To find the mean of Dave's nightly tips over the past two weeks, we need to follow these steps:
1. List the tips from each day for both weeks:
Week 1:
- Sunday: [tex]$100.85
- Monday: $[/tex]166.57
- Tuesday: [tex]$135.74
- Wednesday: $[/tex]148.12
- Thursday: [tex]$113.94
- Friday: $[/tex]190.13
- Saturday: [tex]$235.31
Week 2:
- Sunday: $[/tex]102.57
- Monday: [tex]$124.02
- Tuesday: $[/tex]142.40
- Wednesday: [tex]$108.60
- Thursday: $[/tex]110.50
- Friday: [tex]$163.82
- Saturday: $[/tex]183.01
2. Combine all tips into a single list to represent the 14 days:
[tex]\[100.85, 166.57, 135.74, 148.12, 113.94, 190.13, 235.31, 102.57, 124.02, 142.40, 108.60, 110.50, 163.82, 183.01 \][/tex]
3. Calculate the total sum of tips:
Add all the tips together:
[tex]\[
100.85 + 166.57 + 135.74 + 148.12 + 113.94 + 190.13 + 235.31 + 102.57 + 124.02 + 142.40 + 108.60 + 110.50 + 163.82 + 183.01 = 2025.08
\][/tex]
4. Count the number of days:
There are 7 days in each week, and since Dave is calculating tips over two weeks:
[tex]\[ 7 \text{ days/week} \times 2 \text{ weeks} = 14 \text{ days} \][/tex]
5. Calculate the mean (average) nightly tips:
Divide the total sum by the number of days:
[tex]\[
\frac{2025.08}{14} \approx 144.68
\][/tex]
6. Round to the nearest cent:
[tex]\[
144.68
\][/tex]
Thus, the mean of Dave's nightly tips over the past two weeks, rounded to the nearest cent, is [tex]\(\$144.68\)[/tex].
Therefore, the correct answer is:
b. [tex]\(\$144.68\)[/tex]
