There are 142 coins in a container with a total value of $20.50. If all of the coins are either quarters (x) or nickels (y), which system of equations would you use to determine how many of each type of coin are in the container? No work is needed. Immersive Reader (1 Point)

x + y = 20.50 and .25x + .05y = 142

x + y = 20.50 and .25x + .5y = 142

x + y = 142 and .25x + .5y = 20.50

x + y = 142 and .25x + .05y = 20.50

There were 200 eighth grade students who attended the Disney field trip. Some students rode in vans (v) which hold 5 students each. Some students rode in buses (b) which hold 30 students each. Each vehicle was completely full, and there were 10 total vehicles. Which is the system of equations used to calculate the number of vans and buses? No work is needed. Immersive Reader
(1 Point)

v + b = 10 and 5v + 30b = 200

v + b = 10 and 5v - 30b = 200

v + b = 200 and 5v + 30b = 10

v + b = 200 and 5v + 30b = 200

5050 i think

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.

$6.42

step-by-step explanation: