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Sagot :
To calculate the pay for the given day of a weekly time card, we will follow a detailed, step-by-step process.
### Step 1: Identify the hourly wage
The hourly wage is [tex]\(\$11\)[/tex] per hour.
### Step 2: Calculate the hours worked in the morning
The morning shift is from [tex]\(8:15\)[/tex] AM to [tex]\(12:15\)[/tex] PM.
- Start time (morning in): [tex]\(8\)[/tex] hours and [tex]\(15\)[/tex] minutes
- End time (morning out): [tex]\(12\)[/tex] hours and [tex]\(15\)[/tex] minutes
We calculate the total hours worked in the morning by taking the difference between the end time and start time.
1. Subtract the start hour from the end hour:
[tex]\[ 12 \, \text{hours} - 8 \, \text{hours} = 4 \, \text{hours} \][/tex]
2. Since both times are exactly 15 minutes past the hour, the minutes difference is:
[tex]\[ 15 \, \text{minutes} - 15 \, \text{minutes} = 0 \, \text{minutes} \][/tex]
Thus, the total hours worked in the morning is:
[tex]\[ 4 \, \text{hours} + \frac{0 \, \text{minutes}}{60} = 4.0 \, \text{hours} \][/tex]
### Step 3: Calculate the hours worked in the afternoon
The afternoon shift is from [tex]\(13:15\)[/tex] PM to [tex]\(17:30\)[/tex] PM.
- Start time (afternoon in): [tex]\(13\)[/tex] hours and [tex]\(15\)[/tex] minutes
- End time (afternoon out): [tex]\(17\)[/tex] hours and [tex]\(30\)[/tex] minutes
We calculate the total hours worked in the afternoon by taking the difference between the end time and start time.
1. Subtract the start hour from the end hour:
[tex]\[ 17 \, \text{hours} - 13 \, \text{hours} = 4 \, \text{hours} \][/tex]
2. Calculate the difference in minutes:
[tex]\[ 30 \, \text{minutes} - 15 \, \text{minutes} = 15 \, \text{minutes} \][/tex]
Thus, the total hours worked in the afternoon is:
[tex]\[ 4 \, \text{hours} + \frac{15 \, \text{minutes}}{60} = 4 \frac{15}{60} = 4.25 \, \text{hours} \][/tex]
### Step 4: Calculate the total hours worked
Add the hours worked in the morning and the afternoon to find the total hours worked:
[tex]\[ 4.0 \, \text{hours} + 4.25 \, \text{hours} = 8.25 \, \text{hours} \][/tex]
### Step 5: Calculate the total pay
Multiply the total hours worked by the hourly wage to find the total pay:
[tex]\[ 8.25 \, \text{hours} \times 11 \, \text{dollars/hour} = 90.75 \, \text{dollars} \][/tex]
### Conclusion
The total pay for the given day, rounded to the nearest cent, is:
[tex]\[ \boxed{90.75 \, \text{dollars}} \][/tex]
### Step 1: Identify the hourly wage
The hourly wage is [tex]\(\$11\)[/tex] per hour.
### Step 2: Calculate the hours worked in the morning
The morning shift is from [tex]\(8:15\)[/tex] AM to [tex]\(12:15\)[/tex] PM.
- Start time (morning in): [tex]\(8\)[/tex] hours and [tex]\(15\)[/tex] minutes
- End time (morning out): [tex]\(12\)[/tex] hours and [tex]\(15\)[/tex] minutes
We calculate the total hours worked in the morning by taking the difference between the end time and start time.
1. Subtract the start hour from the end hour:
[tex]\[ 12 \, \text{hours} - 8 \, \text{hours} = 4 \, \text{hours} \][/tex]
2. Since both times are exactly 15 minutes past the hour, the minutes difference is:
[tex]\[ 15 \, \text{minutes} - 15 \, \text{minutes} = 0 \, \text{minutes} \][/tex]
Thus, the total hours worked in the morning is:
[tex]\[ 4 \, \text{hours} + \frac{0 \, \text{minutes}}{60} = 4.0 \, \text{hours} \][/tex]
### Step 3: Calculate the hours worked in the afternoon
The afternoon shift is from [tex]\(13:15\)[/tex] PM to [tex]\(17:30\)[/tex] PM.
- Start time (afternoon in): [tex]\(13\)[/tex] hours and [tex]\(15\)[/tex] minutes
- End time (afternoon out): [tex]\(17\)[/tex] hours and [tex]\(30\)[/tex] minutes
We calculate the total hours worked in the afternoon by taking the difference between the end time and start time.
1. Subtract the start hour from the end hour:
[tex]\[ 17 \, \text{hours} - 13 \, \text{hours} = 4 \, \text{hours} \][/tex]
2. Calculate the difference in minutes:
[tex]\[ 30 \, \text{minutes} - 15 \, \text{minutes} = 15 \, \text{minutes} \][/tex]
Thus, the total hours worked in the afternoon is:
[tex]\[ 4 \, \text{hours} + \frac{15 \, \text{minutes}}{60} = 4 \frac{15}{60} = 4.25 \, \text{hours} \][/tex]
### Step 4: Calculate the total hours worked
Add the hours worked in the morning and the afternoon to find the total hours worked:
[tex]\[ 4.0 \, \text{hours} + 4.25 \, \text{hours} = 8.25 \, \text{hours} \][/tex]
### Step 5: Calculate the total pay
Multiply the total hours worked by the hourly wage to find the total pay:
[tex]\[ 8.25 \, \text{hours} \times 11 \, \text{dollars/hour} = 90.75 \, \text{dollars} \][/tex]
### Conclusion
The total pay for the given day, rounded to the nearest cent, is:
[tex]\[ \boxed{90.75 \, \text{dollars}} \][/tex]
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