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zach099
13.01.2020 •
Mathematics
Of 450 people interviewed, 135 contributed to red house, 180 contributed to blue house, and 180 contributed to yellow house. 27 contributed to red and yellow. 54 contributed to yellow and blue. 45 contributed to red and blue. 63 of the people interviewed contributed to none of the houses. how many contributed to all three houses?
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Ответ:
The number of people who contributed to all three houses is 18.
Step-by-step explanation:
Total number of people interviewed = 450
Number of people who contributed to red house = n(R) = 135
Number of people who contributed to Blue house = n(B) = 180
Number of people who contributed to Yellow house = n(Y) = 180
Also, according to question:
n(R ∩ Y) = 27, n(B ∩ Y) = 54 and n(B ∩ R) = 45
63 people contributed to NONE = 63
So, number of people who contribute at least to any 1 house
= Total people - 63 = 450 - 63 = 387
⇒ n(R ∪ B ∪ Y) = 387
Using : n(R ∪ B ∪ Y) = n(R) + n(B) + n(Y) - n(R ∩ Y) -n(B ∩ Y) - n(B ∩ R) + n(B ∩ R∩Y)
⇒ 387 = 135 + 180 + 180 - 27 - 54 - 45 + n(B ∩ R∩Y)
or, n(B ∩ R∩Y) = 387 - 495 + 126 = 18
or, n(B ∩ R∩Y) = 18
Hence, the number of people who contributed to all three houses is 18.
Ответ:
B
Step-by-step explanation:
We can substitute the x value given, -3, into our equation, y = x^2, to get what the y would be:
y = x^2
y = (-3)^2
When a negative number is squared, it is positive, so (-3)^2 = 9, and:
y = 9
This is option b