Answer:
A. The side opposite the 60° angle has a length of √3/2
C.Sin(60°)=√3/2
E.The other acute angle of the triangle is 30°
Step-by-step explanation:
The diagram has been attached to the answer
A. The side opposite the 60° angle has a length of
B. The side opposite the 60° angle has a length of .
C. sin(60°) =
D. sin(60°) =
E. The other acute angle of the triangle is 30°.
Answer
The side opposite the 60° angle has a length of the square root of 3/2
Opposite side of the 60° angle has a length of √3/2
sin(60°) = the square root of 3/2
Sin(60°)=√3/2
The other acute angle of the triangle is 30°
Proof:
Total angle in a triangle=180°
180°-60°-90°
=30°
Answer:
![s^2 = 0.01](https://tex.z-dn.net/?f=s%5E2%20%3D%200.01)
Step-by-step explanation:
Given
Values: 9/5, 9/5, 2, 9/5
Required
Calculate the sample variance
Sample variance is calculated using:
![s^2 = \frac{\sum (x_i - \overline x)^2}{n - 1}](https://tex.z-dn.net/?f=s%5E2%20%3D%20%5Cfrac%7B%5Csum%20%28x_i%20-%20%5Coverline%20x%29%5E2%7D%7Bn%20-%201%7D)
First, we calculate the mean
![\overline x = \frac{\sum x}{n}](https://tex.z-dn.net/?f=%5Coverline%20x%20%3D%20%5Cfrac%7B%5Csum%20x%7D%7Bn%7D)
![\overline x = \frac{9/5 + 9/5 + 2 + 9/5}{4}](https://tex.z-dn.net/?f=%5Coverline%20x%20%3D%20%5Cfrac%7B9%2F5%20%2B%209%2F5%20%2B%202%20%2B%209%2F5%7D%7B4%7D)
![\overline x = \frac{7.4}{4}](https://tex.z-dn.net/?f=%5Coverline%20x%20%3D%20%5Cfrac%7B7.4%7D%7B4%7D)
![\overline x = 1.85](https://tex.z-dn.net/?f=%5Coverline%20x%20%3D%201.85)
becomes
![s^2 = \frac{(9/5 - 1.85)^2+(9/5 - 1.85)^2+(2 - 1.85)^2+(9/5 - 1.85)^2}{4 - 1}](https://tex.z-dn.net/?f=s%5E2%20%3D%20%5Cfrac%7B%289%2F5%20-%201.85%29%5E2%2B%289%2F5%20-%201.85%29%5E2%2B%282%20-%201.85%29%5E2%2B%289%2F5%20-%201.85%29%5E2%7D%7B4%20-%201%7D)
![s^2 = \frac{(-0.05)^2+(-0.05)^2+(0.15)^2+(-0.05)^2}{4 - 1}](https://tex.z-dn.net/?f=s%5E2%20%3D%20%5Cfrac%7B%28-0.05%29%5E2%2B%28-0.05%29%5E2%2B%280.15%29%5E2%2B%28-0.05%29%5E2%7D%7B4%20-%201%7D)
![s^2 = \frac{0.0025+0.0025+0.0225+0.0025}{3}](https://tex.z-dn.net/?f=s%5E2%20%3D%20%5Cfrac%7B0.0025%2B0.0025%2B0.0225%2B0.0025%7D%7B3%7D)
![s^2 = \frac{0.03}{3}](https://tex.z-dn.net/?f=s%5E2%20%3D%20%5Cfrac%7B0.03%7D%7B3%7D)
![s^2 = 0.01](https://tex.z-dn.net/?f=s%5E2%20%3D%200.01)
<em>Hence, the variance is 0.01</em>
P=(9-7(.75))/(.38)
p=(9-5.25)/.38
p=3.75/.38
p=9.86
"Pieces" are integers so only 9 pieces .38yd are cut
6/11 = 0.5450.545<x<0.67
The only number is 11/8 ( this equal to 6.11)
A good estimate is 29, as 29 squared is 841 which is very close to the added squares of 20 and 21. Hope this helps!