Question

a survey was conducted at a local ballroom dance studio asking students if they had ever competed in the following dance categories: smooth rhythm standard the results were then presented to the owner in the following venn diagram. how many students competed in smooth or rhythm, but not standard? how many students did not compete in rhythm?

Explanation:

Step1: Find students in Smooth or Rhythm but not Standard

Add the numbers in Smooth only ($10$), Rhythm only ($13$), and Smooth - Rhythm intersection ($9$).
$10 + 13+9$

Step2: Calculate the sum

$10+13 + 9=32$

Step3: Find students who did not compete in Rhythm

Sum all non - Rhythm regions: Smooth only ($10$), Standard only ($4$), Smooth - Standard ($11$), and the outside region ($15$).
$10+4 + 11+15$

Step4: Calculate the sum

$10+4+11 + 15=40$

Answer:

For the first question: $32$
For the second question: $40$