ) is given by
![\dfrac{20}{30}\times \dfrac{20}{30}\times \dfrac{20}{30}=(\dfrac{20}{30})^3](https://tex.z-dn.net/?f=%5Cdfrac%7B20%7D%7B30%7D%5Ctimes%20%5Cdfrac%7B20%7D%7B30%7D%5Ctimes%20%5Cdfrac%7B20%7D%7B30%7D%3D%28%5Cdfrac%7B20%7D%7B30%7D%29%5E3)
so, it becomes,
![P(X\geq 1)=1-(\dfrac{20}{30})^3=1-(0.67)^3=0.70](https://tex.z-dn.net/?f=P%28X%5Cgeq%201%29%3D1-%28%5Cdfrac%7B20%7D%7B30%7D%29%5E3%3D1-%280.67%29%5E3%3D0.70)
Hence, the probability that he will get at least one lemon is 0.70.
First you would add the two angles together to get 105. The. you do 180-105 to get 75. That is the missing angle. From there you would correspond the angles with the sides. Therefore the answer is Angle AB, angle BC, angle CA. these are in order from shortest to longest