Problem

A poll asked respondents if they agreed with the statement that colleges should reserve a certain number of scholarships exclusively for minorities and those age $\geq 20$. Hypothetical results of the poll are tabulated in the Venn diagram. How many people who are not African American agreed with the statement?

The number of people who are not African American that agreed with the statement is

Answer

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Answer

Final Answer: The number of people who are not African American that agreed with the statement is \(\boxed{50}\).

Steps

Step 1 :The question is asking for the number of people who agreed with the statement and are not African American. From the Venn diagram, we can see that the total number of people who agreed with the statement is the sum of the number of African Americans who agreed, the number of non-African Americans who agreed, and the number of people who are both African American and agreed with the statement. To find the number of non-African Americans who agreed, we subtract the number of African Americans who agreed and the number of people who are both from the total.

Step 2 :Let's denote the total number of people who agreed as \(total\_agreed\), the number of African Americans who agreed as \(african\_american\_agreed\), the number of people who are both African American and agreed with the statement as \(both\_agreed\), and the number of non-African Americans who agreed as \(non\_african\_american\_agreed\).

Step 3 :From the problem, we know that \(total\_agreed = 100\), \(african\_american\_agreed = 30\), and \(both\_agreed = 20\).

Step 4 :We can find \(non\_african\_american\_agreed\) by subtracting \(african\_american\_agreed\) and \(both\_agreed\) from \(total\_agreed\), which gives us \(non\_african\_american\_agreed = total\_agreed - african\_american\_agreed - both\_agreed\).

Step 5 :Substituting the given values into the equation, we get \(non\_african\_american\_agreed = 100 - 30 - 20 = 50\).

Step 6 :Final Answer: The number of people who are not African American that agreed with the statement is \(\boxed{50}\).

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