A recent study of high school students shows the percentage of females and males who have an after-school job. A simple random sample of high school students was interviewed. The students were asked whether they worked after school. Of the 250 females, 58 answered yes, as did 113 of the 380 males. Part A: Construct and interpret a 95% confidence interval for the difference in population proportions of females and males who have an after-school job. Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (8 points)

Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain. (2 points)

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .

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.

it would be 3 ÷by 6 because the number on each side