Gustavo is the league's home run leader. The probabilities for his total number of home runs for the season are as follows: \text{P(0-19 home runs}) = \dfrac14P(0-19 home runs)= 4 1 start text, P, left parenthesis, 0, negative, 19, space, h, o, m, e, space, r, u, n, s, end text, right parenthesis, equals, start fraction, 1, divided by, 4, end fraction \text{P(20-39 home runs}) = 45\%P(20-39 home runs)=45%start text, P, left parenthesis, 20, negative, 39, space, h, o, m, e, space, r, u, n, s, end text, right parenthesis, equals, 45, percent \text{P(40+ home runs}) = 0.3P(40+ home runs)=0.3start text, P, left parenthesis, 40, plus, space, h, o, m, e, space, r, u, n, s, end text, right parenthesis, equals, 0, point, 3 Put the following events in order from least to most likely.

one that is bigger than 3 1/2

b. b < 1 might be the correct answer

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.