Vol. 8 No 7 - Pi Mu Epsilon

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BowLing Gheen, Kentucky. t by 8m.q &lu~~&on, W u i t w i Kentmcky Uni-vm-ity, The answer to the question as posed is either 0 or 1, depending on whether or not you are, in fact, a liar; presumably "you" know which. The other answer is 95/1094, or less than 9%. The question to which this is the answer is: Given the assumptions of the first three sentences of the problem, suppose a person is chosen at random from the general population and tested. what is the probability that the person is a liar? If the test should be positive, IV. Comment by Pfc-ttx Ge-cie~~, St. Cloud State UnLuuuiLty, St. Cloud, WLnnebota.. The more interesting result is that the probability a person is a truth-teller given that the machine has labeled him a liar is 1 - 0.0868 = 0.9132. That is, the probability that a person is actually a truth-teller given that the machine has labeled him a liar is greater than 0.90: At20 bohed by CHARLES ASHBACHER, Mount Memy CoUege., Cedm Rap-cdA, IA, JAMES E. CAMPBELL, U&&y of, W^&ou~d, Cohbh, MARK EVANS, Lou^VWLe, KY, RICHARD I. HESS, Rancho Pdob V&, HENRY S. LIEBERMAN, Wa.ban, MA, JOHN D. MOORES, CumblMlge., MA, HARRY SEDINGER, St. Bonauewtune UniviusLty, NY, TIMOTHY SIPKA, Alma. College, Aim, MI, and WADE H. SHERARD, F m n U&m-tA/, G&e.enuWLe, SC. AU thebe botvuu uhed Baye~' the.ote.m, the mhod of, Solution 7. GEORGE P. EVANOVICH, E h d t0JUUUia.m~ CoUege, Hacken~ack, NJ, VICTOR G. FESER, U~M.U~AA.~A/ 06 MoAy, 8-Lima~ck, NV, and THOMAS F. SWEENEY, Ru^e^ Sage CoUege, Thoy, NY, oJUL iubmitted ~olu-tton~ that had minoh ~ iou of one bod oh anothe~. 628. [Fall 19861 Phopobed by AÂ Ttxego, Wden, Ma^~acfoue^tA. a) How many 4 x 6 cards can a paper wholesaler cut from a standard 17 x 22-inch sheet of card stock? b) Can the waste be eliminated if one is allowed to cut both 3 x 5 and 4 x 6 cards from the same sheet? I. Solution by W-LVUam P. McIn-to~h, C e W Me^iodcAt CoUe-ge., Fayvite, M-LAi0UA-L. a) Since both dimensions of the cards are even, the number of cards that can be cut from a 17 x 22-inch sheet is the same as the CA, number that can be cut from a 16 x 22 sheet. Since the latter sheet contains 352 square inches and 15 cards would require 360 square inches, it is clear that at most 14 cards can be cut from one sheet. The left diagram below shows one way to cut fourteen 4 x 6 -*: - cards from a 17 x 22 sheet. (b) The waste cannot be eliminated, but can be greatly reduced. Since the areas of the cards are 15 and 24 square inches respectively, both of which are multiples of 3, then the total area of the cards must be a multiple of 3. Since the area of the sheet is 374 square inches, there must be at least 2 square inches of waste. The right-hand figure shows a way to cut eight 4 x 6 cards and twelve 3 x 5 cards from a 17 x 22-inch sheet, with exactly 2 square inches of waste. 11. The. f,Â¥igw~ (below le.f,t]
111. The f,igwtt (preceding page, /Light1
Page 2 and 3: JOURNAL - VOLUME 8 NUMBER 7 Fractal
Page 4 and 5: measure yield varying results. Henc
Page 6 and 7: Figure 2 From THE FRACTAL GEOMETRY
Page 8 and 9: where N represented the number of p
Page 10 and 11: computer. Diversity of graphic imag
Page 12 and 13: medians concur and that the altitud
Page 14 and 15: So by Ceva's Theorem for Chords, AA
Page 16 and 17: THE ISOMORPHISM OF THE LATTICE OF C
Page 18 and 19: - (a,b) E f(Nl V N2) (a,b) E f(S1N2
Page 20 and 21: If f(x) = A(x) is a polynomial of d
Page 22 and 23: PUZZLE SECTION Edited by Jobeph V .
Page 24 and 25: Whacnohtic No. 25 The 302 letters t
Page 26 and 27: 657. Pmpo~ed by R. S. LtLtha~~, Uni
Page 30 and 31: for n = 0, 1, 2, ... and k a given
Page 32 and 33: SIMONSON, Ean,! Tern State UnivmJUL
Page 34 and 35: So&t-tton by Hmy Sedingm and ChffAZ
Page 36 and 37: An Algebraist's View of Competitive

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