Three admission test preparation programs are being evaluated. Suppose the scores obtained by a sample of 20 people who used the programs provided the following data. Program 
A  B  C 
530 450 600
400 530 640
470 400 590
540 420 470
470 490 570
620 360 610
550 560

Use the Kruskal-Wallis test to determine whether there is a significant difference among the three test preparation programs. Use α = 0.05. State the null and alternative hypotheses.

answer: 100

step-by-step explanation:

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.