Students from School A and School B were asked whether they watch TV or use the Internet after finishing their homework. The Venn diagram and the two-way table show the results from the two surveys. Which statement is true?
A. More students do both activities at A than at B.
B. More students watch TV at B than at A.
C. More students do neither activity at $B$ than at $A$.
D. More students were surveyed at A than at B.
Answer (2)
Without the Venn diagram for School A, it's impossible to definitively determine which statement is true. Each statement can be expressed as an inequality involving the number of students in School A who engage in each activity. We need more information to solve this problem.
Explanation
Analyze the problem We are given a two-way table for School B showing the number of students who watch TV and/or use the Internet. We need to compare this data with data from School A, which is represented by a Venn diagram (not provided). The goal is to determine which of the given statements is true.
Analyze School B data Let's analyze the data from School B:
Students who do both (watch TV and use the Internet): 30
Students who watch TV but not the Internet: 5
Students who use the Internet but not watch TV: 11
Students who do neither: 4
Total students surveyed: 50
Represent School A data with variables Now let's represent the corresponding data for School A with variables:
Let a be the number of students at School A who do both activities.
Let b be the number of students at School A who watch TV only.
Let c be the number of students at School A who use the Internet only.
Let d be the number of students at School A who do neither activity.
The total number of students surveyed at School A is a + b + c + d .
Express statements as inequalities Now we will examine each statement and determine the condition under which it would be true:
More students do both activities at A than at B: 30"> a > 30
More students watch TV at B than at A: a + b"> 35 > a + b
More students do neither activity at B than at A: d"> 4 > d
More students were surveyed at A than at B: 50"> a + b + c + d > 50
Conclusion Since we don't have the Venn diagram for School A, we cannot determine the values of a , b , c , and d . Therefore, we cannot definitively say which statement is true. However, let's consider each statement individually and see if we can deduce anything.
Without additional information, we cannot determine which statement is true.
Examples
Consider a scenario where you're comparing the preferences of two groups of people (School A and School B) regarding their after-school activities (watching TV and using the Internet). The two-way table and Venn diagram help organize the data, and by comparing the numbers, you can identify trends and differences in their preferences. For example, you might find that a larger proportion of students in School A prefer using the Internet compared to School B.
Due to the absence of the Venn diagram for School A, we cannot determine which of the statements (A, B, C, or D) is true. Each statement requires specific data comparisons that we do not have. Therefore, more information is needed to provide a definite answer.
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