A shop sells a party hat at x dollars and a mask y dollars. On a particular morning, 3 hats and 4 mask were sold for $27. In the afternoon, 3 hats and 6 mask were sold for $33. Find the cost of each hat and each mask.

Each hat cost = $5

Each mask cost = $3

Step-by-step explanation:

Hat = x dollars

Mask = y dollars

Now,

3 hat and 4 mask sold = $27

We can write:

3x + 4y = 27

Then,

3 hat and 6 mask sold = $33

We can write:

3x + 6y = 33

Adding 2nd equation with (-1 times 1st equation) gives us:

3x + 6y = 33

-1 * (3x + 4y = 27)

3x + 6y = 33

-3x -4y = -27

2y = 6

y = 6/2

y = 3

Now we replace y = 3 into 1st equation and solve for x:

3x + 4y = 27

3x + 4(3) = 27

3x + 12 = 27

3x = 15

x = 15/3

x = 5

Each hat cost = $5

Each mask cost = $3

idk this answer sorry cant on this one.

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.