In an experiment, the number of insects on a randomly selected plant is recorded. a Specify the sample space for this experiment. b Give the set A representing the event of at most three insects being on the plant. c Explain why each of the possible outcomes in the sample space is not equally likely.

{0, 1, 2, 3, 4, 5,} ;

{0, 1, 2, 3} ;

Step-by-step explanation:

Number of insect on a randomly selected plant

The number of insect in such an experiment will be an integer value ;

Hence, sample space will be ;

{0, 1, 2, 3, 4, 5,}

B.) Event of at most three insects:

Number of insects = 0 ;

Number of insect = 1 ;

Number of insect = 2 ;

Number of insect = 3 ;

n ≤ 3 {x : x ≤ 3}

{0, 1, 2, 3}

3.)

Each possible outcome in the sample space cannot be equally likely due to the fact that the number of insects on the selected plants will vary. With some plants having none to large number of insects while some have small amount of insects.

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.