A ballet instructor wants to determine the comfortableness of a new pointe shoe for his ballet students. He decides to divide up all his students based on experience level dancing, either beginner or advanced. He then decides to randomly give each beginner student either a easy, medium, or hard routine to dance with the new point shoes on. He does the same with the advanced students. At the end of each students routine, he has the students rate the comfort level of the shoe on a scale of 1-3.

a. What is the response variable?
b. What is the treatment variable?
c. The experimental units are:
d. The comfort level recorded is a parameter or statistic?
d. What experimental design is being used?

a)  The students rating of the comfort level of the shoe on a scale of 1-3

b) Routine: either a easy, medium, or hard routine to dance with the new point shoes on.

c) Experience level dancing, either beginner or advanced

d) Parameter

e) Randomization

Step-by-step explanation:

a) Response variable is the output or expected output from an experiment. As we are told, at the end of the routine, the students were asked to rate the level of comfort of the shoe on the scale of 1-3. Thus, these ratings is the response variable.

b) The treatment variable is the routine in which the students were randomly assigned. As we are told, all categories of students (either beginner or advanced) were assigned the treatments.

c) The experiment unit is usually the categories. As we are told, there are two categories of students based on dancing experience; beginner and advanced level. Thus, these two units were assigned treatments to test the comfortableness of the new pointed shoe.

d) It is parameter because the outcome is coming from the entire units. That is, the whole population of the instructor ballet students. If we are told a sample is taken, then, we can say is statistics!

e) The experimental design is randomization design (with 2 -levels). This is because, there are two categories of dancers - beginner and experienced. And each were randomly assigned the treatments.

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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