In a survey one-forth like cake only and 20 didn't like cake at all. Also 50% children like ice cream but 12 like none of them. How many like both?

2

Step-by-step explanation:

Let x represent the total number of people. Let C represent those that like cake and let I represent those that like ice cream. Given:

C = (1/4)x = 0.25x, I = 0.5x, (C ∪ I)' = 12, C' = 20

Therefore:

C ∩ I' = C' - (C ∪ I)' = 20 - 12 = 8

C ∩ I = C - C ∩ I' = 0.25x - 8

C' ∩ I = I - C ∩ I = 0.5x - (0.25x - 8) = 0.25x + 8

The total students = (C ∩ I) + (C' ∩ I) + (C ∩ I') + (C ∪ I)'

x = 0.25x - 8 + 0.25x + 8 + 8 + 12

x = 0.5x + 8 + 12

x = 0.5x + 20

0.5x = 20

x = 40

Students that liked both = C ∩ I = 0.25(40) - 8 = 2

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.

7

step-by-step explanation: