Sandy is her uncle at this coffee shop. she observes that, when ordering coffee, 13 of customers select chocolate flavoring. to simulate the behavior of the next 5 customers, she lets the number 1 represent someone ordering chocolate, and she lets the numbers 2 or 3 represent someone ordering a different flavor. she writes the numbers 1, 2, and 3 on cards and mixes them up. sandy then picks one card, records the result, and puts the card back. she does this process four more times to represent 5 customers and to complete 1 trial of the experiment. she repeats this experiment for a total of 10 trials. the results are recorded in the table. 12323 13123 22222 23111 11322 31112 23331 11231 32332 13111 using this simulation, what is the probability that 3 or more of the next 5 customers will order chocolate? enter your answer, as a fraction in simplified form, in the box.

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 explanatio89