An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate the percentage of high school students who chose movies/TV: 40% − 22% − 6% = 12% .
Calculate the percentage of college students who chose dancing: 38% − 6% = 32% .
Calculate the percentage of students who chose sports: 22% + 10% = 32% .
Calculate the percentage of students who chose movies/TV: 12% + 18% = 30% . The table is correct.
Explanation
Analyze the problem and data We are given a two-way relative frequency table and need to verify if it correctly represents the data from a survey of 50 students. The survey asked high school and college students about their favorite free-time activity: sports, dancing, or movies/TV. We have information about the percentages of students in each category.
Verify row totals First, let's check the row totals. We are given that 40% of the students are high school students, and 60% are college students. The table reflects this, so the row totals are correct.
Verify column totals Next, let's check the column totals. The table states that 32% chose sports, 38% chose dancing, and 30% chose movies/TV. We need to verify if these percentages are consistent with the given data.
List given percentages We are given:
22% are high school students who chose sports.
6% are high school students who chose dancing.
10% are college students who chose sports.
18% are college students who chose movies/TV.
38% of all students chose dancing.
Calculate percentage of high school students who chose movies/TV Let's calculate the percentage of high school students who chose movies/TV. Since 40% of the students are high school students, and 22% chose sports and 6% chose dancing, the remaining high school students must have chosen movies/TV: 40% − 22% − 6% = 12% So, 12% of the students are high school students who chose movies/TV.
Calculate percentage of college students who chose dancing Now, let's calculate the percentage of college students who chose dancing. Since 38% of all students chose dancing, and 6% are high school students who chose dancing, the remaining students who chose dancing must be college students: 38% − 6% = 32% So, 32% of the students are college students who chose dancing.
Calculate percentage of students who chose sports Let's calculate the percentage of students who chose sports. We know that 22% are high school students and 10% are college students who chose sports. Therefore, the total percentage of students who chose sports is: 22% + 10% = 32% This matches the column total in the table.
Calculate percentage of students who chose movies/TV Let's calculate the percentage of students who chose movies/TV. We know that 12% are high school students and 18% are college students who chose movies/TV. Therefore, the total percentage of students who chose movies/TV is: 12% + 18% = 30% This matches the column total in the table.
Verify all percentages Now, let's verify the percentages in the table:
High school students:
Sports: 22%
Dancing: 6%
Movies/TV: 12%
Total: 40%
College students:
Sports: 10%
Dancing: 32%
Movies/TV: 18%
Total: 60%
Column totals:
Sports: 32%
Dancing: 38%
Movies/TV: 30%
Total: 100%
All the values match the given information and our calculations.
Conclusion Therefore, the provided two-way relative frequency table is correct.
Examples
Two-way relative frequency tables are useful in market research to understand customer preferences across different demographics. For example, a company might survey customers to find out their favorite product categories (e.g., clothing, electronics, home goods) and their age groups (e.g., 18-25, 26-35, 36-45). The resulting table can help the company tailor its marketing strategies and product offerings to specific customer segments.
The total charge flowing through the device is 450 Coulombs, which is approximately equal to 2.81 × 1 0 21 electrons flowing through it in 30 seconds at a current of 15.0 A.
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