You are serving bratwurst and hamburgers at your annual picnic. you want at least three bratwursts or hamburgers for each of your 40 guests. bratwursts cost $1.35 each and hamburgers $1.2 each. your budget is $175.
let x be the number of bratwursts and y the number of hamburgers. whiichs system of inequalities represents this situation?
options:
x+y< =40 1.35x+1.2y> =175
x+y< =40 1.35x+1.2y< =175
x+y> =120 1.35x+1.2> =175
x+y> =120 1.35x+1.2< =175

Option D - ,

Step-by-step explanation:

Given : You want at least three bratwursts or hamburgers for each of your 40 guests. Bratwursts cost $1.35 each and hamburgers $1.2 each. Your budget is $175.

To find : Which system of inequalities represents this situation?

Solution :

Let x be the number of bratwursts and y the number of hamburgers.

You want at least three bratwursts or hamburgers for each of your 40 guests.

i.e, you want at least  bratwursts or hamburgers.  

We can write the equation as,

Number of bratwursts + number of hamburgers at least 120

Bratwursts cost $1.35 each and hamburgers cost $1.2 each. Your budget is $175.

We can write equations as ,

Cost of bratwursts + cost of hamburgers at most 175

Therefore, The system of linear equation form is ,

Hence, Option D is correct.

you need to show the graph

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.