if you’re good with set theory diagrams and word problems for math 30 please help out with questions 23, 24, 25, and 26

23.Option B is correct

24. Option C is correct

25. Option A is correct

26. Option A is correct

Explanation:

23. The number of students participated in all three activities:

N= 30-(5+1+2+3+4+2+2) = 30-19=11

=> Option B is correct

24.

A. n(C⋂D⋂F)=2, not 8 (as shown in picture) => incorrect

B. n(D⋂F⋂C)=2, not 0 (as shown in picture) => incorrect

C. n(D⋂F⋂C)=2, => correct

D n(D⋂F⋂C)'= 7+6+1+9+5+12+0=40, not 7 => incorrect.

25.

According to the picture and the given data:

n(F⋂B)= 3

n(F⋂B) = ii = 3  

=> There is no error in ii (Option B is incorrect)

n(F) = 12

n(F) = i + ii = 12 + 3 = 15

=> error in i (ii is correct), i should be equal to n(F) - ii = 12 - 3 = 9

=> Option A is correct  ( (there is error in i)

n(B) = 7

n(B) = ii + iii = 3 + 4 = 7

=> no error in iii (Option C is incorrect)

n(F⋃B)' = n(F+B-(F⋂B))'=20-(12+7-3)=4

n(F⋃B)' = iv = 4

=> no error in iv (Option D is incorrect)

26.

B, (A⋂B⋂C) = {2}, not empty => incorrect

C, (A⋂B⋂C) = {3}, not empty => incorrect

D, (A⋂B⋂C) = {4, 3}, not empty => incorrect

=> Option A is correct

your answer is the frist one

hop i

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.