Answer:
r = 0.9825; good correlation.
Step-by-step explanation:
One formula for the correlation coefficient is
![r = \dfrac{n\sum{xy} - \sum{x} \sum{y}}{\sqrt{n\left [\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [\sum{y}^{2}-\left (\sum{y}\right )^{2}\right]}}](https://tex.z-dn.net/?f=r%20%3D%20%5Cdfrac%7Bn%5Csum%7Bxy%7D%20-%20%5Csum%7Bx%7D%20%5Csum%7By%7D%7D%7B%5Csqrt%7Bn%5Cleft%20%5B%5Csum%7Bx%7D%5E%7B2%7D-%5Cleft%20%28%5Csum%7Bx%7D%5Cright%20%29%5E%7B2%7D%5Cright%5D%5Cleft%20%5B%5Csum%7By%7D%5E%7B2%7D-%5Cleft%20%28%5Csum%7By%7D%5Cright%20%29%5E%7B2%7D%5Cright%5D%7D%7D)
The calculation is not difficult, but it is tedious.
1. Calculate the intermediate numbers
We can display them in a table.
<u> </u><u>x</u> <u> y </u> <u> xy </u> <u> x² </u> <u> y² </u>
-3 -40 120 9 1600
1 12 12 1 144
5 72 360 25 5184
<u> 7</u> <u>137</u> <u> 959</u> <u>49</u> <u>18769
</u>
Σ = 10 181 1451 84 25697
2. Calculate the correlation coefficient
![r = \dfrac{n\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2}-\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{4\times 1451 - 10\times 181}{\sqrt{[4\times 84 - 10^{2}][4\times25697 - 181^{2}]}}\\\\= \dfrac{5804 - 1810}{\sqrt{[336 - 100][102788 - 32761]}}\\\\= \dfrac{3994}{\sqrt{236\times70027}}\\\\= \dfrac{3994}{\sqrt{16526372}}\\\\= \dfrac{3994}{4065}\\\\= \mathbf{0.9825}](https://tex.z-dn.net/?f=r%20%3D%20%5Cdfrac%7Bn%5Csum%7Bxy%7D%20-%20%5Csum%7Bx%7D%20%5Csum%7By%7D%7D%7B%5Csqrt%7B%5Cleft%20%5Bn%5Csum%7Bx%7D%5E%7B2%7D-%5Cleft%20%28%5Csum%7Bx%7D%5Cright%20%29%5E%7B2%7D%5Cright%5D%5Cleft%20%5Bn%5Csum%7By%7D%5E%7B2%7D-%5Cleft%20%28%5Csum%7By%7D%5Cright%20%29%5E%7B2%7D%5Cright%5D%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B4%5Ctimes%201451%20-%2010%5Ctimes%20181%7D%7B%5Csqrt%7B%5B4%5Ctimes%2084%20-%2010%5E%7B2%7D%5D%5B4%5Ctimes25697%20-%20181%5E%7B2%7D%5D%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B5804%20-%201810%7D%7B%5Csqrt%7B%5B336%20-%20100%5D%5B102788%20-%2032761%5D%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B3994%7D%7B%5Csqrt%7B236%5Ctimes70027%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B3994%7D%7B%5Csqrt%7B16526372%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B3994%7D%7B4065%7D%5C%5C%5C%5C%3D%20%5Cmathbf%7B0.9825%7D)
The closer the value of r is to +1 or -1, the better the correlation is. The values of x and y are highly correlated.
If there are no notebooks purchased, then Eula may buy 5 binders. If no binders are bought, then Eula may buy 10 notebooks. If 7 notebooks are purchased, then one binder may be purchased; this will also cause Eula to have $2 extra (maybe for tax).
Answer:
the speed btn sonya and issac would make a right angled trangle hence easy 2 solve through pythogoras
then find the
![\sqrt[?]{?}](https://tex.z-dn.net/?f=%20%5Csqrt%5B%3F%5D%7B%3F%7D%20)
hence get 45
since it was 12 mins we need 2 multiply by 12
hence
Therefore it's 540mph
Given :
Liam has a bag of b beads.
He gives 20 beads to his sister.
He then makes 4 necklaces with the same of beads on each necklace using all of the remaining beads.
To Find :
Write an expression that represents the number of beads on each necklace.
Solution :
Number of necklace remains after giving 20 beads to his sister is ( b - 20 ).
Number of beads on each necklace using all of the remaining beads is :
Hence, this is the required solution.
