Given:
The pair of points.
5. P(1, 1), Q(–1, –1)
6. ![E\left(\dfrac{1}{2},4\dfrac{1}{4}\right), F\left(5,-\dfrac{1}{2}\right)](https://tex.z-dn.net/?f=E%5Cleft%28%5Cdfrac%7B1%7D%7B2%7D%2C4%5Cdfrac%7B1%7D%7B4%7D%5Cright%29%2C%20F%5Cleft%285%2C-%5Cdfrac%7B1%7D%7B2%7D%5Cright%29)
To find:
The distance between the pair of points.
Solution:
Distance formula:
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
5.
The distance between the pair of points P(1, 1) and Q(–1, –1) is:
![PQ=\sqrt{(-1-1)^2+(-1-1)^2}](https://tex.z-dn.net/?f=PQ%3D%5Csqrt%7B%28-1-1%29%5E2%2B%28-1-1%29%5E2%7D)
![PQ=\sqrt{(-2)^2+(-2)^2}](https://tex.z-dn.net/?f=PQ%3D%5Csqrt%7B%28-2%29%5E2%2B%28-2%29%5E2%7D)
![PQ=\sqrt{4+4}](https://tex.z-dn.net/?f=PQ%3D%5Csqrt%7B4%2B4%7D)
![PQ=\sqrt{8}](https://tex.z-dn.net/?f=PQ%3D%5Csqrt%7B8%7D)
![PQ=2\sqrt{2}](https://tex.z-dn.net/?f=PQ%3D2%5Csqrt%7B2%7D)
Therefore, the distance between P and Q is
.
6.
The distance between the pair of point
is:
![EF=\sqrt{\left(5-\dfrac{1}{2}\right)^2+\left(-\dfrac{1}{2}-4\dfrac{1}{4}\right)^2}](https://tex.z-dn.net/?f=EF%3D%5Csqrt%7B%5Cleft%285-%5Cdfrac%7B1%7D%7B2%7D%5Cright%29%5E2%2B%5Cleft%28-%5Cdfrac%7B1%7D%7B2%7D-4%5Cdfrac%7B1%7D%7B4%7D%5Cright%29%5E2%7D)
![EF=\sqrt{\left(\dfrac{10-1}{2}\right)^2+\left(-\dfrac{1}{2}-\dfrac{17}{4}\right)^2}](https://tex.z-dn.net/?f=EF%3D%5Csqrt%7B%5Cleft%28%5Cdfrac%7B10-1%7D%7B2%7D%5Cright%29%5E2%2B%5Cleft%28-%5Cdfrac%7B1%7D%7B2%7D-%5Cdfrac%7B17%7D%7B4%7D%5Cright%29%5E2%7D)
![EF=\sqrt{\left(\dfrac{9}{2}\right)^2+\left(\dfrac{-2-17}{4}\right)^2}](https://tex.z-dn.net/?f=EF%3D%5Csqrt%7B%5Cleft%28%5Cdfrac%7B9%7D%7B2%7D%5Cright%29%5E2%2B%5Cleft%28%5Cdfrac%7B-2-17%7D%7B4%7D%5Cright%29%5E2%7D)
![EF=\sqrt{\dfrac{81}{4}+\left(\dfrac{-19}{4}\right)^2}](https://tex.z-dn.net/?f=EF%3D%5Csqrt%7B%5Cdfrac%7B81%7D%7B4%7D%2B%5Cleft%28%5Cdfrac%7B-19%7D%7B4%7D%5Cright%29%5E2%7D)
On further simplification, we get
![EF=\sqrt{\dfrac{81}{4}+\dfrac{361}{16}}](https://tex.z-dn.net/?f=EF%3D%5Csqrt%7B%5Cdfrac%7B81%7D%7B4%7D%2B%5Cdfrac%7B361%7D%7B16%7D%7D)
![EF=\sqrt{\dfrac{324+361}{16}}](https://tex.z-dn.net/?f=EF%3D%5Csqrt%7B%5Cdfrac%7B324%2B361%7D%7B16%7D%7D)
![EF=\sqrt{\dfrac{685}{16}}](https://tex.z-dn.net/?f=EF%3D%5Csqrt%7B%5Cdfrac%7B685%7D%7B16%7D%7D)
![EF=\sqrt{42.8125 }](https://tex.z-dn.net/?f=EF%3D%5Csqrt%7B42.8125%0A%7D)
![EF\approx 6.5](https://tex.z-dn.net/?f=EF%5Capprox%206.5)
Therefore, the distance between E and F is 6.5 units.
Answer:
This is cluster sampling.
Step-by-step explanation:
American Airlines randomly selects 110 flights during a certain week and surveys all passengers on the flights.
This is a type of cluster sampling.
This type of sampling is done by dividing the population into different groups and a simple random sample of clusters is selected from the population.
Answer:
1/1 i think (srry if wrong)
3x + 4x + 6x = 104
13x = 104
x = 104 / 13
x = 8
So the sides are
24
32 and
48
$156.65
103.00 x .55 = 56.65
103.00 + 56..65 = $156.65