Decide whether the exercise involves permutations or combinations, and then solve the problem. marbles are being drawn without replacement from a bag containing 1414 marbles. (a) how many samples of 44 marbles can be drawn? (b) how many samples of 22 marbles can be drawn? (c) if the bag contains 44 yellow, 22 white, and 88 blue marbles, how many samples of 33 marbles can be drawn in which all marbles are blue? does the problem involve permutations or combinations?

Combinations

Step-by-step explanation:

Given that marbles are drawn without replacement from a bag containing 14 marbles

Since it is without replacement and also order does not matter, we find that only combinations can be used here.

a) 4 marbles can be drawn from total 14 marbles in

b) 2 marbles can be drawn in

c) If 4 yellow, 2 white and 8 blue, 3 blue marbles can be drawn in

This problem involves combinations.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240