Finite Mathematics and Application Calculus (Looseleaf) - Text Only
7th Edition
ISBN: 9781337291484
Author: Waner
Publisher: Cengage
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Chapter 7.4, Problem 65E
Elimination Tournaments In an elimination tournament the teams are arranged in opponent pairs for the first round, and the winner of each round goes on to the next round until the champion emerges. The following diagram illustrates a 16-team tournament bracket, in which the 16 participating teams are arranged on the left under Round 1 and the winners of each round are added as the tournament progresses. The top team in each game is considered the “home” team, so the top-to-bottom order matters.
To seed a tournament means to select which teams to play each other in the first round according to their preliminary ranking. For instance, in professional tennis and NCAA basketball the seeding is set up in the following order based on the preliminary rankings: 1 versus 16, 8 versus 9, 5 versus 12, 4 versus 13, 6 versus 11, 3 versus 14, 7 versus 10, and 2 versus 15.23 Exercises 65–68 are based on various types of elimination tournaments. (Leave each answer as a formula.)
a. How many different seedings of a 16-team tournament are possible? (Express the answer as a formula.)
b. In how many seedings will the top-ranked team play the bottom-ranked team, the second-ranked team play the second-lowest-ranked team, and so on?
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3.1 Limits
1. If lim f(x)=-6 and lim f(x)=5, then lim f(x). Explain your choice.
x+3°
x+3*
x+3
(a) Is 5
(c) Does not exist
(b) is 6
(d) is infinite
1 pts
Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and
G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is
Question 1
-0.246
0.072
-0.934
0.478
-0.914
-0.855
0.710
0.262
.
2. Answer the following questions.
(A) [50%] Given the vector field F(x, y, z) = (x²y, e", yz²), verify the differential identity
Vx (VF) V(V •F) - V²F
(B) [50%] Remark. You are confined to use the differential identities.
Let u and v be scalar fields, and F be a vector field given by
F = (Vu) x (Vv)
(i) Show that F is solenoidal (or incompressible).
(ii) Show that
G =
(uvv – vVu)
is a vector potential for F.
Chapter 7 Solutions
Finite Mathematics and Application Calculus (Looseleaf) - Text Only
Ch. 7.1 - Prob. 1ECh. 7.1 - Prob. 2ECh. 7.1 - Prob. 3ECh. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10E
Ch. 7.1 - Prob. 11ECh. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - In Exercises 1720, draw a Venn diagram that...Ch. 7.1 - Prob. 18ECh. 7.1 - In Exercises 1720, draw a Venn diagram that...Ch. 7.1 - Prob. 20ECh. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - Prob. 37ECh. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - Prob. 39ECh. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - Prob. 41ECh. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - Prob. 43ECh. 7.1 - Let A={H, T} be the set of outcomes when a coin is...Ch. 7.1 - Prob. 45ECh. 7.1 - Let A={H, T} be the set of outcomes when a coin is...Ch. 7.1 - Prob. 47ECh. 7.1 - Prob. 48ECh. 7.1 - Prob. 49ECh. 7.1 - Prob. 50ECh. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Prob. 66ECh. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - You sell iPads and jPads. Let I be the set of all...Ch. 7.1 - Prob. 72ECh. 7.1 - You are searching online for techno music that is...Ch. 7.1 - Prob. 74ECh. 7.1 - Prob. 75ECh. 7.1 - Prob. 76ECh. 7.1 - Prob. 77ECh. 7.1 - Prob. 78ECh. 7.1 - Prob. 79ECh. 7.1 - Prob. 80ECh. 7.1 - Prob. 81ECh. 7.1 - Prob. 82ECh. 7.1 - When this book was being written, the copy editor...Ch. 7.1 - Prob. 84ECh. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Verify that n(AB)=n(A)+n(B)n(AB) with A and B as...Ch. 7.2 - Verify that n(AC)=n(A)+n(C)n(AC) with A and C as...