Asurvey is taken among customers of a fast-food restaurant to determine preference for hamburger or chicken. of 200 respondents selected, 75 were children and 125 were adults. 120 preferred hamburger and 80 preferred chickens. 55 of the children preferred hamburger and 20 preferred chickens. set up a 2x2 contingency table using this information and answer the following questions: foodage hamburger chicken totalchild 55 20 75adult 65 60 125total 120 80 200a) what is the probability that a randomly selected individual is an adult? b) what is the probability that a randomly selected individual is a child and prefers chicken? c) given the person is a child, what is the probability that this child prefers a hamburger? d) assume we know that a person has ordered chicken, what is the probability that this individual is an adult?

                          Hamburger       Chicken

Adults                    65                        60         125

children                 55                        20          75

                             120                        80         200

a)What is the probability that a randomly selected individual is an adult?

Total no. of adults = 125

Total no. of people  200

The probability that a randomly selected individual is an adult =

b) What is the probability that a randomly selected individual is a child and prefers chicken?

No. of child prefers chicken = 20

The probability that a randomly selected individual is a child and prefers chicken=

c)Given the person is a child, what is the probability that this child prefers a hamburger?

No. of children prefer hamburger = 55

No. of child = 75

The probability that this child prefers a hamburger=

d) Assume we know that a person has ordered chicken, what is the probability that this individual is an adult?

No. of adults prefer chicken = 60

No. of total people like chicken = 80

A person has ordered chicken, the probability that this individual is an adult=

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: