Question

for parts (a) and (b) below, choose the correct description. fill in the blanks as necessary. (a) customers of a certain credit card earn points for using the card. the table below shows the number of points earned for the amount spent. number of points 27 36 81 dollars spent 3 4 9 choose the correct description. ○ each dollar spent does not always earn the same number of points. ○ each dollar spent appears to earn the same number of points. predicted number of points for spending $10: (b) a local store is keeping track of service times. the table below shows the number of customers served and the time it took. number of customers 2 3 8 time (in minutes) 6 9 24 choose the correct description. ○ it does not always take the same amount of time to serve each customer ○ it appears to take the same amount of time to serve each customer. predicted number of customers served in 27 minutes:

Explanation:

Part (a)

Step1: Check points per dollar

For the first pair: \( \frac{27}{3} = 9 \) points per dollar.
For the second pair: \( \frac{36}{4} = 9 \) points per dollar.
For the third pair: \( \frac{81}{9} = 9 \) points per dollar.
So each dollar earns the same points.

Step2: Predict for $10

Points = \( 9 \times 10 = 90 \).

Step1: Check time per customer

For the first pair: \( \frac{6}{2} = 3 \) minutes per customer.
For the second pair: \( \frac{9}{3} = 3 \) minutes per customer.
For the third pair: \( \frac{24}{8} = 3 \) minutes per customer.
So each customer takes the same time.

Step2: Predict for 27 minutes

Customers = \( \frac{27}{3} = 9 \).

Answer:

Each dollar spent appears to earn the same number of points.
Predicted number of points for spending $10: \( 90 \)

Part (b)