Bundle: Nature Of Mathematics, Loose-leaf Version, 13th + Webassign Printed Access Card For Smith's Nature Of Mathematics, 13th Edition, Single-term
13th Edition
ISBN: 9781337605076
Author: karl J. smith
Publisher: Cengage Learning
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Chapter 1.1, Problem 1PS
IN YOUR OWN WORDS In the text, it was stated that “the most important prerequisite for this course is an openness to try out new ideas-a willingness to experience the suggested activities rather than to sit on the sideline as a spectator.” Do you agree or disagree that this is the most important prerequisite? Discuss.
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Pidgeonhole Principle
1. The floor of x, written [x], also called the integral part, integer part, or greatest integer, is defined
as the greatest integer less than or equal to x. Similarly the ceiling of x, written [x], is the smallest
integer greater than or equal to x. Try figuring out the answers to the following:
(a) [2.1]
(b) [2]
(c) [2.9]
(d) [2.1]
(e) [2]
(f) [2.9]
2. The simple pidgeonhole principle states that, if you have N places and k items (k> N), then at
least one hole must have more than one item in it. We tried this with chairs and students: Assume you
have N = 12 chairs and k = 18 students. Then at least one chair must have more than one student on
it.
3. The general pidgeonhole principle states that, if you have N places and k items, then at least one
hole must have [] items or more in it. Try this out with
(a) n = 10 chairs and k = 15 students
(b) n = 10 chairs and k = 23 students
(c) n = 10 chairs and k = 20 students
4. There are 34 problems on these pages, and we…
Determine if the set of vectors is linearly independent or linearly dependent.
linearly independent
O linearly dependent
Save Answer
Q2.2
1 Point
Determine if the set of vectors spans R³.
they span R³
they do not span R³
Save Answer
23
Q2.3
1 Point
Determine if the set of vectors is linearly independent or linearly dependent.
linearly independent
O linearly dependent
Save Answer
1111
1110
Q2.4
1 Point
Determine if the set of vectors spans R4.
O they span R4
they do not span IR4
1000;
111O'
The everything combined problem
Suppose that a computer science laboratory has 15 workstations and 10 servers. A cable can be used to
directly connect a workstation to a server. For each server, only one direct connection to that server can be
active at any time.
1. How many cables would you need to connect each station to each server?
2. How many stations can be used at one time?
3. How many stations can not be used at any one time?
4. How many ways are there to pick 10 stations out of 15?
5. (This one is tricky) We want to guarantee that at any time any set of 10 or fewer workstations can
simultaneously access different servers via direct connections. What is the minimum number of direct
connections needed to achieve this goal?
Chapter 1 Solutions
Bundle: Nature Of Mathematics, Loose-leaf Version, 13th + Webassign Printed Access Card For Smith's Nature Of Mathematics, 13th Edition, Single-term
Ch. 1.1 - IN YOUR OWN WORDS In the text, it was stated that...Ch. 1.1 - IN YOUR OWN WORDS What do you think the primary...Ch. 1.1 - Prob. 3PSCh. 1.1 - Prob. 4PSCh. 1.1 - IN YOUR OWN WORDS In Example 1, we concluded that...Ch. 1.1 - Prob. 6PSCh. 1.1 - Describe the location of the numbers 1, 2,3, 4,5,...Ch. 1.1 - Describe the location of the numbers 1,4,10,20,35,...Ch. 1.1 - a.If family has 5 children, in how many ways could...Ch. 1.1 - a. If a family has 7 children, in how many ways...
