A survey asked 50 students if they play an instrument and if they are in band. 1.25 students play an instrument.
2. 20 students are in band.
3. 30 students are not in band.
Which table shows these data correctly entered in a two-way frequency table?
Band
Not in band Total
0
20
20
O A.
Play instrument
Don't play instrument
Total
5
25
25
30
50
25
Band
Don't play
instrument
Total
20
Not in band
5
B.
25
0
25
Play instrument
Total
25
50
20
30
Band
Not in band Total
5 25
Play instrument
20
C.
Don't play instrument
0
25
25

probability for j is 1/4

while

a is 1/6

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.

27

step-by-step explanation:

10 b/c 5*2 =10

step-by-step explanation: