Question

in a local high school, there are 164 seniors. of those seniors, 84 are enrolled in ap english, 72 are enrolled in ap calculus, and 52 are enrolled in both ap english and ap calculus. create a venn diagram to represent this situation and use it to answer the questions below. how many students are taking neither ap english nor ap calculus? students how many students are taking ap english but not ap calculus? 32 students how many students are taking ap english or ap calculus? 104 students

Explanation:

Step1: Calculate the number of students taking AP English or AP Calculus

Use the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Here \(n(A) = 84\) (AP English), \(n(B)=72\) (AP Calculus), \(n(A\cap B) = 52\).
\(n(A\cup B)=84 + 72-52\)
\(n(A\cup B)=104\)

Step2: Calculate the number of students taking neither

Total number of seniors \(N = 164\). Let \(x\) be the number of students taking neither. Then \(x=N - n(A\cup B)\)
\(x=164-104\)

Answer:

\(60\) students