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Effectus [21]
4 years ago
9

Is every linear relationship a direct variation. Explain please

Mathematics
1 answer:
pychu [463]4 years ago
3 0
Direct variation: y=kx where k is some number thats not 0

that means if x is 2, y is 2k. if x is 1, y is k. if x is 0, y is 0.

notice: no matter what k is, when you put 0 in for x, y will always be 0. that means that a direct variation always goes through the origin, a.k.a. (0,0).

do all lines go through the origin? nah. a line is y=mx+b, where m and b are some numbers. a line is only a direct variation if b is 0. this makes sense because if b is 0, then the y-intercept is 0, so the line goes through the origin.

in conclusion, no, not all linear relationships are direct varations, but all direct variations are linear relationships.
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b) 0.764 (76.4%)

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P(F) = probability that the study was sponsored by food industry * probability that the product is favorable given that it was sponsored + probability that the study had no corporate ties * probability that the product is favorable given that it was not sponsored = 0.70 * 0.68 + 0.30 * 0.49 = 0.623

b) for conditional probability we use the theorem of Bayes , then defining the event S= the study was sponsored by the food industry , we have:

P(S/F)=P(S∩F)/P(F)= 0.70 * 0.68/0.623 = 0.764 (76.4%)

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P(S∩F)=probability that the study was sponsored by food industry and the product was found favorable

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c) for U= the product was found unfavourable , doing the same procedure as in a)

P(U)= 0.70 * 0.10 + 0.30 * 0.35 = 0.175

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