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In order to better decide how to market a new line of clothing, Mary is researching the demographics of the customers of a certain clothing store. She counted the number of customers who visited the store over the course of a month and found out how many of the customers were high school students. Her collected data is in the table below.

[tex]
\[
\begin{tabular}{|c|c|c|c|c|}
\hline
Week & 1 & 2 & 3 & 4 \\
\hline
Customers & 2,848 & 3,141 & 3,861 & 3,911 \\
\hline
Students & 2,033 & 1,937 & 2,076 & 1,721 \\
\hline
\end{tabular}
\]
[/tex]

Mary predicts that the store will see 4,238 customers next week. Approximately how many high school students should the store expect next week?

A. 1,865
B. 2,392
C. 2,446
D. 3,025

Answer :

Sure! Let's go through the steps to determine approximately how many high school students the store should expect next week given the predicted number of customers.

1. Collect Data from Each Week:
- Week 1: 2,848 customers and 2,033 students
- Week 2: 3,141 customers and 1,937 students
- Week 3: 3,861 customers and 2,076 students
- Week 4: 3,911 customers and 1,721 students

2. Calculate Total Customers and Total Students Over Four Weeks:
- Total Customers: [tex]\(2,848 + 3,141 + 3,861 + 3,911 = 13,761\)[/tex]
- Total Students: [tex]\(2,033 + 1,937 + 2,076 + 1,721 = 7,767\)[/tex]

3. Determine the Average Percentage of Customers Who Are Students:
- Average Student Percentage = [tex]\(\frac{\text{Total Students}}{\text{Total Customers}} = \frac{7,767}{13,761}\)[/tex]

4. Convert the Fraction to a Percentage:
- Calculate the fraction: [tex]\(\approx 0.5645\)[/tex]

5. Predicting Students for Next Week:
- Mary predicts 4,238 customers next week.
- Estimated number of high school students next week = [tex]\(0.5645 \times 4,238\)[/tex]

6. Calculate the Expected Number of Students:
- Perform the multiplication: [tex]\( \approx 2,392\)[/tex]

Therefore, approximately 2,392 high school students should be expected to visit the store next week. The correct answer is b. 2,392.

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