Question

corey and dione both love to practice soccer in their backyards. let c represent the number of goals corey made in a week, and let d represent the number of goals dione made in a week. the mean of the total amount, s = c + d, of goals made in a typical week is 138. what is the correct interpretation of this value?
on average, dione makes 138 goals per week.
corey makes 138 more goals per week than dione.
on average, corey and dione make 138 goals in a typical week.
if two weeks are randomly chosen, the sum of the number of goals made by corey and dione will be 138.

Explanation:

1. Analyze the first option: The mean of \( S = C + D \) is 138, not the mean of \( D \) (Dione's goals). So this option is wrong.
2. Analyze the second option: The mean of the sum \( C + D \) being 138 does not imply Corey makes 138 more goals than Dione. There's no information about the difference here. So this option is wrong.
3. Analyze the third option: Since \( S = C + D \) represents the total goals of Corey and Dione in a week, and the mean of \( S \) is 138, it means on average, the total goals (Corey + Dione) in a typical week is 138. This matches the interpretation.
4. Analyze the fourth option: The mean is an average over many weeks, not a guarantee for two randomly chosen weeks. So this option is wrong.

Answer:

On average, Corey and Dione make 138 goals in a typical week.