Mathematical Ideas (13th Edition) - Standalone book
13th Edition
ISBN: 9780321977076
Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren
Publisher: PEARSON
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Chapter 1.2, Problem 29E
To determine
To calculate:
The next equation and verify that it is indeed a true statement.
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6. Let A, B, and C be arbitrary sets. Prove that A - (BNC) = (A - B) U (A – C)
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{-2, 1, 4, 7, 10,..., 52}
{{7,9}, 2, {1, 2, 3, 4, 7}, {9}, {0}}
A system of inequalities is shown.
y
5
3
2
1
X
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2
3
4
5
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Which system is represented in the graph?
Oy>-x²-x+1
y 2x²+3
-2
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Chapter 1 Solutions
Mathematical Ideas (13th Edition) - Standalone book
Ch. 1.1 - The next number in the pattern 2,4,6,8,10 is 12Ch. 1.1 - My dog barked and woke me up at 1:02 a.m., 2:03...Ch. 1.1 - To find the perimeter P of a square with side of...Ch. 1.1 - A company charges a 10% re-stocking fee for...Ch. 1.1 - In Exercises 1-16, determine whether the reasoning...Ch. 1.1 - 6. If you take your medicine, you’ll feel a lot...Ch. 1.1 - It has rained every day for the past six days, and...Ch. 1.1 - 8. Carrie’s first five children were boys. If she...Ch. 1.1 - 9. The 2000 movie Cast Away stars Tom Hanks as the...Ch. 1.1 - 10. If the same number is subtracted from both...
Ch. 1.1 - If you build it, they will come. You build it....Ch. 1.1 - 12. All men are mortal. Socrates is a man....Ch. 1.1 - It is a fact that every student who ever attended...Ch. 1.1 - For the past 126 years, a rare plant has bloomed...Ch. 1.1 - 15. In the sequence 5, 10, 15, 20, 25,..., the...Ch. 1.1 - 16. (This anecdote is adapted from a story by...Ch. 1.1 - 17. Discuss the differences between inductive and...Ch. 1.1 - 18. Give an example of faulty inductive...Ch. 1.1 - Determine the most probable next term in each of...Ch. 1.1 - Determine the most probable next term in each of...Ch. 1.1 - 21. 3, 12, 48, 192, 768
Ch. 1.1 - 32, 16,8,4,2Ch. 1.1 - 3, 6, 9, 15, 24, 39Ch. 1.1 - 13,35,57,79,911Ch. 1.1 - 25.
Ch. 1.1 - 1,4, 9, 16, 25Ch. 1.1 - 27. 1, 8, 27, 64, 125
Ch. 1.1 - 28. 2, 6, 12, 20, 30, 42
Ch. 1.1 - Determine the most probable next term in each of...Ch. 1.1 - 30. 27, 21, 16, 12, 9
Ch. 1.1 - 31. 5, 3, 5, 5, 3, 5, 5, 5, 3, 5, 5, 5, 5, 3, 5,...Ch. 1.1 - 8, 2, 8, 2, 2, 8, 2, 2, 2, 8, 2, 2, 2, 2, 8, 2, 2,...Ch. 1.1 - 33. Construct a list of numbers similar to those...Ch. 1.1 - 34. Construct a list of numbers similar to those...Ch. 1.1 - Prob. 35ECh. 1.1 - 36.
Ch. 1.1 - 37.
Ch. 1.1 - 38.
Ch. 1.1 - 39.
Ch. 1.1 - 40.
Ch. 1.1 - 41.
Ch. 1.1 - 42.
Ch. 1.1 - 43.
Ch. 1.1 - 3=3(31)23+9=3(91)23+9+27=3(271)23+9+27+81=3(811)2Ch. 1.1 - 12=11212+14=11412+14+18=11812+14+18+116=1116Ch. 1.1 - 46.
Ch. 1.1 - Prob. 47ECh. 1.1 - 48.
Ch. 1.1 - 1+2+3++800Ch. 1.1 - 1+2+3++2000Ch. 1.1 - Modify the procedure of Gauss to find the sum .
Ch. 1.1 - Explain in your own words how the procedure of...Ch. 1.1 - Prob. 53ECh. 1.1 - 53. Modify the procedure of Gauss to find the sum...Ch. 1.1 - 55. What is the most probable next number in this...Ch. 1.1 - Prob. 56ECh. 1.1 - 57. Choose any three-digit number with all...Ch. 1.1 - 58. Choose any number, and follow these steps.
a....Ch. 1.1 - Complete the following....Ch. 1.1 -
60. Refer to Figures 2 (b)–(e) and Figure 3....Ch. 1.2 - For each sequence, determine if it is an...Ch. 1.2 - For each sequence, determine if it is an...Ch. 1.2 - For each sequence, determine if it is an...Ch. 1.2 - For each sequence, determine if it is an...Ch. 1.2 - For each sequence, determine if it is an...Ch. 1.2 - Prob. 6ECh. 1.2 - Prob. 7ECh. 1.2 - For each sequence, determine if it is an...Ch. 1.2 - For each sequence, determine if it is an...Ch. 1.2 - For each sequence, determine if it is an...Ch. 1.2 - Prob. 11ECh. 1.2 - Prob. 12ECh. 1.2 - Use the method of successive differences to...Ch. 1.2 - 3, 14, 31, 54, 83, 118, Use the method of...Ch. 1.2 - Use the method of successive differences to...Ch. 1.2 - Use the method of successive differences to...Ch. 1.2 - Use the method of successive differences to...Ch. 1.2 - Use the method of successive differences to...Ch. 1.2 - Use the method of successive differences to...Ch. 1.2 - Use the method of successive differences to...Ch. 1.2 - Prob. 21ECh. 1.2 - 22. The 1952 film Hans Christian Andersen stars...Ch. 1.2 - Prob. 23ECh. 1.2 - Prob. 24ECh. 1.2 - Prob. 25ECh. 1.2 - In Exercises 23-32, several equations are given...Ch. 1.2 - Prob. 27ECh. 1.2 - Prob. 28ECh. 1.2 - Prob. 29ECh. 1.2 - Prob. 30ECh. 1.2 - Prob. 31ECh. 1.2 - Prob. 32ECh. 1.2 - Use the formula S=1(n+1)2 to find each sum....Ch. 1.2 - Prob. 34ECh. 1.2 - Prob. 35ECh. 1.2 - Prob. 36ECh. 1.2 - Prob. 37ECh. 1.2 - Prob. 38ECh. 1.2 - Use the formula S=n2 to find each sum (Hint: To...Ch. 1.2 - Prob. 40ECh. 1.2 - Prob. 41ECh. 1.2 - Prob. 42ECh. 1.2 - Prob. 43ECh. 1.2 - Prob. 44ECh. 1.2 - Prob. 45ECh. 1.2 - Prob. 46ECh. 1.2 - Prob. 47ECh. 1.2 - Prob. 48ECh. 1.2 - Prob. 49ECh. 1.2 - 50. Exercises 48 and 49 are specific cases of the...Ch. 1.2 - Prob. 51ECh. 1.2 - Prob. 52ECh. 1.2 - Prob. 53ECh. 1.2 - Prob. 54ECh. 1.2 - the ninth pentagonal numbers SCh. 1.2 - 56. the seventh hexagonal number
Ch. 1.2 - 57. the tenth heptagonal number |
Ch. 1.2 - Prob. 58ECh. 1.2 - Prob. 59ECh. 1.2 - Prob. 60ECh. 1.2 - Prob. 61ECh. 1.2 - Prob. 62ECh. 1.2 - Prob. 63ECh. 1.2 - Prob. 64ECh. 1.2 - Prob. 65ECh. 1.2 - Prob. 66ECh. 1.2 - Prob. 67ECh. 1.2 - 68. The 36th term of 8, 38, 68, 98,...
