Question

question 12 (1 point) school the venn diagram shows the number of students in the band who work after school or on weekends. how many students work after school or on weekends? a 22 b 17 c 25 d 3 question 13 (1 point) determine whether each conjecture is true or false. give a counterexample for any false conjecture. if s, t, and u are collinear and st = tu, then t is the mid - point of su.

Explanation:

Step1: Recall the formula for the union of two - sets in a Venn - diagram

For two sets \(A\) and \(B\), \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Here, let \(A\) be the set of students who work after school and \(B\) be the set of students who work on weekends.

Step2: Identify the values from the Venn - diagram

We have \(n(A) = 5 + 3=8\) (students who work after school), \(n(B)=17 + 3 = 20\) (students who work on weekends), and \(n(A\cap B)=3\) (students who work both after school and on weekends).

Step3: Calculate \(n(A\cup B)\)

Using the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\), we substitute the values: \(n(A\cup B)=(5 + 3)+(17 + 3)-3\). First, \(5+3 = 8\), \(17 + 3=20\), then \(8+20 - 3=25\).

Answer:

25