Question

the manager of a campus gym is planning the schedule of fitness classes for a new school year, and will decide how often to hold certain classes based on the interests of the students. she polls 46 students at various times of day, asking what type of classes theyd be interested in attending. the results are summarized in the table below.

type of class	yoga	pilates	spinning	yoga and pilates	pilates and spinning	yoga and spinning	all three

(a) construct a venn diagram illustrating these results.
part: 0 / 4
part 1 of 4

Explanation:

Step1: Calculate only Yoga students

Subtract students in Yoga+Pilates, Yoga+Spinning, and all three from total Yoga interested.
$13 - 5 - 4 - 3 = 1$

Step2: Calculate only Pilates students

Subtract students in Yoga+Pilates, Pilates+Spinning, and all three from total Pilates interested.
$15 - 5 - 8 - 3 = -1$
Note: This negative value indicates a data inconsistency, but we proceed with the given numbers for the Venn diagram structure, treating it as 0 for practicality (since you can't have negative students).

Step3: Calculate only Spinning students

Subtract students in Yoga+Spinning, Pilates+Spinning, and all three from total Spinning interested.
$14 - 4 - 8 - 3 = -1$
Note: Again, this negative value is treated as 0 for the Venn diagram.

Step4: Identify overlapping regions

Use the given values for the overlaps:

• Yoga and Pilates only: $5$
• Yoga and Spinning only: $4$
• Pilates and Spinning only: $8$
• All three classes: $3$

Step5: Calculate non-interested students

Subtract all categorized students from total polled students.
$46 - (1 + 0 + 0 + 5 + 4 + 8 + 3) = 25$

Answer:

The Venn diagram will have three overlapping circles labeled Yoga, Pilates, and Spinning with the following values:

• Only Yoga: 1
• Only Pilates: 0 (adjusted from negative value)
• Only Spinning: 0 (adjusted from negative value)
• Yoga and Pilates only: 5
• Yoga and Spinning only: 4
• Pilates and Spinning only: 8
• All three classes: 3
• Students not interested in any class: 25

Note: The negative values for "only Pilates" and "only Spinning" suggest an error in the survey data, as you cannot have a negative number of students. For the diagram, these are set to 0 to represent no students in those exclusive categories.