Question

in a medium - sized city, the chamber of commerce often holds fundraisers. it has been studying the attendance at its events based upon the number of hundreds of flyers distributed. it has found that the line of best - fit is represented by event attendance = 2,400 + 67(hundred flyers). find and interpret the residual for the attendance if the chamber hands out 5,700 flyers and has 7,000 people attend the fundraiser. the residual is \square. (type an integer or a decimal.)

Explanation:

Step1: Identify the number of hundred flyers

The number of flyers is 5,700, so the number of hundred flyers is \( \frac{5700}{100} = 57 \).

Step2: Calculate the predicted attendance

Using the line of best - fit equation \( \text{event attendance}=2400 + 67(\text{hundred flyers}) \), substitute the number of hundred flyers (57) into the equation:
\( \text{Predicted attendance}=2400+67\times57 \)
First, calculate \( 67\times57 = 67\times(50 + 7)=67\times50+67\times7 = 3350+469 = 3819 \)
Then, \( 2400 + 3819=6219 \)

Step3: Calculate the residual

The residual is calculated as the actual value minus the predicted value. The actual attendance is 7000, and the predicted attendance is 6219.
So, \( \text{Residual}=7000 - 6219=781 \)

Answer:

781