Students at a local high school were randomly selected to participate in a math fluency program. The program is designed to increase their math fluency. A total of 12 students each took a pretest before the program and posttest after the program. The mean of the differences in the posttest and pretest scores is 13. The administration decided that all students in the school would participate in the program next school year. Let µD denote the mean difference in the student scores. The 95 percent confidence interval estimate of the mean difference for all students is (8, 18). What is an appropriate interpretation of the confidence interval? For any µD, the sample result is quite likely. For any µD with 8 < µD < 18, the sample result is quite likely. µD is positive, with a probability of 0.95. µD is negative, with a probability of 0.95. µD is between 8 and 18.

this linear equation would have just one solution.

step-by-step explanation:

the reason why this would have one solution is that it is an expression with just one variable. since that variable is not raised to a power, it will always have just one solution.

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.

b) k’(6, 4); l’(3, 3)

step-by-step explanation:

a 270° clockwise rotation maps every point (x, y) to (y, -x). (it negates the x-coordinate and then switches it and the y-coordinate.)

this means the endpoints of the side congruent to kl, k' and l', would be mapped as:

k'(-4, 6)→(6, 4)

l'(-3, 3)→(3, 3)