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - If n(A)=43,n(B)=20, and n(AB)=3, find n(AB).Ch. 7.2 - If n(A)=60, n(B)=20, and n(AB)=1 find n(AB).Ch. 7.2 - If n(AB)=100andn(A)=n(B)=60, fi0nd n(AB).Ch. 7.2 - If n(A)=100,n(AB)=150, and n(AB)=40, find n(B).Ch. 7.2 - Prob. 19ECh. 7.2 - Prob. 20ECh. 7.2 - Prob. 21ECh. 7.2 - Prob. 22ECh. 7.2 - Prob. 23ECh. 7.2 - Prob. 24ECh. 7.2 - Prob. 25ECh. 7.2 - With S,A,andB as above, verify that...Ch. 7.2 - Prob. 27ECh. 7.2 - In Exercises 2730, use the given information to...Ch. 7.2 - In Exercises 2730, use the given information to...Ch. 7.2 - Prob. 30ECh. 7.2 - Web Searches In November 2011 a search using the...Ch. 7.2 - Web Searches In November 2011 a search using the...Ch. 7.2 - Amusement On a particularly boring transatlantic...Ch. 7.2 - Restaurant Menus While scanning through the...Ch. 7.2 - Mobile Gamers Of a total of 132 million mobile...Ch. 7.2 - Mobile Gamers Of a total of 208 million mobile...Ch. 7.2 - Prob. 37ECh. 7.2 - Prob. 38ECh. 7.2 - Prob. 39ECh. 7.2 - Prob. 40ECh. 7.2 - Prob. 41ECh. 7.2 - Prob. 42ECh. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Medicine In a study of Tibetan children,10 a total...Ch. 7.2 - Medicine In a study of Tibetan children,11 a total...Ch. 7.2 - Entertainment According to a survey of 100 people...Ch. 7.2 - Athletics Of the 4,700 students at Medium Suburban...Ch. 7.2 - Entertainment In a survey of 100 Enormous State...Ch. 7.2 - Entertainment Refer back to Exercise 59. You are...Ch. 7.2 - Prob. 61ECh. 7.2 - Prob. 62ECh. 7.2 - Why is the Cartesian product referred to as a...Ch. 7.2 - Refer back to your answer to Exercise 63. What set...Ch. 7.2 - Formulate an interesting application whose answer...Ch. 7.2 - Formulate an interesting application whose answer...Ch. 7.2 - When is n(AB)n(A)+n(B)?Ch. 7.2 - When is n(AB)=n(A)?Ch. 7.2 - When is n(AB)=n(A)?Ch. 7.2 - When is n(AB)=n(A)?Ch. 7.2 - Use a Venn diagram or some other method to obtain...Ch. 7.2 - Prob. 72ECh. 7.3 - An experiment requires a choice among three...Ch. 7.3 - Prob. 2ECh. 7.3 - An experiment requires a sequence of three steps....Ch. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - Prob. 10ECh. 7.3 - Prob. 11ECh. 7.3 - Prob. 12ECh. 7.3 - How many different four-letter sequences can be...Ch. 7.3 - Prob. 14ECh. 7.3 - Ice Cream When Baskin-Robbins was founded in 1945,...Ch. 7.3 - Prob. 16ECh. 7.3 - Prob. 17ECh. 7.3 - Ternary Codes A ternary digit is either 0, 1, or...Ch. 7.3 - Ternary Codes A ternary digit is either 0, 1, or...Ch. 7.3 - Binary Codes A binary digit, or bit, is either 0...Ch. 7.3 - Reward While selecting candy for students in his...Ch. 7.3 - Productivity Professor Oger must choose between an...Ch. 7.3 - Prob. 23ECh. 7.3 - Radar Detectors Radar detectors are either powered...Ch. 7.3 - Multiple-Choice Tests Professor Easys final...Ch. 7.3 - Multiple-Choice Tests Professor Toughs final...Ch. 7.3 - Tests A test requires that you answer either Part...Ch. 7.3 - Tests A test requires that you answer first Part A...Ch. 7.3 - Stock Portfolios Your broker has suggested that...Ch. 7.3 - Prob. 30ECh. 7.3 - Computer Codes A computer byte consists of eight...Ch. 7.3 - Prob. 32ECh. