Help please State whether the graph of the linear relationship is a solid line or a set of unconnected points. Complete the explanation of your reasoning.

The relationship between the number of $3 lunches you buy with a $150 school lunch card and the money remaining on the card

The relationship is a ( set of unconnected points, solid line )
because you (can, cannot) buy a ( positive number of lunches, fractional part of a lunch)

The relationship is a solid line because you can buy a positive number of lunches.

Step-by-step explanation:

$3 lunches $150 school lunch card

Let number of lunches = x

Let number of amount remaining on card = y

y = 150 - 3x

When you buy 1 lunch

y = 150 - 3(1)

     150 - 3

y = 147

When you buy 2 lunches

y = 150 - 3(2)

     150 - 6

y = 144

The decrease in the amount is constant and you can see on the graph that it is linear.

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.