Question

thirty-three cities were researched to determine whether they had a professional sports team, a symphony, or a children’s museum. of these cities, 16 had a professional sports team, 17 had a symphony, 14 had a children’s museum, 10 had a professional sports team and a symphony, 5 had a professional sports team and a children’s museum, 7 had a symphony and a children’s museum, and 3 had all three activities. complete parts a) through e) below. a) how many of the cities surveyed had only a professional sports team? 4 (simplify your answer ) b) how many of the cities surveyed had a professional sports team and a symphony, but not a children’s museum? □ (simplify your answer )

Explanation:

Step1: Identify the number of cities with both sports and symphony, and those with all three.

We know 10 cities have a professional sports team and a symphony, and 3 have all three (sports, symphony, and children's museum).

Step2: Subtract the number of cities with all three from those with sports and symphony.

To find the number of cities with sports and symphony but not children's museum, we calculate \(10 - 3\).
\(10 - 3 = 7\)

Answer:

7