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - Prob. 36ECh. 7.3 - Tournaments How many ways are there of filling in...Ch. 7.3 - Prob. 38ECh. 7.3 - Prob. 39ECh. 7.3 - Prob. 40ECh. 7.3 - Prob. 41ECh. 7.3 - Prob. 42ECh. 7.3 - DNA Chains: Life in Nature DNA (deoxyribonucleic...Ch. 7.3 - Prob. 44ECh. 7.3 - Prob. 45ECh. 7.3 - Telephone Numbers In the past, a local telephone...Ch. 7.3 - Romeo and Juliet Here is a list of the main...Ch. 7.3 - Prob. 48ECh. 7.3 - Prob. 49ECh. 7.3 - Prob. 50ECh. 7.3 - Mazes a. How many four-letter sequences are...Ch. 7.3 - Prob. 52ECh. 7.3 - Prob. 53ECh. 7.3 - Prob. 54ECh. 7.3 - Prob. 55ECh. 7.3 - Combination Locks Dripping wet after your shower,...Ch. 7.3 - Prob. 57ECh. 7.3 - Prob. 58ECh. 7.3 - Prob. 59ECh. 7.3 - Prob. 60ECh. 7.3 - Prob. 61ECh. 7.3 - Programming in Java Script (Some programming...Ch. 7.3 - Prob. 63ECh. 7.3 - Prob. 64ECh. 7.3 - Prob. 65ECh. 7.3 - Numbers How many odd numbers between 10 and 99...Ch. 7.3 - Prob. 67ECh. 7.3 - Prob. 68ECh. 7.3 - Prob. 69ECh. 7.3 - Prob. 70ECh. 7.3 - Prob. 71ECh. 7.3 - Find an interesting application that requires a...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - Prob. 2ECh. 7.4 - Prob. 3ECh. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - Prob. 5ECh. 7.4 - Prob. 6ECh. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Prob. 14ECh. 7.4 - Prob. 15ECh. 7.4 - Prob. 16ECh. 7.4 - How many ordered lists are there of four items...Ch. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - Prob. 20ECh. 7.4 - Prob. 21ECh. 7.4 - Prob. 22ECh. 7.4 - Prob. 23ECh. 7.4 - Prob. 24ECh. 7.4 - Prob. 25ECh. 7.4 - Prob. 26ECh. 7.4 - How many six-letter sequences are possible that...Ch. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Prob. 31ECh. 7.4 - Prob. 32ECh. 7.4 - Prob. 33ECh. 7.4 - Prob. 34ECh. 7.4 - Prob. 35ECh. 7.4 - Marbles For Exercises 2942, a bag contains three...Ch. 7.4 - Prob. 37ECh. 7.4 - Prob. 38ECh. 7.4 - Prob. 39ECh. 7.4 - Prob. 40ECh. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - Prob. 44ECh. 7.4 - Prob. 45ECh. 7.4 - Prob. 46ECh. 7.4 - Prob. 47ECh. 7.4 - In Exercises 4752, calculate how many different...Ch. 7.4 - Prob. 49ECh. 7.4 - Prob. 50ECh. 7.4 - Prob. 51ECh. 7.4 - Prob. 52ECh. 7.4 - Prob. 53ECh. 7.4 - Prob. 54ECh. 7.4 - Poker Hands A poker hand consists of 5 cards from...Ch. 7.4 - Prob. 56ECh. 7.4 - Prob. 57ECh. 7.4 - Prob. 58ECh. 7.4 - Prob. 59ECh. 7.4 - Prob. 60ECh. 7.4 - Dogs of the Dow The Dogs of the Dow are the stocks...Ch. 7.4 - Dogs of the Dow The Dogs of the Dow are the stocks...Ch. 7.4 - Day Trading Day traders typically buy and sell...Ch. 7.4 - Day Trading Day traders typically buy and sell...Ch. 7.4 - Elimination Tournaments In an elimination...Ch. 7.4 - Elimination Tournaments In an elimination...Ch. 7.4 - Prob. 67ECh. 7.4 - Elimination Tournaments In an elimination...Ch. 7.4 - Prob. 69ECh. 7.4 - Prob. 70ECh. 7.4 - Prob. 71ECh. 7.4 - Prob. 72ECh. 7.4 - Prob. 73ECh. 7.4 - Prob. 74ECh. 7.4 - Prob. 75ECh. 7.4 - Prob. 76ECh. 7.4 - Prob. 77ECh. 7.4 - Prob. 78ECh. 7.4 - Prob. 79ECh. 7.4 - Prob. 80ECh. 7.4 - Prob. 81ECh. 7.4 - Prob. 82ECh. 7.4 - Prob. 83ECh. 7.4 - Prob. 84ECh. 7.4 - Prob. 85ECh. 7.4 - Prob. 86ECh. 7.4 - Prob. 87ECh. 7.4 - Complete the following: If a counting procedure...Ch. 7.4 - Prob. 89ECh. 7.4 - Prob. 90ECh. 7 - Prob. 1RECh. 7 - Prob. 2RECh. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 11RECh. 7 - Prob. 12RECh. 7 - Prob. 13RECh. 7 - Prob. 14RECh. 7 - Prob. 15RECh. 7 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - In Exercises 1924, consider a bag containing four...Ch. 7 - Prob. 20RECh. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Inventories OHaganBooks.com currently operates...Ch. 7 - Prob. 27RECh. 7 - Inventories OHaganBooks.com currently operates...Ch. 7 - Inventories OHaganBooks.com currently operates...Ch. 7 - Prob. 30RECh. 7 - Prob. 31RECh. 7 - Prob. 32RECh. 7 - Prob. 33RECh. 7 - Prob. 34RECh. 7 - Prob. 35RECh. 7 - Prob. 36RECh. 7 - Prob. 37RECh. 7 - Prob. 38RECh. 7 - Online IDs As the customer base at OHaganBooks.com...Ch. 7 - Online IDs As the customer base at OHaganBooks.com...Ch. 7 - Prob. 41RECh. 7 - Prob. 42RECh. 7 - Prob. 43RE
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