Tracy goes on a 3 day and night school band trip. there is no cost for travel and each band member only pays half the cost of the hotel room. however, each person is responsible for the cost of their own meals. his portion of the hotel bill is $49 per night and tracy leaves a 10% tip for the maid service. before tax, tracy spends $32 per day on eating out plus 15% of this amount in tips. if tracy spends a total of $280.74 on the band trip, what percent tax was tracy charged on his food?

The correct answer is:

9%

Explanation:

Tracy spends $49 per night for 3 nights. This is 49(3) = $147. She also adds a 10% tip; this is 0.10(147) = $14.70, for a total of $147+$14.70=$161.70 on the hotel.

He spends $32 per day on meals, with a 15% tip. This is 32(3) = 96 before tips, and 0.15(96) = $14.40 on tips, for a total (pre-tax) of 96+14.40 = $110.40 on meals.

This gives us $110.40+$161.70 = $272.10 before tax on meals. This leaves $280.74-$272.10 = $8.64 from the total.

8.64/3 = 2.88; this means the amount of tax per meal was $2.88.

This gives us a percent for tax of 2.88/32 = 0.09, or 9%.

Hotel $49/ night x 3 nights + 10% Maid Tip = $161.70

Meal $32 (before taxes) / day x 3 days + 15% Tips  = $110.4

Meal $32 x 3 = $96.00

Total Expense (before taxes)= $272.10

Actual Expense = $280.74

Difference = $8.64

Meal (after taxes): Meal (before taxes and tip) $96.00 + Difference $8.64 = $104.64

Tax Percentage = Difference = $8.64 / Meal (after taxes) $104.64 x 100 = 8.03%

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.

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step-by-step explanation: