Twenty people work at a small startup. A six-person committee is to be formed. (a) Let D denote the set of all possible committees. Find |D|. (b) Two of the workers, Alice and Beth, will be unhappy if they have to serve together. Let P be the set of possible committees with both Alice and Beth. Find |P|. (c) Beth will also be unhappy if she has to serve with both Frank and Grace. Let Q be the set of possible committees on which Beth, Frank, and Grace would all serve together. Find |Q|. (d) Find |P ∩Q|. (e) Let S be the set of all possible committees on which there is at least one unhappy employee. Express S in terms of only P and Q. (f) Find |S|. (g) How many committees can we form with no unhappy employees? (h) Instead of one committee, we decide to form two six-person committees. Each employee can be on at most one committee. How many ways can we form these committees, if employee happiness is not taken into consideration?

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correct answer is c. just did it

step-by-step explanation:

the answer for your question is

step-by-step explanation:

hello!

to begin with, we're given that on earth, a rock weighs 20 pounds, and while on jupiter, that same rock weighs 42 pounds. now, we're trying to find the weight of a rock that weighs 10.5 pounds on earth, on jupiter.

to solve this, first, set up a proportion, cross-multiply, and solve it algebraically.

setting up the proportion is the hardest and the most confusing part of the problem, but it's simple.

if on earth, the rock weighs 20 lbs, and on jupiter it weighs 42 lbs, our first part of our proportion is 20/42 lbs. the second part has to be equal to each other. this means that 10.5 has to be on the numerator of the fraction, and x, the value we're trying to find, has to be on the denominator. remember that the rock weighs 10.5 lbs on earth, and we're trying to find the weight of it on jupiter (which is x).

20/42 = 10.5/x

next, you would cross-multiply.

20x = 42(10.5)

20x = 441

now, solve it algebraically by using division.

x = 22.05 lbs

this can be rounded to 22.1 lbs.

therefore, the weight of the rock on jupiter is 22.1 lbs, the fourth choice.