Respuesta :
Using Venn sets, it is found that 30 athletes own none of the items.
What is the missing information?
The missing information is the question, which asks how many athletes own none of the items.
What are the Venn Sets?
For this problem, we consider the following sets:
- Set A: athletes that have a convertible.
- Set B: athletes that have a giant screen TV.
- Set C: athletes that owned a sporting goods store.
10 owned all three items, hence:
(A ∩ B ∩ C) = 10.
57 owned a convertible and a TV, hence:
(A ∩ B) + (A ∩ B ∩ C) = 57.
(A ∩ B) = 47.
50 owned a TV and a store, hence:
(B ∩ C) + (A ∩ B ∩ C) = 50
(B ∩ C) = 40.
29 owned a convertible and a store, hence:
(A ∩ C) + (A ∩ B ∩ C) = 29.
(A ∩ C) = 19.
136 owned a sporting goods store, hence:
C + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 136
C + 19 + 40 + 10 = 136
C = 67.
117 of them owned a giant screen TV, hence:
B + (A ∩ B) + (B ∩ C) + (A ∩ B ∩ C) = 117
B + 47 + 40 + 10 = 117
B = 20.
135 of them owned a convertible, hence:
A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 135
A + 47 + 19 + 10 = 135
A = 59.
There were 292 athletes on the survey, hence the number who owned none is given as follows:
None + A + B + C + (A ∩ B) + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 292
None + 59 + 20 + 67 + 47 + 19 + 40 + 10 = 292
None + 262 = 292
None = 30.
30 athletes own none of the items.
More can be learned about Venn sets at brainly.com/question/24388608
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