Answer:
98
Step-by-step explanation:
there are 12 inches in one foot so if 5x12=60
12x8=96
Answer:
see explanation
Step-by-step explanation:
the ratio of the opposite interior angles = 8 : 9 = 8x : 9x
The exterior angle of a triangle = sum of the opposite interior angles, hence
8x + 9x = 119
17x = 119 ( divide both sides by 17 )
x = 7
8 parts = 8x = 8 × 7 = 56
9 parts = 9x = 9 × 7 = 63
The sum of the 3 angles in a triangle = 180°
subtract the sum of the 2 angles from 180 for third angle in triangle
180° - (56 + 63)° = 180° - 119° = 61°
The 3 angles of the triangle are 56°, 61°, 63°
Our data are:
0.19
0.78
0.96
1.31
2.78
3.16
4.15
4.67
4.85
6.50
7.35
8.01
8.27
12.06
31.75
32.52
33.91
36.71
72.89
From this data we have n=19
Mean is
equal to:
![\bar{x} = \frac{\sum x_i}{n}](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%20%3D%20%5Cfrac%7B%5Csum%20x_i%7D%7Bn%7D)
We summarize all the values and divide them by the total number of samples.
![\bar{x}=\frac{272.82}{19}](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%3D%5Cfrac%7B272.82%7D%7B19%7D)
![\bar{x} = 14.3589](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%20%3D%2014.3589)
In another hand we have that Standard Variation is equal to
![s=\sqrt{\frac{\sum(x_i-\bar{x})^2}{n-1}}](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B%5Cfrac%7B%5Csum%28x_i-%5Cbar%7Bx%7D%29%5E2%7D%7Bn-1%7D%7D)
For this case we take the value of each of our samples, we subtract the average and we square it to that value. We do this with each of the data and in the end we divide them by the total population of the sample (n) minus 1.
![s= \frac{(0.19-14.3589)^2.... (72.89-14.35)^2}{19-1}](https://tex.z-dn.net/?f=s%3D%20%5Cfrac%7B%280.19-14.3589%29%5E2....%20%2872.89-14.35%29%5E2%7D%7B19-1%7D)
![s=18.880](https://tex.z-dn.net/?f=s%3D18.880)
Answer:
119°
Step-by-step explanation:
if sum of two angles=180,then they are supplementary.
61+x=180
x=180-61=119
Answer:
![\frac{11x}{3y}](https://tex.z-dn.net/?f=%5Cfrac%7B11x%7D%7B3y%7D)
Step-by-step explanation:
![\frac{7x}{3y} + \frac{12x}{9y}](https://tex.z-dn.net/?f=%5Cfrac%7B7x%7D%7B3y%7D%20%2B%20%5Cfrac%7B12x%7D%7B9y%7D)
To add the two fractions, you need a common denominator. In this case, the lowest common denominator (LCD) is 9y. That's because 9y is divisible by both 3y and 9y.
The first fraction must be changed so that its denominator is 9y. Do this by multiplying both numerator and denominator by 3.
![\frac{7x}{3y}\cdot\frac{3}{3}+\frac{21x}{9y}=\frac{21x}{9y}+\frac{12x}{9y}\\=\frac{21x+12x}{9y}\\=\frac{33x}{9y}](https://tex.z-dn.net/?f=%5Cfrac%7B7x%7D%7B3y%7D%5Ccdot%5Cfrac%7B3%7D%7B3%7D%2B%5Cfrac%7B21x%7D%7B9y%7D%3D%5Cfrac%7B21x%7D%7B9y%7D%2B%5Cfrac%7B12x%7D%7B9y%7D%5C%5C%3D%5Cfrac%7B21x%2B12x%7D%7B9y%7D%5C%5C%3D%5Cfrac%7B33x%7D%7B9y%7D)
Finally, this answer can be simplified ("reduced") by dividing both numerator and denominator by 3, their greatest common factor.