Verified answer

Answer:

a.) 29 got medals in music only

b.) 8 got medals in arts only

c.) 14 got medals in sports only

Step-by-step explanation:

3-CIRCLE VENN DIAGRAM ILLUSTRATION:

Given:

• 90 – total number of medals

Total number in each circle:

• 33 – medals in arts

• 45 – medals in sports

• 55 – medals in music

The total number of medals in the overlapping areas shared by two circles:

• 12 – medals in arts and music
• 18 – medals in sports and music
• 17 – medals in arts and sports

Total number in the overlapping areas shared by three circles:

• 4 – medals in arts, music, and sports

Each set is represented by a circle:

- One circle for arts

- One circle for sports

- One circle for music

To illustrate, draw three overlapping circles to explain how the elements of three sets are related.

POPULATING THE AREAS:

1.) The easiest way to start populating the areas is to write the total number of medals shared by three circles, which is 4. (See attached image #1)

2.) Next, we populate the area shared by two circles:

• Since the total number shared by music and arts is 12, we subtract 4 to get the number in the remaining unshaded area.

Formula: (arts and music) – (arts, music, and sports) = (arts and music ONLY)

= 12 – 4 = 8 (arts and music only)

• Next, the total number of medals shared by sports and music is 18. Following the steps earlier, we then again subtract 4.

Formula: (sports and music) – (arts, music, and sports) = (sports and music ONLY)

= 18 – 4 = 14 (sports and music only)

• Another is the overlapping areas shared by arts and sports which has a total number of 17 medals.

Formula: (arts and sports) – (arts, music, and sports) = (arts and sports ONLY)

= 17 – 4 = 13 (arts and sports only)

3.) Lastly, we populate the arts only, sports only, and music only areas.

• How many got medals in music only?

Formula: (Total number of medals in music) – [(arts, music, and sports) + (arts and music only) + (sports and music only)]

= 55 – (4 + 8 + 14)  

= 55 – 26

= 29

Therefore, 29 got medals in music only

• How many got medals in arts only?

Formula: (Total number of medals in arts) – [(arts, music, and sports) + (arts and music only) + (arts and sports only)]

= 33 – (4 + 8 + 13)

= 33 – 25

= 8

Therefore, 8 got medals in arts only

• How many got medals in sports only?

Formula: (Total number of medals in sports) – [(arts, music, and sports) + (sports and music only) + (arts and sports only)

= 45 – (4 + 14 + 13)

= 45 – 31

= 14

Therefore, 14 got medals in sports only.

4.) Adding all the numbers in all the three circles, we’ll get:

14 + 14 + 4 + 13 + 8 + 8 + 29 = 90 medals

Want to learn more? Just click the link below.

• Other operations on sets: brainly.ph/question/3093830

#BRAINLYFAST