Ch. 1.2 - Prob. 69ECh. 1.2 - Prob. 70ECh. 1.2 - Prob. 71ECh. 1.2 - Prob. 72ECh. 1.2 - Prob. 73ECh. 1.2 - Prob. 74ECh. 1.2 - Prob. 75ECh. 1.2 - Prob. 76ECh. 1.2 - Prob. 77ECh. 1.2 - Prob. 78ECh. 1.2 - Prob. 79ECh. 1.2 - Prob. 80ECh. 1.2 - Prob. 81ECh. 1.2 - Prob. 82ECh. 1.3 - Broken Elevator A man enters a building on the...Ch. 1.3 - Use the various problem-solving strategies to...Ch. 1.3 - Do You Have a Match? Move 4 of the matches in the...Ch. 1.3 - Sudoku Sudoku is an puzzle that requires the...Ch. 1.3 - Use the various problem-solving strategies to...Ch. 1.3 - A Real Problem We are given the following...Ch. 1.3 - How Old Is Mommy? A mother has two children whose...Ch. 1.3 - An Alarming Situation You have three alarms in...Ch. 1.3 - Laundry Day Every Monday evening, a mathematics...Ch. 1.3 - Pick an Envelope Three envelopes contain a total...Ch. 1.3 - Class Members A classroom contains an equal number...Ch. 1.3 - Prob. 12ECh. 1.3 - Missing Digit Look for a pattern and find the...Ch. 1.3 - 14. Abundancy An integer is abundant if the sum...Ch. 1.3 - Cross-Country Competition The schools in an...Ch. 1.3 - Gone Fishing Four friends go fishing one day and...Ch. 1.3 - Cutting a Square in Half In how many ways can a...Ch. 1.3 - You Lie! Max, Sam, and Brett were playing...Ch. 1.3 - Bookworm Snack A 26-volume encyclopedia (one for...Ch. 1.3 - Pick a Card, Any Card Three face cards from an...Ch. 1.3 - 21. Catwoman’s Cats If you ask Batman’s nemesis,...Ch. 1.3 - Pencil Collection Bob gave four-fifths of his...Ch. 1.3 - Adding Gasoline The gasoline gauge on a van...Ch. 1.3 - 24. Gasoline Tank Capacity When 6 gallons of...Ch. 1.3 - Number Pattern What is the relationship between...Ch. 1.3 - 26. Locking Boxes You and I each have one lock and...Ch. 1.3 - 27. Number in a Sequence In the sequence 16, 80,...Ch. 1.3 - Unknown Number Cindy was asked by her teacher to...Ch. 1.3 - 29. Unfolding and Folding a Box An unfolded box is...Ch. 1.3 - Prob. 30ECh. 1.3 - Labeling Boxes You are working in a store that has...Ch. 1.3 - Mr. Greens Age At his birthday party, Mr. Green...Ch. 1.3 - 33. Sum of Hidden Dots on Dice Three dice with...Ch. 1.3 - 34. Age of the Bus Driver Today is your first day...Ch. 1.3 - 35. Matching Triangles and Squares How can you...Ch. 1.3 - 36. Forming Perfect Square Sums How must one place...Ch. 1.3 - Difference Triangle Balls numbered 1 through 6 are...Ch. 1.3 - Clock Face By drawing two straight lines, divide...Ch. 1.3 - Alphametric If a, b, and c are digits for which...Ch. 1.3 - Perfect Square Only one of these numbers is a...Ch. 1.3 - Sleeping on the Way to Grandmas House While...Ch. 1.3 - Buckets of Water You have brought two unmarked...Ch. 1.3 - Counting Puzzle (Rectangles) How many rectangles...Ch. 1.3 - Digit Puzzle Place each of the digits 1, 2, 3, 4,...Ch. 1.3 - 45. Palindromic Number (Note: A palindromic number...Ch. 1.3 - 46. How Much Is That Doggie in the Window? A man...Ch. 1.3 - Final Digits of a Power of 7 What are the final...Ch. 1.3 - 48. Units Digit of a Power of 3 If you raise 3 to...Ch. 1.3 - Summing the Digits When 10 - 50 is expressed as a...Ch. 1.3 - 50. Frog Climbing up a Well A frog is at the...Ch. 1.3 - 51. Units Digit of a Power of 7 What is the units...Ch. 1.3 - Prob. 52ECh. 1.3 - Going Postal Joanie wants to mail a package that...Ch. 1.3 - 54. Counting Puzzle (Squares) How many squares are...Ch. 1.3 - Matching Socks A drawer contains 20 black socks...Ch. 1.3 - Prob. 56ECh. 1.3 - 57. Perfect Number A perfect number is a counting...Ch. 1.3 - Naming Children Beckys mother has three daughters....Ch. 1.3 - 59. Growth of a Lily Pad A lily pad grows so that...Ch. 1.3 - Prob. 60ECh. 1.3 - Prob. 61ECh. 1.3 - Prob. 62ECh. 1.3 - Adam and Eves Assets Eve said to Adam, If you give...Ch. 1.3 - Prob. 64ECh. 1.3 - Prob. 65ECh. 1.3 - Prob. 66ECh. 1.3 - Prob. 67ECh. 1.3 - Prob. 68ECh. 1.3 - 69. Pitches in a Baseball Game What is the minimum...Ch. 1.3 - 70. Weighing Coins You have eight coins. Seven are...Ch. 1.3 - 71. Geometry Puzzle When the diagram shown is...Ch. 1.3 - Prob. 72ECh. 1.3 - Prob. 73ECh. 1.3 - Prob. 74ECh. 1.3 - 75. Paying for a Mint Brian has an unlimited...Ch. 1.3 - Prob. 76ECh. 1.3 - Prob. 77ECh. 1.3 - Prob. 78ECh. 1.3 - Prob. 79ECh. 1.3 - Prob. 80ECh. 1.3 - Prob. 81ECh. 1.3 - Making Change Webster has some pennies, dimes, and...Ch. 1.4 - 39.7+(8.24.1)Ch. 1.4 - Prob. 2ECh. 1.4 - Prob. 3ECh. 1.4 - Prob. 4ECh. 1.4 - Prob. 5ECh. 1.4 - Prob. 6ECh. 1.4 - Prob. 7ECh. 1.4 - Prob. 8ECh. 1.4 - 5.765Ch. 1.4 - Prob. 10ECh. 1.4 - Prob. 11ECh. 1.4 - Prob. 12ECh. 1.4 - Prob. 13ECh. 1.4 - Prob. 14ECh. 1.4 - Prob. 15ECh. 1.4 - Prob. 16ECh. 1.4 - Prob. 17ECh. 1.4 - Prob. 18ECh. 1.4 - Prob. 19ECh. 1.4 - Prob. 20ECh. 1.4 - Prob. 21ECh. 1.4 - Prob. 22ECh. 1.4 - Prob. 23ECh. 1.4 - Prob. 24ECh. 1.4 - Prob. 25ECh. 1.4 - Prob. 26ECh. 1.4 - Prob. 27ECh. 1.4 - Prob. 28ECh. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.4 - Prob. 31ECh. 1.4 - Prob. 32ECh. 1.4 - Find the decimal representation of 16 on your...Ch. 1.4 - Prob. 34ECh. 1.4 - 35. Choose any digit except 0. Multiply it by 429....Ch. 1.4 - Prob. 36ECh. 1.4 - 37. Pages to Store Trading Cards A plastic page...Ch. 1.4 - Prob. 38ECh. 1.4 - Prob. 39ECh. 1.4 - Prob. 40ECh. 1.4 - Price per Acre of Land To build a millennium clock...Ch. 1.4 - Prob. 42ECh. 1.4 - In Exercises 41-46, use estimation to determine...Ch. 1.4 - 44. Revolutions of Mercury The planet Mercury...Ch. 1.4 - Reception Average In 2013, A. J. Green of the...Ch. 1.4 - Prob. 46ECh. 1.4 - Foreign-Born Americans Approximately 37.5 million...Ch. 1.4 - Prob. 48ECh. 1.4 - Prob. 49ECh. 1.4 - Prob. 50ECh. 1.4 - Prob. 51ECh. 1.4 - Prob. 52ECh. 1.4 - Prob. 53ECh. 1.4 - Describe the change from 2004 to 2010. U.S. Car...Ch. 1.4 - Prob. 55ECh. 1.4 - Prob. 56ECh. 1.4 - Prob. 57ECh. 1.4 - Prob. 58ECh. 1.4 - Prob. 59ECh. 1.4 - The Simpsons The longest-running animated...Ch. 1.4 - Donald in Mathmagic Land One of the most popular...Ch. 