To raise money for the music program, your choir sells programs for $.50 and CDs of its music for $5. It costs $.15 to produce each program and $1.75 for each CD. Everything sells for $400 yielding a profit of $265. How many CDs were made?

60 CDs

Step-by-step explanation:

Given that :

Price of program = $0.5

Price of music = $5

Cost of production :

Program = $0.15 per program

CD = $1.75 per CD

Revenue made= $400

Profit made = $265

Number of CD produced =?

Let Number of CD's = x and program = y

$(0.5y + 5x) = 400

Y = (400 - 5x) / 0.5

y = 800 - 10x

Production :

$(1.75x + 0.15y)

Total cost of production - Revenue made = profit

(1.75x + 0.15y) - (5x + 0.5y) = 265

1.75x + 0.15y - 5x - 0.5y = 265

1.75x - 5x 0.15y - 0.15y = 265

3.25x + 0.35y = 265 - - - (2)

Put y = 800 - 10x in (2)

3.25x + 0.35y = 265

3.25x + 0.35(800 - 10x) = 265

3.25x + 280 - 3.5x = 265

-0.25x = - 15

x = 15/ 0.25

x = 60

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation:

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.