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Four couriers are represented by points (t, d), where t is total time in hours and d is total distance in miles: A(3/4, 27/8), B(5/6, 7/4), C(2/3, 5/3), D(7/8, 2). Which courier had the greatest average speed? | A | algebra |
Determine the polar coordinates (r, theta), with r > 0 and 0 <= theta < 2pi, of the point (-7, 24). | (25, pi - arctan(24/7)) | precalculus |
A craftsperson makes regular polygon frames from identical straight segments, so a regular pentagon and a regular decagon he makes have the same side length. Each pentagon frame has perimeter 40 cm. Material costs $0.05 per cm of frame. He sells pentagon frames for $6 each and decagon frames in bundles of 3 for $25. On... | 107 | prealgebra |
Let t be a positive real number. Determine the least value of t such that all roots of the cubic 2x^3 + 2t x^2 + (2 - t)x - (t + 4) are real. | sqrt(7) | intermediate_algebra |
Let N = 11·22·33·...·110 (the product of the first ten positive multiples of 11). How many positive divisors of N are multiples of 11? | 2700 | number_theory |
A right circular cylinder has a string wrapped tightly around its base; the string’s length is 16π cm. The cylinder’s volume is 256π cubic centimeters. What is the cylinder’s height? | 4 cm | geometry |
Along each side of a regular 18-gon, an identical regular pentagon is attached externally so that it shares exactly that side. If the perimeter of one pentagon is 65 cm, what is the perimeter of the 18-gon? | 234 cm | prealgebra |
Find the polar coordinates (r, θ), with r > 0 and θ ∈ [0, 2π), of the point (−4, 4√3). | (8, 2π/3) | precalculus |
Ten distinct people, including Alice, Bob, and Carol, are to sit around a round table. How many distinct seatings, considered the same up to rotation, are there in which Carol sits next to neither Alice nor Bob? | 211680 | counting__probability |
To reach a target amount A exactly two months from now, Dana deposits 40% of A today and 30% of A one month from today into an account that compounds monthly at a fixed rate r. What is the smallest monthly interest rate r (as a percentage) that ensures the account has at least A on the target date? | 25% | algebra |
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