Ch. 1.1 - In Problems 11-14, what is the number of direct...Ch. 1.1 - In Problems 11-14, what is the number of direct...Ch. 1.1 - In Problems 11-14, what is the number of direct...Ch. 1.1 - In Problems 1114, what is the number of direct...Ch. 1.1 - Use the map in Figure 1.6 to determine the number...Ch. 1.1 - Prob. 16PSCh. 1.1 - Prob. 17PSCh. 1.1 - Prob. 18PSCh. 1.1 - A car pulls onto the USS Nimitz, which is now a...Ch. 1.1 - The ferry portion on the USS Nimitz, houses 10...Ch. 1.1 - Ten full crates of walnuts weith 410 pounds,...Ch. 1.1 - There are three separate, equal-size boxes, and...Ch. 1.1 - Prob. 23PSCh. 1.1 - Prob. 24PSCh. 1.1 - a. What is the sum of the numbers in row 1 of...Ch. 1.1 - What is the sum of the numbers in row n of Pascals...Ch. 1.1 - Use the map in Figure 1.6 to determine the number...Ch. 1.1 - Prob. 28PSCh. 1.1 - Prob. 29PSCh. 1.1 - Use the map in Figure 1.6 to determine the number...Ch. 1.1 - Problems 31-44 are not typical math problems but...Ch. 1.1 - Problems 31-44 are not typical math problems but...Ch. 1.1 - Problems 31-44 are not typical math problems but...Ch. 1.1 - Problems 31-44 are not typical math problems but...Ch. 1.1 - Prob. 35PSCh. 1.1 - Prob. 36PSCh. 1.1 - Prob. 37PSCh. 1.1 - Prob. 38PSCh. 1.1 - Problems 31-44 are not typical math problems but...Ch. 1.1 - Prob. 40PSCh. 1.1 - Prob. 41PSCh. 1.1 - Problems 31-44 are not typical math problems but...Ch. 1.1 - Problems 31-44 are not typical math problems but...Ch. 1.1 - Prob. 44PSCh. 1.1 - Prob. 45PSCh. 1.1 - Prob. 46PSCh. 1.1 - Prob. 47PSCh. 1.1 - Prob. 48PSCh. 1.1 - A boy cyclist and a girl cyclist are 10 miles...Ch. 1.1 - Prob. 50PSCh. 1.1 - Alex, Beverly, and Cal live on the same straight...Ch. 1.1 - In a different language, liro cas means red...Ch. 1.1 - Prob. 53PSCh. 1.1 - Prob. 54PSCh. 1.1 - Prob. 55PSCh. 1.1 - The number 6 has four divisorsnamely, 1,2,3, and...Ch. 1.1 - Consider the routes from A to B and notice that...Ch. 1.1 - HISTORICAL QUEST Thoth, an ancient Egyptian god of...Ch. 1.1 - A magician divides a deck of cards into two equal...Ch. 1.1 - Prob. 60PSCh. 1.2 - IN YOUR OWN WORDS Discuss the nature of inductive...Ch. 1.2 - IN YOUR OWN WORDS Explain what is meant by the...Ch. 1.2 - IN YOUR OWN WORDS What do you mean by order of...Ch. 1.2 - IN YOUR OWN WORDS What is the scientific method?Ch. 1.2 - IN YOUR OWN WORDS Explain inductive reasoning....Ch. 1.2 - IN YOUR OWN WORDS Explain deductive reasoning....Ch. 1.2 - Perform the operations in Problems 7-18. a. 5+26...Ch. 1.2 - Perform the operations in Problems 7-18. a. 14+63...Ch. 1.2 - Perform the operations in Problems 7-18. a. 38+37...Ch. 1.2 - Perform the operations in Problems 7-18. a. (8+6)2...Ch. 1.2 - Prob. 11PSCh. 1.2 - Prob. 12PSCh. 1.2 - Prob. 13PSCh. 1.2 - Prob. 14PSCh. 1.2 - Prob. 15PSCh. 1.2 - Prob. 16PSCh. 1.2 - Prob. 17PSCh. 1.2 - Perform the operations in Problems 7-18. a....Ch. 1.2 - Does the B.C. cartoon illustrate inductive or...Ch. 1.2 - Does the news clip below illustrate inductive or...Ch. 1.2 - Problems 21-24 are modelled after Example 1. Find...Ch. 1.2 - Problems 21-24 are modelled after Example 1. Find...Ch. 1.2 - Problems 21-24 are modelled after Example 1. Find...Ch. 1.2 - Problems 21-24 are modelled after Example 1. Find...Ch. 1.2 - a. What is the sum of the first 25 consecutive odd...Ch. 1.2 - a. What is the sum of the first 50 consecutive odd...Ch. 1.2 - The first known example of a magic square comes...Ch. 1.2 - HISTORICAL QUEST The Lo-shu magic square in...Ch. 1.2 - Consider the square shown in Figure 1.11. 