It takes Dimitri 9 minutes to make a simple bracelet and 20 minutes to make a deluxe bracelet. He has been making bracelets for longer than 120 minutes. If x represents the number of simple bracelets that he has made and y represents the number of deluxe bracelets he has made, the inequality 9x + 20y > 120 represents the scenario. Which is a possible combination of bracelets that Dimitri may have made? 3 simple bracelets and 4 deluxe bracelets 0 simple bracelets and 6 deluxe bracelets 12 simple bracelets and 0 deluxe bracelets 7 simple bracelets and 3 deluxe bracelets

7 simple bracelets and 3 deluxe bracelets

Step-by-step explanation:

Let x be the number of simple bracelets

Dimitri takes 9 minutes to make a simple bracelet

So, Time taken by him to make x bracelets = 9x

Let y be the number of deluxe bracelets

He takes 20 minutes to make a deluxe bracelet

So,Time taken by him to make y deluxe bracelets = 20y

We are given that He has been making bracelets for longer than 120 minutes.

So, 9x+20y>120

A)3 simple bracelets and 4 deluxe bracelets

So,9(3)+20(4)>120

So, it is not a possible combination

B) 0 simple bracelets and 6 deluxe bracelets

9(0)+20(6)>120

So, it is not a possible combination

C) 12 simple bracelets and 0 deluxe bracelets

9(12)+20(0)>120

So, it is not a possible combination

D) 7 simple bracelets and 3 deluxe bracelets

9(7)+20(3)>120

123>120

So, it is a possible combination

So, Option D is true

tube or goog would be a great resource to with that question

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.