Astatistics teacher conducted an experiment to test whether the use of a new review booklet will improve her students' semester grades. the teacher randomly selected 20 students from her class and assigned the new review booklet to 10 of the students. the remaining 10 students did not use any review material. at the end of the semester, the teacher reviewed the students' semester grades. the semester grades of the students who used the new review booklet were the same as the semester grades of the students who did not. what can be concluded from the teacher's observations? a. it can be concluded that the new review booklet does not improve students' semester grades. b. it can be concluded that the new review booklet reduces students' semester grades. c. there is not enough information to make any conclusions regarding the new review booklet. d. it can be concluded that the new review booklet improves students' semester grades.

C. There is not enough information to make any conclusions regarding the new review booklet.

Step-by-step explanation:

Given that A statistics teacher conducted an experiment to test whether the use of a new review booklet will improve her students' semester grades.

also given that The teacher randomly selected 20 students from her class and assigned the new review booklet to 10 of the students. The remaining 10 students did not use any review material.

The semester grades did not differ for both groups.

But we cannot conclude the booklet has no effect because,

i) The sample size is very small, only 10.  Hence not reliable

ii) We do not know the previous performance of both the groups. To ensure improvement the grades the students got in the previous exam also should be considered.

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

y + 11 = (1/4)(x + 16)

step-by-step explanation: