MYLAB MATH FOR EXCURSIONS IN MATHEMATIC
9th Edition
ISBN: 9780136415893
Author: Tannenbaum
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Textbook Question
Chapter 3, Problem 59E
Ana, Belle, and Chloe are dividing 3 Choko bars, 3 Minto bars, and 3 Frooto bars among themselves using the method of markers. The players’ value systems are as follows:
Figure 3-37
a. Describe the placement of each player's markers. (Use A1. and A2 for Ana's markers, B1 and B2 for Belle's markers, and C1 and C2 for Chloe's markers.)
(Hint: For each player, compute the value of each piece as a fraction of the value of the booty first. This will help you figure out where the players would place their markers.)
b. Describe the allocation of candy to each player and which pieces of candy are left over.
c. Suppose that the players decide to divide the left over pieces by a random lottery in which each player gets to chose one piece. Suppose that Belle gets to choose first, Chloe second, and Ana last. Describe the division of the leftover pieces.
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πT
| cos x |³ dx
59
2
2. Consider the ODE
u' = ƒ (u) = u² + r
where r is a parameter that can take the values r = −1, −0.5, -0.1, 0.1. For each value of r:
(a) Sketch ƒ(u) = u² + r and determine the equilibrium points.
(b) Draw the phase line.
(d) Determine the stability of the equilibrium points.
(d) Plot the direction field and some sample solutions,i.e., u(t)
(e) Describe how location of the equilibrium points and their stability change as you increase the
parameter r.
(f) Using the matlab program phaseline.m generate a solution for each value of r and the initial
condition u(0) = 0.9. Print and turn in your result for r = −1. Do not forget to add a figure caption.
(g) In the matlab program phaseline.m set the initial condition to u(0) = 1.1 and simulate the ode
over the time interval t = [0, 10] for different values of r. What happens? Why? You do not need to
turn in a plot for (g), just describe what happens.
The following are suggested designs for group sequential studies. Using PROCSEQDESIGN, provide the following for the design O’Brien Fleming and Pocock.• The critical boundary values for each analysis of the data• The expected sample sizes at each interim analysisAssume the standardized Z score method for calculating boundaries.Investigators are evaluating the success rate of a novel drug for treating a certain type ofbacterial wound infection. Since no existing treatment exists, they have planned a one-armstudy. They wish to test whether the success rate of the drug is better than 50%, whichthey have defined as the null success rate. Preliminary testing has estimated the successrate of the drug at 55%. The investigators are eager to get the drug into production andwould like to plan for 9 interim analyses (10 analyzes in total) of the data. Assume thesignificance level is 5% and power is 90%.Besides, draw a combined boundary plot (OBF, POC, and HP)
Chapter 3 Solutions
MYLAB MATH FOR EXCURSIONS IN MATHEMATIC
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