Knowledge Bowl is a trivia competition. Each math question is worth 15 points, each science question is worth 10 points, and a team loses 5 points for answering any question incorrectly.
On the day of the Bowl, a team attempted to answer a total of 14 questions, earning 125 points. If the team doubled the number of science questions answered correctly and
swapped the number of questions it answered incorrectly with the number of math questions it got correct, its score would have been 10 points lower. Given that m, s, and i
represent the number of each type of question answered, find a system of equations that could model this situation. Select all the equations in the system.
•5m +20s + 151 = 115
•15m + 10s - 51 - 125
•15m + 10s +51 = 125
•m+s + i = 14
•-5m +20s +151 - 115

associative property hopes this ! : )

step-by-step explanation:

center= (-2,0)

radius= sqrt2/2

step-by-step explanation:

to find the perimeter of the rectangle this is the expression:

x-9+x-9+3x-4+3x-4=138

if we simplify it:

8x-26=138

remember, 138 is what it all adds up to

the length is 11.5cm

the width is 57.5cm

the area is 661.25cm^2

the answers might not be correct use at own risk

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.