Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
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Chapter 16, Problem 74E
To determine
(a)
To find:
The probability of getting 5 heads and 5 tails.
To determine
(b)
To find:
The probability of getting 3 heads and 7 tails.
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Students have asked these similar questions
b) Solve the following linear program using the 2-phase simplex algorithm. You should give
the initial tableau, and each further tableau produced during the execution of the
algorithm. If the program has an optimal solution, give this solution and state its
objective value. If it does not have an optimal solution, say why.
maximize ₁ - 2x2+x34x4
subject to 2x1+x22x3x41,
5x1 + x2-x3-×4 ≤ −1,
2x1+x2-x3-34
2,
1, 2, 3, 40.
Suppose we have a linear program in standard equation form
maximize cTx
subject to Ax = b.
x ≥ 0.
and suppose u, v, and w are all optimal solutions to this linear program.
(a) Prove that zu+v+w is an optimal solution.
(b) If you try to adapt your proof from part (a) to prove that that u+v+w
is an optimal solution, say exactly which part(s) of the proof go wrong.
(c) If you try to adapt your proof from part (a) to prove that u+v-w is an
optimal solution, say exactly which part(s) of the proof go wrong.
a) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program in
standard inequality form (with 3 variables and 4 constraints) and suppose that we have
reached a point where we have obtained the following tableau. Apply one more pivot
operation, indicating the highlighted row and column and the row operations you carry
out. What can you conclude from your updated tableau?
x1
x2 x3
81 82
83
84
81
-2 0
1 1 0
0
0
3
82
3 0
-2 0
1
2
0
6
12
1
1
-3
0
0
1
0
2
84
-3 0
2
0
0 -1
1
4
-2 -2 0
11
0
0-4
0
-8
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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- Microsoft Excel snapshot for random sampling: Also note the formula used for the last column 02 x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51)) A B 1 No. States 2 1 ALABAMA Rand No. 0.925957526 3 2 ALASKA 0.372999976 4 3 ARIZONA 0.941323044 5 4 ARKANSAS 0.071266381 Random Sample CALIFORNIA NORTH CAROLINA ARKANSAS WASHINGTON G7 Microsoft Excel snapshot for systematic sampling: xfx INDEX(SD52:50551, F7) A B E F G 1 No. States Rand No. Random Sample population 50 2 1 ALABAMA 0.5296685 NEW HAMPSHIRE sample 10 3 2 ALASKA 0.4493186 OKLAHOMA k 5 4 3 ARIZONA 0.707914 KANSAS 5 4 ARKANSAS 0.4831379 NORTH DAKOTA 6 5 CALIFORNIA 0.7277162 INDIANA Random Sample Sample Name 7 6 COLORADO 0.5865002 MISSISSIPPI 8 7:ONNECTICU 0.7640596 ILLINOIS 9 8 DELAWARE 0.5783029 MISSOURI 525 10 15 INDIANA MARYLAND COLORADOarrow_forwardThe spread of an infectious disease is often modeled using the following autonomous differential equation: dI - - BI(N − I) − MI, dt where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of transmission, and μ is the rate at which people recover from infection. Close a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria. b) (5 points) For the equilbria in part a), determine whether each is stable or unstable. c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the dt function by hand.) Identify the equilibria as stable or unstable in the graph. d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.arrow_forwardFind the indefinite integral. Check Answer: 7x 4 + 1x dxarrow_forward
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