To find the missing tip earnings, we first need to calculate the total amount of tips Yasmine earned over the 8 nights, given that her mean earnings were $46.
The mean (average) is calculated by dividing the total earnings by the number of nights (8). Therefore, we can set up the equation:
\[ \text{Total Tips} = \text{Mean} \times \text{Number of Nights} = 46 \times 8 = 368 \]
Now, we can sum the known tip earnings:
- $35.80
- $79.60
- $38.10
- $20.50
- $10.45
- $96.78
- $45.90
Adding these amounts together:
\[ 35.80 + 79.60 + 38.10 + 20.50 + 10.45 + 96.78 + 45.90 = 326.13 \]
Now, to find the missing tip amount, we will subtract the sum of the known tips from the total required tips:
\[ \text{Missing Tip} = \text{Total Tips} - \text{Sum of Known Tips} \] \[ \text{Missing Tip} = 368 - 326.13 = 41.87 \]
Thus, the value of the missing tip earnings is $41.87.