The rectangle shown is rotated about line k. Rectangle A B C D is shown. A line of rotation goes through the midpoint of sides A B and D C to cut the side into two equal lengths of 5 inches. Side A D has a length of 4 inches. What is the approximate base area of the resulting figure? Area of a circle: A = πr2 31 sq. in. 50 sq. in. 79 sq. in. 314 sq. in.

Find the value of p for which the polynomial 3x^3 -x^2 + px +1 is exactly divisible by x-1, hence factorise the polynomial

Atheater wants to build movable steps that they can use to go on and off the stage. they want the steps to have enough space inside so they can also be used to store props. how much space is inside the steps?

Christine wong has asked dave and mike to her move into a new apartment on sunday morning. she has asked them both, in case one of them does not show up. from past experience, christine knows that there is a 40% chance that dave will not show up and a 30% chance that mik a. what is the probability that both dave and mike will show up? (round your answer to 2 decimal places.) b. what is the probability that at least one of them will show up? c. what is the probability that neither dave nor mike will show up? (round your answer to 2 decimal places.)e will not show up. dave and mike do not know each other and their decisions can be assumed to be independent.