Apunch bow is filled with 500 marbles which are represented by four colors. there are 50 red marbles, 250 white marbles, 125 green marbles, and 75 black marbles. a flat scoop with 25 marble size dimples can be used to randomly select 25 marbles from the punch bowl. the same contains 1 red marble, 14 white marbles, 7 green marbles, and 3 black marbles. what is the same space (s)? that is, the set of all possible outcomes?

54

step-by-step explanation:

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.

the function makes a strait line horizontally with no x intercept but a y intercept at 9.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt