Answer:
75%.
Step-by-step explanation:
In total, there are 3 gnarly boards in the first shop and 1 gnarly board in the second. We know that he has selected one gnarly board out of the 3 + 1 = 4 existing boards.
The probability the board came from the first shop is 3 / 4 = 0.75 = 75%.
Hope this helps!
8(t+2)-3(t-4) = 6(t-7)+8
8t+16-3t+12=6t-42+8
5t+28=6t-34
t = 62
When two lines are parallel they have the same slope
slope of this line y=-5\4x is -5\4
Slope of the parallel line is also -5\4
Answer:
(a) Shown below
(b) There is a positive relation between the number of assemblers and production.
(c) The correlation coefficient is 0.9272.
Step-by-step explanation:
Let <em>X</em> = number of assemblers and <em>Y</em> = number of units produced in an hour.
(a)
Consider the scatter plot below.
(b)
Based on the scatter plot it can be concluded that there is a positive relationship between the variables <em>X</em> and <em>Y</em>, i.e. as the value of <em>X</em> increases <em>Y</em> also increases.
(c)
The formula to compute the correlation coefficient is:
![r=\frac{n\sum XY-\sum X\sum Y}{\sqrt{[n\sum X^{2}-(\sum X)^{2}][n\sum Y^{2}-(\sum Y)^{2}]}} }](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bn%5Csum%20XY-%5Csum%20X%5Csum%20Y%7D%7B%5Csqrt%7B%5Bn%5Csum%20X%5E%7B2%7D-%28%5Csum%20X%29%5E%7B2%7D%5D%5Bn%5Csum%20Y%5E%7B2%7D-%28%5Csum%20Y%29%5E%7B2%7D%5D%7D%7D%20%7D)
Compute the correlation coefficient between <em>X</em> and <em>Y</em> as follows:
![r=\frac{n\sum XY-\sum X\sum Y}{\sqrt{[n\sum X^{2}-(\sum X)^{2}][n\sum Y^{2}-(\sum Y)^{2}]}} }=\frac{(5\times430)-(15\times120)}{\sqrt{[(5\times55)-15^{2}][(5\times3450)-120^{2}]}} =0.9272](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bn%5Csum%20XY-%5Csum%20X%5Csum%20Y%7D%7B%5Csqrt%7B%5Bn%5Csum%20X%5E%7B2%7D-%28%5Csum%20X%29%5E%7B2%7D%5D%5Bn%5Csum%20Y%5E%7B2%7D-%28%5Csum%20Y%29%5E%7B2%7D%5D%7D%7D%20%7D%3D%5Cfrac%7B%285%5Ctimes430%29-%2815%5Ctimes120%29%7D%7B%5Csqrt%7B%5B%285%5Ctimes55%29-15%5E%7B2%7D%5D%5B%285%5Ctimes3450%29-120%5E%7B2%7D%5D%7D%7D%20%3D0.9272)
Thus, the correlation coefficient is 0.9272.