10 7 8...Ch. 1.2 - Prob. 30PSCh. 1.2 - HISTORICAL QUEST Magic squares remind us of Sudoku...Ch. 1.2 - HISTORICAL QUEST Magic squares remind us of Sudoku...Ch. 1.2 - Prob. 33PSCh. 1.2 - Prob. 34PSCh. 1.2 - Use Euler circles to check the validity of the...Ch. 1.2 - Use Euler circles to check the validity of the...Ch. 1.2 - Prob. 37PSCh. 1.2 - Use Euler circles to check the validity of the...Ch. 1.2 - Use Euler circles to check the validity of the...Ch. 1.2 - Use Euler circles to check the validity of the...Ch. 1.2 - Use Euler circles to check the validity of the...Ch. 1.2 - Use Euler circles to check the validity of the...Ch. 1.2 - Prob. 43PSCh. 1.2 - Prob. 44PSCh. 1.2 - Prob. 45PSCh. 1.2 - Prob. 46PSCh. 1.2 - Prob. 47PSCh. 1.2 - Prob. 48PSCh. 1.2 - Which direction is the bus travelling? Did you...Ch. 1.2 - Prob. 50PSCh. 1.2 - Consider the following pattern:...Ch. 1.2 - Consider the following pattern:...Ch. 1.2 - What is the sum of the digits in 3333333342. Did...Ch. 1.2 - Prob. 54PSCh. 1.2 - How many squares are there in Figure 1.11? FIGURE...Ch. 1.2 - How many triangles are there in Figure 1.12?...Ch. 1.2 - You have 9 coins, but you are told that one of the...Ch. 1.2 - Prob. 58PSCh. 1.2 - Prob. 59PSCh. 1.2 - Prob. 60PSCh. 1.3 - Level 1 IN YOUR OWN WORDS What do we mean by...Ch. 1.3 - Level 1 IN YOUR OWN WORDS Define scientific...Ch. 1.3 - Level 1 IN YOUR OWN WORDS Do you plan to use a...Ch. 1.3 - Level 1 4. IN YOUR OWN WORDS Describe differences...Ch. 1.3 - Level 1 IN YOUR OWN WORDS What is the largest...Ch. 1.3 - Level 1 IN YOUR OWN WORDS What is a trillion? Do...Ch. 1.3 - Level 1 Write each of the numbers in Problems 7-10...Ch. 1.3 - Level 1 Write each of the numbers in Problems 7-10...Ch. 1.3 - Level 1 Write each of the numbers in Problems 7-10...Ch. 1.3 - Level 1 Write each of the numbers in Problems 7-10...Ch. 1.3 - Prob. 11PSCh. 1.3 - Prob. 12PSCh. 1.3 - Prob. 13PSCh. 1.3 - Prob. 14PSCh. 1.3 - Prob. 15PSCh. 1.3 - Level 1 Write each of the numbers in Problemc15-18...Ch. 1.3 - Level 1 Write each of the numbers in Problemc15-18...Ch. 1.3 - Prob. 18PSCh. 1.3 - Prob. 19PSCh. 1.3 - Prob. 20PSCh. 1.3 - Prob. 21PSCh. 1.3 - Prob. 22PSCh. 1.3 - Prob. 23PSCh. 1.3 - Prob. 24PSCh. 1.3 - Prob. 25PSCh. 1.3 - Prob. 26PSCh. 1.3 - Prob. 27PSCh. 1.3 - Prob. 28PSCh. 1.3 - Level 1 In problems 25-30, first estimate your...Ch. 1.3 - Prob. 30PSCh. 1.3 - Prob. 31PSCh. 1.3 - Prob. 32PSCh. 1.3 - Prob. 33PSCh. 1.3 - Level 2 Compute the results in Problems 31-36....Ch. 1.3 - Prob. 35PSCh. 1.3 - Level 2 Compute the results in Problems 31-36....Ch. 1.3 - Prob. 37PSCh. 1.3 - Prob. 38PSCh. 1.3 - Prob. 39PSCh. 1.3 - Prob. 40PSCh. 1.3 - Prob. 41PSCh. 1.3 - Prob. 42PSCh. 1.3 - Prob. 43PSCh. 1.3 - Prob. 44PSCh. 1.3 - Prob. 45PSCh. 1.3 - Level 2 In Problems 41-48, you need to make some...Ch. 1.3 - Prob. 47PSCh. 1.3 - Prob. 49PSCh. 1.3 - Level 3 HISTORICAL QUEST Zerah Colburn 1804-1840...Ch. 1.3 - Prob. 51PSCh. 1.3 - Prob. 52PSCh. 1.3 - Level 3 The Library of Congress contains about 35...Ch. 1.3 - Level 3 A sheet of notebook paper is approximately...Ch. 1.3 - Prob. 55PSCh. 1.3 - Problem Solving Level 3 If it takes one second to...Ch. 1.3 - Prob. 57PSCh. 1.3 - Prob. 58PSCh. 1.3 - Prob. 59PSCh. 1.3 - Problem Solving Level 3 It is known that a persons...Ch. 1.CR - In your own words Compare and contrast the...Ch. 1.CR - IN YOUR OWN WORDS Describe Polyas problem-solving...Ch. 1.CR - Prob. 3CRCh. 1.CR - Compute 111,111,111111,111,111. Do not use direct...Ch. 1.CR - Prob. 5CRCh. 1.CR - Prob. 6CRCh. 1.CR - Prob. 7CRCh. 1.CR - Prob. 8CRCh. 1.CR - Prob. 9CRCh. 1.CR - Prob. 10CRCh. 1.CR - Prob. 11CRCh. 1.CR - Prob. 12CRCh. 1.CR - Rearrange the cards in the formation shown here so...Ch. 1.CR - Prob. 15CRCh. 1.CR - Prob. 16CRCh. 1.CR - Prob. 17CRCh. 1.CR - Prob. 18CRCh. 1.CR - Prob. 19CRCh. 1.CR - Prob. 20CR
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