Question

15. The number of snowboarders + skiers at a resort per day and the amount of new snow the resort reportedthat morning are shown in the table. Graph the paired data below for the five days listed, and then draw anddetermine the equation of the line of best fit through the data. (1/2 point)Amount of NewSnow (in inches) (x)Number ofSnowsliders (y)2+Equation for Line of Best Fit:468101146 1556 1976 2395 2490Number of Snowsliders25002000150010005000ty14 8 12New Snow (in.)16. If the resort reports 15 inches of new snow, how many skiers and snowboarders would you expect to be atthe resort that day? You should use your equation from the previous problem. (1/2 point)

Answer 1

To determine the equation of theline of best fit, we will be needing a few things. First, we need to calculate the average (mean) of the x-values.

To find the mean, we simply add all of the x-values, then divide it by the number of addends.

The mean x-value is 6, calculated as follows:

`(2+4+6+8+10)/(5)=6`

Then, we also do the same for the y-values; wee look for the mean.

`(1146+1556+1976+2395+2490)/(5)=1912.6`

The mean y-value is 1,912.6.

We will use theses means t osolve for the slope m using the equation:

`m=\frac{\sum_{i\mathop{=}1}^n(x_i-\bar{x})(y_i-\bar{y})}{\sum_{i\mathop{=}1}^n(x_i-\bar{x})^2}`

So m = 176.35.

Finally, we solve for b using the equation:

`b=\bar{y}-m\bar{x}`
`\begin{gathered} b=1912.6-176.35(6) \\ b=854.5 \end{gathered}`

So b = 854.5.

Now we can write the full equation of the best-fit line:

y = 176.35x + 854.5

If the resort reports 15 inches of new snow, then we use x = 15 to solve for y using the equation of the best-fit line to approximate the number of snowsliders.

`\begin{gathered} y=176.35x+854.5 \\ y=176.35(15)+854.5 \\ y=3499.75 \end{gathered}`

We round off this value to 3,500 since we are looking for number of people.

The answer is 3,500.