Answer:
first blank- technological skills
second blank- vision
Step-by-step explanation:
This is a binomial distribution.
p = 0.71, q = 1 - p = 1 - 0.71 = 0.29, n = 20
P(x ≤ 19) =1 - P(x = 20) = 1- 20C20 x (0.71)^(20 - 20) x (0.29)^20 = 1 - 0.29^20 = 1 - 0 = 1
V(cylinder)=πR²H
Radius of the cylinder R=x, height of the cylinder H=y.
We can write for the cylinder
V(cylinder)=πx²y
V(cone) =(1/3)πr²h
Radius of the cone r=2x.
We can write for the cone
V(cone)= (1/3)π(2x)²h=(1/3)π *4*x²h
V(cylinder) =V(cone)
πx²y=(1/3)π *4*x²h
y=(4/3)*h
h=(3/4)*y
The regression equation of Y on X is given by the following formula:
![Y-\bar{Y}=b_{yx}(X-\bar{X})](https://tex.z-dn.net/?f=Y-%5Cbar%7BY%7D%3Db_%7Byx%7D%28X-%5Cbar%7BX%7D%29)
Where byx is given by the formula:
![b_{yx}=\frac{N\sum^{}_{}XY-\sum^{}_{}X\sum^{}_{}Y}{N\sum^{}_{}X^2-(\sum^{}_{}X)^2}](https://tex.z-dn.net/?f=b_%7Byx%7D%3D%5Cfrac%7BN%5Csum%5E%7B%7D_%7B%7DXY-%5Csum%5E%7B%7D_%7B%7DX%5Csum%5E%7B%7D_%7B%7DY%7D%7BN%5Csum%5E%7B%7D_%7B%7DX%5E2-%28%5Csum%5E%7B%7D_%7B%7DX%29%5E2%7D)
Where N is the number of values (N=8). We need to find the sum of X values, the sum of Y values, the average of X, the average of Y, the sum of X*Y and the sum of X^2.
The table of values is:
The values we need to know are on the following table:
By replacing the known values in the formula we obtain:
![\begin{gathered} b_{yx}=\frac{8\cdot26125-167\cdot995}{8\cdot4649-(167)^2} \\ b_{yx}=\frac{209000-166165}{37192-27889} \\ b_{yx}=\frac{42835}{9303} \\ b_{yx}=4.6 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20b_%7Byx%7D%3D%5Cfrac%7B8%5Ccdot26125-167%5Ccdot995%7D%7B8%5Ccdot4649-%28167%29%5E2%7D%20%5C%5C%20b_%7Byx%7D%3D%5Cfrac%7B209000-166165%7D%7B37192-27889%7D%20%5C%5C%20b_%7Byx%7D%3D%5Cfrac%7B42835%7D%7B9303%7D%20%5C%5C%20b_%7Byx%7D%3D4.6%20%5Cend%7Bgathered%7D)
Now, the average of X and Y is the sum divided by N, then:
![\begin{gathered} \bar{X}=\frac{167}{8}=20.87 \\ \bar{Y}=\frac{995}{8}=124.37 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cbar%7BX%7D%3D%5Cfrac%7B167%7D%7B8%7D%3D20.87%20%5C%5C%20%5Cbar%7BY%7D%3D%5Cfrac%7B995%7D%7B8%7D%3D124.37%20%5Cend%7Bgathered%7D)
Replace these values in the formula and find the regression equation as follows:
![\begin{gathered} Y-124.37=4.6(X-20.87) \\ Y-124.37=4.6X-4.6\cdot20.87 \\ Y=4.6X-96.11+124.37 \\ Y=4.6X+28.26 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20Y-124.37%3D4.6%28X-20.87%29%20%5C%5C%20Y-124.37%3D4.6X-4.6%5Ccdot20.87%20%5C%5C%20Y%3D4.6X-96.11%2B124.37%20%5C%5C%20Y%3D4.6X%2B28.26%20%5Cend%7Bgathered%7D)
The answer is a) y=4.6x+28.26