Appearance
question:A segment with endpoints at A(2, -2) and B(14, 4) is extended through B to point C. If BC = frac{1}{3} cdot AB, what are the coordinates for point C? Express your answer as an ordered pair.
answer:The vector from A to B is begin{pmatrix} 14-2 4-(-2) end{pmatrix} = begin{pmatrix} 12 6 end{pmatrix}. Since BC = frac{1}{3} cdot AB, the vector from B to C is frac{1}{3} cdot begin{pmatrix} 12 6 end{pmatrix} = begin{pmatrix} 4 2 end{pmatrix}. Adding this vector to the coordinates of B, we find that the coordinates of C are begin{pmatrix} 14 4 end{pmatrix} + begin{pmatrix} 4 2 end{pmatrix} = boxed{begin{pmatrix} 18 6 end{pmatrix}}. The answer is: (18,6)
question:f Bill double-counted 8 toddlers and missed 3 who were hiding, but he believes he counted a total of 26 toddlers, what is the actual number of toddlers present?
answer:If Bill double-counted 8 toddlers, then the actual number of toddlers he counted is 26 - 8 = 18 If he missed 3 toddlers, then the actual number of toddlers present is 18 + 3 = 21 21 The answer is: 21
question:f Ellianna cooked and served 40 herring, 40 eel, and 40 pike, where a herring has 40 oz of fat, an eel has 20 oz, and a pike has 10 more oz of fat than an eel, what is the total number of ounces of fat she served?
answer:Ellianna served 40 herrings, each with 40 oz of fat, so she served 40 * 40 = 1600 oz of fat from herrings. Ellianna also served 40 eels, each with 20 oz of fat, so she served 40 * 20 = 800 oz of fat from eels. A pike has 10 more oz of fat than an eel, so Ellianna served 20 + 10 = 30 oz of fat from each pike. Ellianna served 40 pikes, each with 30 oz of fat, so she served 40 * 30 = 1200 oz of fat from pikes. In total, Ellianna served 1600 + 800 + 1200 = 3600 oz of fat. 3600 The answer is: 3600
question:At a meeting with 25 businessmen, twelve businessmen drank coffee, and ten businessmen drank tea. Five businessmen drank both coffee and tea. How many businessmen drank neither coffee nor tea?
answer:Let x be the number of businessmen who drank neither coffee nor tea. By the principle of inclusion-exclusion, the total number of businessmen who drank either coffee or tea is 12 + 10 - 5 = 17. Since there are 25 businessmen in total, the number of businessmen who drank neither coffee nor tea is 25 - 17 = boxed{8}.The answer is: 8