A rational number is a number that can be written into a fraction. pi, some square roots, e, etc., are irrational numbers(numbers that cannot be written into a fraction).

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A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the manager's sales representa

Aleksandr [31]

Answer:

$y=3.529 x +37.91$

We can predict the sales representative travelled 8 miles replacing x =8 and we got:

$y(8) = 3.529*8 + 37.91= 66.142$

And we can predict the sales representative travelled 11 miles replacing x =11 and we got:

$y(11) = 3.529*11 + 37.91= 76.729$

Step-by-step explanation:

For this case we have the following data:

Miles Traveled x: 2,3,10,7,8,15,3,1,11

Sales y :31,33,78,62,65,61,48,55,120

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i =60$

$\sum_{i=1}^n y_i =553$

$\sum_{i=1}^n x^2_i =582$

$\sum_{i=1}^n y^2_i =39653$

$\sum_{i=1}^n x_i y_i =4329$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=582-\frac{60^2}{9}=182$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=4329-\frac{60*553}{9}=642.33$

And the slope would be:

$m=\frac{642.33}{182}=3.529$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{60}{9}=6.67$

$\bar y= \frac{\sum y_i}{n}=\frac{553}{9}=61.44$

And we can find the intercept using this:

$b=\bar y -m \bar x=61.44-(3.529*6.67)=37.91$

So the line would be given by: