An alarming number of U. S. adults are either overweight or obese. The distinction between overweight and obese is made on the basis of body mass index (BMI), expressed as weight/height2. An adult is considered overweight if the BMI is 25 or more but less than 30. An obese adult will have a BMI of 30 or greater. According to a January 2012 article in the Journal of the American Medical Association, 33.1% of the adult population in the United States is overweight and 35.7% is obese. Use this information to answer the following questions.

a.
What is the probability that a randomly selected adult is either overweight or obese? (Round your answer to 3 decimal places.)

Probability

b.
What is the probability that a randomly selected adult is neither overweight nor obese? (Round your answer to 3 decimal places.)

Probability

(a) The probability that a randomly selected adult is either overweight or obese is 0.569.

(b) The probability that a randomly selected adult is neither overweight nor obese is 0.431.

Step-by-step explanation:

Let A = a person is over weight and B = a person is obese.

The information provided is:

An adult is considered overweight if the BMI ≥ 25 but BMI < 30.

An obese adult will have a BMI ≥ 30.

According to the range of BMI the events A and B are independent.

P (A) = 0.331 and P (B) = 0.357.

(a)

Compute the probability that a randomly selected adult is either overweight or obese as follows:

P (A ∪ B) = P (A) + P (B) - P (A ∩ B)

               = P (A) + P (B) - P (A)×P (B)

Thus, the probability that a randomly selected adult is either overweight or obese is 0.569.

(b)

Compute the probability that a randomly selected adult is neither overweight nor obese as follows:

Thus, the probability that a randomly selected adult is neither overweight nor obese is 0.431.

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.

definitely a. the others have almost all data points on one side of the line.

step-by-step explanation: