1. a bag contains 5 red marbles and 4 green marbles.

what is the probability of choosing a red marble then a green marble, without replacement?
25/81
20/81
5/18
25/72

2. adam, jack and sheila are the three seniors who have been elected to student council. the president and vice president are randomly selected from these three seniors by drawing their names from a hat.

what is the probability that jack will be selected first for president and sheila will be selected second for vice president?
5/6
1/9
2/3
1/6

3. john rolls a six-sided number cube twice.

what is the probability of getting an even number and then an odd number?
1/2
1/6
5/6
1/4

4. on a true-false quiz of six questions, karen answers all the questions.

what is the probability that she answers the first three questions correctly and the last three questions incorrectly?
1/8
1/64
1/32
1/4

answer: at first, in 1635, the evening meetings had been just for women . .

what relationship between ideas is shown in the text above?

question 1 options:

location of events

similarity of events

timing of events

examples of an idea

step-by-step explanation:

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.