The two-way frequency table below shows the results taken from a survey of 500 randomly selected
adults aged 25 to 49. they were surveyed on their preference between two brands of pasta sauces. in
another survey of people aged 25-49, a total of 400 people preferred sauce b. based on the data
below, how many of those 400 people would be expected to be age 40-44? !
pasta sauce preference for survey of 500 adults
sauce b
total
age group
25-
29
30-34
35-39
sauce a
39
41
38
43
37
198
101
96
103
106
94
500
55
65
63
57
302
40-44
45-49
total
238
242

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.

5.762159

step-by-step explanation:

it would be 9 because when it is the nine is over five so that would mean it rounds up to 90 or 9

i believe it is the square root of 122 because when you turn it on it's side, to where the 5 inches is on the bottom, it looks like it is the same length.