The mean number of hours that Raphael worked over the past four weeks is 35.75 . If he works 41 hours this week, what will the mean number of hours be that he will have worked over the five-week period? What is the five-week mean? \( \square \) (Simplify your answer.)

To find the mean number of hours Raphael will have worked over the five-week period, we first need to calculate the total number of hours he worked over the first four weeks and then add the hours he worked this week. 1. **Calculate the total hours worked over the first four weeks:** \[ \text{Mean hours for 4 weeks} = 35.75 \] \[ \text{Total hours for 4 weeks} = \text{Mean} \times \text{Number of weeks} = 35.75 \times 4 = 143 \] 2. **Add the hours worked this week:** \[ \text{Hours worked this week} = 41 \] \[ \text{Total hours for 5 weeks} = 143 + 41 = 184 \] 3. **Calculate the mean for the five-week period:** \[ \text{Mean hours for 5 weeks} = \frac{\text{Total hours for 5 weeks}}{\text{Number of weeks}} = \frac{184}{5} = 36.8 \] Thus, the mean number of hours Raphael will have worked over the five-week period is \( \boxed{36.8} \).