Marcelina uses a blend of white corn and yellow corn to make tortilla chips at her restaurant. She needs to
buy 50 kg of corn in total for her next order. White corn costs $0.30 per kilogram, yellow corn costs $0.15
per kilogram, and she wants to spend $12 total.
Here's a graph that shows a system of equations for this scenario where x is the amount of white corn she
buys and y is the amount of yellow corn she buys.
y (yellow)
line a : 0.30 +0.15y = 12
D
line b:
+y = 50
→ z (white)
70 80
10
20
30
40 50 60
What does point D represent in this context?

Option C. Marcelina spends less that the intended amount of money and buy the correct amount of corn

Step-by-step explanation:

The complete picture of the question in the attached figure

Let

x---->  is the amount of white corn she buys

y ---> is the amount of yellow corn she buys

we know that

She needs to buy 50 kg of corn in total

so

----> equation A

She wants to spend $12 dollars total

so

----> equation B

The solution of the system of equations is the intersection point both graphs

The solution is the point (30,20)

That means

Marcelina needs to buy 30 kg of white corn and 20 kg of yellow corn

we have the ordered pair D(15.35)

That means

15 kg of white corn and 35 kg of yellow corn

therefore

Total kg of corn bought is

Total spend is

therefore

Marcelina spends less that the intended amount of money and buy the correct amount of corn

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.