Answer: Question 1 is correct and Question 2 is 12 degrees :)
Step-by-step explanation: hope this helped!
the answer is (A) you cant have 11 it should be 1.1 x 10^22
Given:
The vertices of the rectangle ABCD are A(0,1), B(2,4), C(6,0), D(4,-3).
To find:
The area of the rectangle.
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)
Using the distance formula, we get
![AB=\sqrt{(2-0)^2+(4-1)^2}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%282-0%29%5E2%2B%284-1%29%5E2%7D)
![AB=\sqrt{(2)^2+(3)^2}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%282%29%5E2%2B%283%29%5E2%7D)
![AB=\sqrt{4+9}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B4%2B9%7D)
![AB=\sqrt{13}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B13%7D)
Similarly,
![BC=\sqrt{(6-2)^2+(0-4)^2}](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B%286-2%29%5E2%2B%280-4%29%5E2%7D)
![BC=\sqrt{(4)^2+(-4)^2}](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B%284%29%5E2%2B%28-4%29%5E2%7D)
![BC=\sqrt{16+16}](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B16%2B16%7D)
![BC=\sqrt{32}](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B32%7D)
![BC=4\sqrt{2}](https://tex.z-dn.net/?f=BC%3D4%5Csqrt%7B2%7D)
Now, the length of the rectangle is
and the width of the rectangle is
. So, the area of the rectangle is:
![A=length \times width](https://tex.z-dn.net/?f=A%3Dlength%20%5Ctimes%20width)
![A=\sqrt{13}\times 4\sqrt{2}](https://tex.z-dn.net/?f=A%3D%5Csqrt%7B13%7D%5Ctimes%204%5Csqrt%7B2%7D)
![A=4\sqrt{26}](https://tex.z-dn.net/?f=A%3D4%5Csqrt%7B26%7D)
![A\approx 20](https://tex.z-dn.net/?f=A%5Capprox%2020)
Therefore, the area of the rectangle is 20 square units.
9514 1404 393
Answer:
36
Step-by-step explanation:
The parallel lines divide the segments proportionally.
GH/HI = GK/KJ
GH = HI(GK/KJ) = 48(30/40)
GH = 36
Answer:
For a height of 66 inches, Z = 0.65.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The average height was about 64.3 inches; the SD was about 2.6 inches.
This means that ![\mu = 64.3, \sigma = 2.6](https://tex.z-dn.net/?f=%5Cmu%20%3D%2064.3%2C%20%5Csigma%20%3D%202.6)
66 inches:
The z-score for a height of 66 inches is:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{66 - 64.3}{2.6}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B66%20-%2064.3%7D%7B2.6%7D)
![Z = 0.65](https://tex.z-dn.net/?f=Z%20%3D%200.65)
For a height of 66 inches, Z = 0.65.