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?

Explanation:

Step1: Identify relevant regions

We need to find students in Smooth or Rhythm but not Standard. This means we consider the non - overlapping parts of Smooth and Rhythm with Standard and their intersection (excluding the part that also intersects with Standard).

Step2: Calculate the number

The number of students only in Smooth is 11, the number of students only in Rhythm is 15, and the number of students in the intersection of Smooth and Rhythm but not in Standard is 9.
We add these values: $11 + 15+9=35$.

Answer:

35