1.4 - Prob. 62ECh. 1 - In Exercises 1 and 2 decide whether the reasoning...Ch. 1 - In Exercises 1 and 2, decide whether the reasoning...Ch. 1 - Counting Puzzle (Rectangles) How many rectangles...Ch. 1 - Use the list of equations and inductive reasoning...Ch. 1 - Use the method of successive differences to find...Ch. 1 - Find the sum 1+2+3++250.Ch. 1 - 7 Consider the following equations, where the left...Ch. 1 - Use the result of Exercise 7 and the method of...Ch. 1 - 9 Describe the pattern used to obtain the terms of...Ch. 1 - Use problem-solving strategies to solve each...Ch. 1 - Units Digit of a Power of 9 What is the units...Ch. 1 - Counting Puzzle (Triangles) How many triangles are...Ch. 1 - Make Them Equal Consider the following...Ch. 1 - Prob. 14TCh. 1 - 15 Units Digit of a Sum Find the units digit (ones...Ch. 1 - Prob. 16TCh. 1 - Prob. 17TCh. 1 - Use your calculator to evaluate each of the...Ch. 1 - Prob. 19TCh. 1 - Unemployment Rate The line graph shows the overall...
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- Which set of systems of equations represents the solution to the graph? -5 -4 -3 -2 Of(x) = x² + 2x + 1 g(x) = x²+1 f(x) = x²+2x+1 g(x) = x²-1 f(x) = −x² + 2x + 1 g(x) = x²+1 f(x) = x² + 2x + 1 g(x) = x²-1 -1 5 y 4 3 2 1 0 -1- -2 -3- -4. -5 1 2 3 4 5arrow_forwardWhich of the graphs below correctly solves for x in the equation -x² - 3x-1=-x-4? о 10 8 (0,2) -10 -8 -6 -2 2 4 6 8 10 (-4,-2) -2 + (0,2) (4,6) -10-8-6-4-2 -2 2 4 6 8 10 (-3, -1) -2 2 (1-5) -6 -8 -10 10 -10-8-6-4-2 2 6 8 10 (2,0)arrow_forwardUnit 1: Logic 1. Let P be the statement "x > 5” and let Q be the statement “y +3≤ x," and let R be the statement “y Є Z.” (a) Translate the following statements to English. (b) Negate the statements symbolically (c) Write the negated statements in English. The negations should not include any implications. • (QV¬R) AP • (P⇒¬Q) VR • (PVQ)¬R 2. Let R, S, and T be arbitrary statements. Write out truth tables for the following statements. Determine whether they are a tautology or a contradiction or neither, with justification. ⚫ (RAS) V (¬R ⇒ S) (R¬S) V (RAS) • (TA (SV¬R)) ^ [T⇒ (R^¬S)]arrow_forward
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- 8. Give three statements that are logically equivalent to x ≥ 0⇒ (x² = 0V −x < 0). You may use any equivalences that you like.arrow_forward3. Let P, Q, and R be arbitrary statements, and let x E R. Determine whether the statements below are equivalent using whatever method you like. • • -[-P → (QVR)] and ¬(¬P V Q) A¬R (PA¬Q) ⇒(¬PVS) and (SVP) VQ • x = 4 and √√√x=2 x = 4 and x2. = 16arrow_forward2. Claim events on a portfolio of insurance policies follow a Poisson process with parameter A. Individual claim amounts follow a distribution X with density: f(x)=0.0122re001, g>0. The insurance company calculates premiums using a premium loading of 45%. (a) Derive the moment generating function Mx(t).arrow_forward
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