Question

a survey was conducted at a local ballroom dance studio asking students what dances they competed in at the most recent competition. below are the results for the dances swing, mambo, and paso doble: use the venn diagram to answer the questions below. a) how many students competed in swing or paso doble? b) how many students competed in swing? c) how many students did not compete in paso doble? d) how many students competed in mambo and paso doble? e) how many students competed in none of these three dances?

Explanation:

Step1: Find students in Swing OR Paso Doble

Add all sections in Swing and Paso Doble: \(8 + 12+5 + 14+9+10\)
$$8 + 12+5 + 14+9+10=58$$

Step2: Find students in Swing

Add all sections in Swing: \(8 + 12+5 + 9\)
$$8 + 12+5 + 9=34$$

Step3: Find students NOT in Paso Doble

Total students: \(8 + 12+11+5 + 9+10+14+6=75\)
Students in Paso Doble: \(5 + 9+10+14 = 38\)
Subtract: \(75-38\)
$$75 - 38=37$$

Step4: Find students in Mambo AND Paso Doble

Intersection of Mambo and Paso Doble: \(10 + 9\)
$$10 + 9=19$$

Step5: Find students in none of three dances

Value outside all circles: \(6\)

Answer:

a) \(58\)
b) \(34\)
c) \(37\)
d) \(19\)
e) \(6\)