Concept explainers
Exercises 39 and 40 refer to the following: Arthur, Brian, and Carl are dividing the cake shown in Fig.
Figure
Suppose that Carl and Arthur are the dividers and Brian is the chooser. In the first division, Carl makes the cut shown in Fig.
Figure
a. Describe which share (
b. Describe how Carl might subdivide the other share.
c. Based on the subdivisions in (a) and (b), describe a possible final fair division of the cake.
d. For the final fair division you described in (c), find the value of each share (as a percentage of the total value of the cake) in the eyes of the player receiving it.
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Chapter 3 Solutions
Excursions In Modern Mathematics, 9th Edition
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- Suppose 50 percent of the customers at Pizza Palooza order a square pizza, 70 percent order a soft drink, and 35 percent order both a square pizza and a soft drink. Is ordering a soft drink independent of ordering a square pizza? Mutiple Choice:a. No b. Yesarrow_forward4. Alejandro has three ladders that are 15, 10, and 12 feet in length. If he is trying to reach a window that is 8 feet from the ground, then... Part A: How far from the wall does the bottom of the ladder need to be if Alejandro wants to use the 15-foot ladder?arrow_forwardThree investors are dividing a piece of land worth $300,000. Each investor's value in thousands for each of the three pieces of the land is shown below. Which piece does each person receive? Do they receive a fair share using the lone divider method? Piece 1 Piece 2 Piece 3 Henry 80 100 120 Juan 100 100 100 Sarah 60 90 150 Henry's bid: Piece 2 and Piece 3 Sarah's bid: Piece 3 a. Henry receives Piece 2, Sarah receives 3, and Juan receives Piece 1. Everyone receives a fair share. X b. Henry receives Piece 3, Sarah receives 3, and Juan receives Piece 2. Everyone receives a fair share. c. Henry receives Piece 2, Sarah receives 3, and Juan receives Piece 1. No one receives a fair share. d. Henry receives Piece 2, Sarah receives 1, and Juan receives Piece 3. Everyone receives a fair share.arrow_forward
- Jimmy is at the Grand opening celebration of a supermarket. She spends a wheel with 10 equal size slices, as shown. The wheel has 7 black slices, 2 gray slices, and 1 white slice. When the wheel is spun the arrow stops on a slice at random. If the arrow stops on the border of two slices the wheel is spun again.arrow_forwardAn archery target consists of a gold circle with radius of 5 inches surrounded by a red ring whose diameter is 20 inches. Next, there are three progressively larger rings – blue, black, and white. The diameter of each ring is 10 inches larger than the diameter of the previous ring. John is a beginner so his aim is poor and, if his arrow hits the target, its location on the target is completely at random. John shoots and then yells, “I hit it!” Without using your calculator, find the following probabilities. Write the answers as a percentage. a) The probability his arrow landed in the gold circle is ______. b) The probability his arrow landed in the white area is ______. c) The probability his arrow landed in the red or the blue area is ______.arrow_forwardThere is another surprising way of characterizing the ged. For two mumbers a and b, we think about all the numbers you can get by adding multiples of a and b together. We can imaging this by thinking of a and b as dollar values of bills and then asking what prices can paid with them. For example, if your country only issues a 6 dollar bill and a 14 dollar bill, can you buy something that costs 10 dollars? Yes - you pay with two 14 dollar bills and get three 6 dollar bills back in change. Can you buy something that costs 15 dollars? No - all the bills are worth an even number of dollars so there is no way to get an odd net transaction. Formulated more abstractly: Let S(a, b) = {na + mb : n, m € Z}. Problem 0.1. If e is a common divisor of a and b then cls for all s E S(a, b) Problem 0.2. If s € S(a, b) then ged(a, b)|s. Problem 0.3. If s € S(a, b) then sr € S(a, b) for all r € Z Problem 0.4. If S(a, b) = Z if and only if 1 € S Problem 0.5. The set S(0,0) is {0}. For any other a and b…arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
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