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Fill in the Venn Diagram and Answer the Questions.

Fill in the Venn Diagram and Answer the Questions

Answer :

The Venn Diagram is shown at the end of the answer.

Then the amounts are given as follows:

  • History or did not take dance: 1769.
  • History or math, but not dance: 917.
  • Dance and Math, but not history: 343.
  • History, Dance or Math: 2153.
  • None: 248.

How to fill the Venn Diagram?

The Venn Diagram is filled starting at the intervals involving most variables, that is, the intersections.

286 students took all three courses, hence:

V = 286.

629 students were taking history and dance, hence:

VI + V = 629

VI + 286 = 629

VI = 343.

605 students took history and math, hence:

IV + V = 605

IV = 605 - 286

IV = 319.

604 students took dance and math, hence:

II + V = 604

II = 318.

1236 students took dance, hence:

III + II + VI + V = 1236

III + 318 + 343 + 286 = 1236

III = 1236 - (318 + 343 + 286)

III = 289

1295 students took math, hence:

VIII + IV + V + VI = 1295

VIII + 319 + 286 + 343 = 1295

VIII = 1295 - (319 + 286 + 343)

VII = 347

1174 students took history, hence:

I + II + IV + V = 1174

I + 318 + 319 + 286 = 1174

I = 1174 - (318 + 319 + 286)

I = 251

Then the number of students who took at least one of the subjects is of:

251 + 318 + 289 + 319 + 286 + 343 + 347 = 2153.

The number of students who took none of the subjects is of:

2401 - 2153 = 248.

(VIII = 248 on the diagram).

The remaining amounts are then calculated as follows:

  • History or did not take dance: 1174(history) + 347(math) + 248(none) = 1769.
  • History or math, but not dance: I + IV + VII = 251 + 319 + 347 = 917.
  • Dance and Math, but not history: VI = 343.

More can be learned about Venn Diagrams at brainly.com/question/24713052

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