62.PS-11
Question Help
A researcher asked five of his dentist friends if they thought the new Brand X mouthwash that he
developed was effective. Four responded "yes." The researcher used the results to write a TV
advertisement claiming that "4 out of 5 dentists prefer Brand X mouthwash." Is this a valid inference?
Explain
Use pencil and paper. Explain all of the factors that are necessary for an inference to be valid.
Is the inference valid? Explain. Choose the correct answer below.
A. Yes, because the dentists asked are a representative sample of the population of dentists.
OB. No, because the dentists asked are not a representative sample of the population of dentists.
C. Yes, because 4 dentists said yes out of 5 who were asked.
OD. No, because 4 dentists said yes out of 9 who were asked.

c

step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

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step-by-step explanation:

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answer: the correct answer is -32

step-by-step explanation: