Suppose that vehicles taking a particular freeway exit can turn right (r), turn left (l), or go straight (s). consider observing the direction for each of three successive vehicles. (enter your answers in set notation. enter empty or ∅ for the empty ) list all outcomes in the event a that all three vehicles go in the same direction. a = (b) list all outcomes in the event b that all three vehicles take different directions. b = (c) list all outcomes in the event c that exactly two of the three vehicles turn right. c = (d) list all outcomes in the event d that exactly two vehicles go in the same direction. d = (e) list outcomes in d'.d' = list outcomes in c ∪ d. c ∪ d = list outcomes in c ∩ d. c ∩ d =

16

step-by-step explanation:

2 x 40 = 80

80/5

= 16

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.