Answer:
Each of the three friends will get one-sixth of the Thomas's enitre marble collection.
Step-by-step explanation:
Fraction of the total marble collection brought by Thomas = 
Now, Thomas divides these marbles equally among his three friends. So, each of the three friends will get one-third of the total marble collection brought by Thomas.
Fraction of total marble collection got by each friend = 
= 
∴ Each of the three friends of Thomas will get one-sixth of his entire collection of marbles.
Answer:
a=-5
Step-by-step explanation:
divide both sides by -2: -5=a
a=-5
Answer:
The coordinates of H′ are (-2,0).
Step-by-step explanation:
It is given that square EFGH stretches vertically by a factor of 2.5 with respect to the x-axis to create rectangle E′F′G′H′.
If a figure stretches vertically by a factor of 2.5 with respect to the x-axis, then the x-coordinates remains same and the points which lie on the axis are also remains the same after stretch.
It is given that the coordinates of H are (-2,0). This point lie on the x-axis, therefore it will remains the same after stretch.
Therefore the coordinates of H′ are (-2,0).
Answer:
a) ![r=\frac{4(333)-(200)(5.37)}{\sqrt{[4(12000) -(200)^2][4(9.3501) -(5.37)^2]}}=0.9857](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%28333%29-%28200%29%285.37%29%7D%7B%5Csqrt%7B%5B4%2812000%29%20-%28200%29%5E2%5D%5B4%289.3501%29%20-%285.37%29%5E2%5D%7D%7D%3D0.9857)
The correlation coefficient for this case is very near to 1 so then we can ensure that we have linear correlation between the two variables
b) 
Now we can find the means for x and y like this:
So the line would be given by:
Step-by-step explanation:
Part a
The correlation coeffcient is given by this formula:
![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%28%5Csum%20xy%29-%28%5Csum%20x%29%28%5Csum%20y%29%7D%7B%5Csqrt%7B%5Bn%5Csum%20x%5E2%20-%28%5Csum%20x%29%5E2%5D%5Bn%5Csum%20y%5E2%20-%28%5Csum%20y%29%5E2%5D%7D%7D)
For our case we have this:
n=4 
The correlation coefficient for this case is very near to 1 so then we can ensure that we have linear correlation between the two variables
Part b
Where:
With these we can find the sums:
And the slope would be:
Now we can find the means for x and y like this:
And we can find the intercept using this:
So the line would be given by:
Your final answer will be 2 157/500 for the decimal 2.314
