In the last election, candidate a recieved twice as many votes as candidate b. candidate c recieved 15,000 fewer votes than candidate b. if a total of 109,000 votes were cast, how many votes did candidate a recieve

A=62,000 votes

Step-by-step explanation:

Candidate A=2B

Candidate C=B –15,000

Total Votes =

A + B +C = 109,000

(2B)+B+(B–15,000)=109,000

3B+B–15,000=109,000

4B=109,000+15,000=124,000

B=124,000÷4=31,000

Therefore,

A=2B

A=2(31,000)

A=62,000

C=B–15,000

C=31,000–15,000

C=16,000

You can add them back to confirm

ie. (62,000 + 31,000 + 16,000 = 109,000 votes total)

$25

step-by-step explanation:

25 - 4.50 = 20.5

20.5 / 2 = 10.25

10.25 + 10 = 20.25

20.25 - 12.50 = 7.75

therefore the answer is $25 as shown as the first number.

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.