Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
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Chapter 16, Problem 61E
Suppose that you roll a pair of honest dice. If you roll a total of 7, you win $18; if you roll a total of 11, you win $54; if you roll any other total, you lose $9. Find the expected payoff for this game.
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Could you please solve this question on a note book. please dont use AI because this is the third time i upload it and they send an AI answer. If you cant solve handwritten dont use the question send it back. Thank you.
(b) Consider the equation Ux - 2Ut
=
-3.
(i) Find the characteristics of this equation.
(ii) Find the general solutions of this equation.
(iii) Solve the following initial value problem for this equation
Ux - 2U₁ = −3
U(x, 0) = 0.
Question 4
(a) Find all possible values of a, b such that [sin(ax)]ebt solves the heat equation
U₁ = Uxx, x > 0.
(b) Consider the solution U(x,t) = (sin x)et of the heat equation U₁ = Uxx. Find the
location of its maxima and minima in the rectangle
πT
{0≤ x ≤½,0≤ t≤T}
2'
(c) Solve the following heat equation with boundary and initial condition on the half
line {x>0} (explain your reasonings for every steps).
Ut
=
Uxx, x > 0
Ux(0,t) = 0
U(x, 0) =
= =1
[4]
[6]
[10]
Chapter 16 Solutions
Excursions in Modern Mathematics (9th Edition)
Ch. 16 - Using set notation, write out the sample space for...Ch. 16 - Using set notation, write out the sample space for...Ch. 16 - Using set notation, write out the sample space for...Ch. 16 - Using set notation, write out the sample space for...Ch. 16 - The board of directors of Fibber Corporation has...Ch. 16 - You reach into a large jar containing jelly beans...Ch. 16 - In Exerxises 7 through 10, the sample spaces are...Ch. 16 - In Exerxises 7 through 10, the sample spaces are...Ch. 16 - Prob. 9ECh. 16 - In Exerxises 7 through 10, the sample spaces are...
Ch. 16 - A coin is tossed three times in a row The...Ch. 16 - A student randomly guesses the answers to a...Ch. 16 - A pair of dice is rolled. The observation is the...Ch. 16 - A card is drawn out of a standard deck of 52...Ch. 16 - A coin is tossed 10 times in a row. The...Ch. 16 - Five candidates (A,B,C,D,andE) have a chance to be...Ch. 16 - A California license plate starts with a digit...Ch. 16 - A computer password consists of four letters A...Ch. 16 - Jack packs two pairs of shoes, one pair of boots,...Ch. 16 - A French restaurant offers a menu consisting of...Ch. 16 - A set of reference books consists of eight volumes...Ch. 16 - Nine people four men and five women line up at a...Ch. 16 - 7. Nine people four men and five women line up at...Ch. 16 - Prob. 24ECh. 16 - Determine the number of outcomes N in each sample...Ch. 16 - Determine the number of outcomes N in each sample...Ch. 16 - In Exercises 27 through 30, you are asked to give...Ch. 16 - In Exercises 27 through 30, you are asked to give...Ch. 16 - In Exercises 27 through 30, you are asked to give...Ch. 16 - In Exercises 27 through 30, you are asked to give...Ch. 16 - A major league baseball team roster consists of 40...Ch. 16 - Bob has 20 different dress shirts in his wardrobe....Ch. 16 - Consider the sample space S={o1,o2,o3,o4,o5}....Ch. 16 - Consider the sample space S={o1,o2,o3,o4}. Suppose...Ch. 16 - Four candidates are running for mayor of...Ch. 16 - Seven horses A, B, C, D, E, F, and G are running...Ch. 16 - An honest coin is tossed three times in a row....Ch. 16 - A student randomly guesses the answers to a...Ch. 16 - A pair of honest dice is rolled. Find the...Ch. 16 - A card is drawn at random out of a well-shuffled...Ch. 16 - An honest coin is tossed 10 times in a row. Find...Ch. 16 - Five candidates A, B, C, D, and E have a chance to...Ch. 16 - A student takes a 10-question true-or-false quiz...Ch. 16 - Suppose that the probability of giving birth to a...Ch. 16 - The Tasmania State University glee club has 15...Ch. 16 - Ten professional basketball teams are...Ch. 16 - An honest coin is tossed 10 times in a row. The...Ch. 16 - Imagine a game in which you roll an honest die...Ch. 16 - Find the odds of each of the following events. a....Ch. 16 - Find the odds of each of the following events. a....Ch. 16 - In each case, find the probability of an event E...Ch. 16 - In each case, find the probability of an event E...Ch. 16 - Prob. 53ECh. 16 - Table 16-19 shows the aggregate scores of a golf...Ch. 16 - At Thomas Jefferson High School, the student body...Ch. 16 - In 2005 the Middletown Zoo averaged 4000 visitors...Ch. 16 - Prob. 57ECh. 16 - A basketball player shoots two consecutive free...Ch. 16 - Prob. 59ECh. 16 - A pair of honest dice is rolled once. Find the...Ch. 16 - Suppose that you roll a pair of honest dice. If...Ch. 16 - On an American roulette wheel, there are 18 red...Ch. 16 - On an American roulette wheel, there are 38...Ch. 16 - Suppose that you roll a single die. If an odd...Ch. 16 - Prob. 65ECh. 16 - Jackie is buying a new MP3 player from Better Buy....Ch. 16 - The service history of the Prego SUV is as...Ch. 16 - An insurance company plans to sell a 250,000...Ch. 16 - The ski club at Tasmania State University has 35...Ch. 16 - Prob. 70ECh. 16 - Prob. 71ECh. 16 - Two teams call them X and Y play against each...Ch. 16 - An urn contains seven red balls and three blue...Ch. 16 - Prob. 74ECh. 16 - Prob. 75ECh. 16 - A draw poker hand consists of 5 cards taken from a...Ch. 16 - Prob. 77ECh. 16 - Prob. 78ECh. 16 - Yahtzee. Yahtzee is a dice game in which five...Ch. 16 - In head-to-head, 7-card stud poker you make your...
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