Respuesta :
Treating the amounts as Venn sets, we have that 161 students signed up for only Math, considering that 40 did not sign for any.
What are the Venn sets?
For this problem, we consider the following sets:
- Set A: Students that have signed up for Arts.
- Set B: Students that have signed up for Humanities.
- Set C: Students that have signed up for Math.
4 students had signed up for all three courses students, hence:
(A ∩ B ∩ C) = 4.
8 students had signed up for both a Math and Humanities, hence:
(B ∩ C) + (A ∩ B ∩ C) = 8
(B ∩ C) = 8.
18 students had signed up for both a Math and Language Arts, hence:
(A ∩ C) + (A ∩ B ∩ C) = 18
(A ∩ C) = 14.
9 students had signed up for both a Language Arts and Humanities, hence:
(A ∩ B) + (A ∩ B ∩ C) = 9
(A ∩ B) = 5.
36 students had signed up for a Humanities course, hence:
B + (A ∩ B) + (B ∩ C) + (A ∩ B ∩ C) = 36
B + 5 + 8 + 4 = 36
B = 19.
51 students had signed up for a Language Arts course, hence:
A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 36
A + 5 + 14 + 4 = 51
A = 28.
Considering that there are 279 students, and supposing 40 did not sign for any course, we have that:
A + B + C + (A ∩ B) + (B ∩ C) + (A ∩ C) + (A ∩ B ∩ C) + 40 = 279.
28 + 19 + C + 5 + 8 + 14 + 4 + 40 = 279
118 + C = 279
C = 161
161 students signed up for only Math, considering that 40 did not sign for any.
More can be learned about Venn sets at https://brainly.com/question/24388608
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