For the following represent the sample space in set notation and sate how many outcomes are possible
1. A bag contains 3 blue marbles 2 red marbles, and 4 green marbles. you draw one marble
2 A spinner can land on the numbers 1-5. You spin twice.

I got blue 3 and green 7

Step-by-step explanation:

why it is blue 3 is because there are 3 of the blue and for the green there are 4 it landed on the 3 green and that was the 7th one

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.