Answer:
![d=5](https://tex.z-dn.net/?f=d%3D5)
Step-by-step explanation:
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)
Simply plug in the 2 coordinates into the formula to find distance <em>d</em>:
![d=\sqrt{(4-1)^2+(-1-3)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%284-1%29%5E2%2B%28-1-3%29%5E2%7D)
![d=\sqrt{(3)^2+(-4)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%283%29%5E2%2B%28-4%29%5E2%7D)
![d=\sqrt{9+16}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B9%2B16%7D)
![d=\sqrt{25}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B25%7D)
![d=5](https://tex.z-dn.net/?f=d%3D5)
Supplementary angle = 180 degrees
angle 1 = x
angle 2 = 3x (three times the supplementary)
3x + x = 180
4x = 180
x = 45 degrees
angle 1 = 45 degrees
angle 2 = 135 degrees
X= 22.5 get the x by itself by dividing by 2
Answer:
c
Step-by-step explanation:
Answer: 0.030
Step-by-step explanation:
Given: The percent of the items produced by a machine are defective :![P=10\%=0.10](https://tex.z-dn.net/?f=P%3D10%5C%25%3D0.10)
The percent of the items produced by machine which are not defective:![Q=1-0.1=0.9](https://tex.z-dn.net/?f=Q%3D1-0.1%3D0.9)
Sample size : n = 100
Now, the standard error of the proportion is given by :-
![\text{S.E.}=\sqrt{\dfrac{0.1\times0.9}{100}}\\\\\Rightarrow\text{S.E.}=0.030](https://tex.z-dn.net/?f=%5Ctext%7BS.E.%7D%3D%5Csqrt%7B%5Cdfrac%7B0.1%5Ctimes0.9%7D%7B100%7D%7D%5C%5C%5C%5C%5CRightarrow%5Ctext%7BS.E.%7D%3D0.030)
Hence, the the standard error of the distribution of the sample proportions=0.030