30 POINTS Latisha owns two spas, one in Pine township and the other in Adams township. Each spa offers a 30-minute face, head, and neck massage to reduce muscle tension. However, therapists first ask each patient questions about their type of tension and stop about five minutes before the end of the 30 minutes to have time to prepare for the next patient. The number of minutes each therapist massages the patients at both spas is approximately Normally distributed, with the Pine spa having a mean of 22.6 minutes and a standard deviation of 1.7 minutes and the Adams spa having a mean of 21.0 minutes and a standard deviation of 2.8 minutes. If Latisha randomly selects 8 massage times from Pine and 9 from Adams, what is the probability that the mean time for Pine is longer than the mean time for Adams?

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.

1. perpendicular

2. parallel

3. perpendicular

i don't see any

step-by-step explanation: