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All Textbook Solutions for Nature of Mathematics (MindTap Course List)

IN YOUR OWN WORDS The prologue provides a historical overview and asks the question, Why Math? This question seems appropriate at the beginning of a college mathematics course. Why do you think it is important to study mathematics?IN YOUR OWN WORDS The epilogue for this text provides an essay of how the material of this text relates specifically to the natural sciences, social sciences, and humanities. In a sense, this is a recap of the question in Problem 1. In the prologue you are looking forward to the text and in the epilogue you are looking backward at what you did in the text. In epilogue, we ask the question, Why not Math?To answer this question, write a few paragraphs about why someone would not study mathematics.HISTORICAL QUEST What are the five chronological historical periods into which the prologue is divided? Which period seems the most interesting to you, and why?HISTORICAL QUEST Select what you believe to be the most interesting cultural event and the most interesting mathematical event of the Ancient Period.HISTORICAL QUEST Select what you believe to be the most interesting cultural event and the most interesting mathematical event of the Hindu and Persian Period.HISTORICAL QUEST Select what you believe to be the most interesting cultural event and the most interesting mathematical event of the Transition Period.HISTORICAL QUEST Select what you believe to be the most interesting cultural event and the most interesting mathematical event of the Age of Reason.HISTORICAL QUEST Select what you believe to be the most interesting cultural event and the most interesting mathematical event of the Modern Period.IN YOUR OWN WORDS This prologue has 60 problems as does every problem set in this text, but at this point you have no basis for working the problems in this set. Read, but DO NOT WORK, Problems 11-60. a. From this set of problems, name 10 problems that you think you might be able to answer correctly. b. From this set of problems, name 10 problems that you know you would not able to answer correctly.IN YOUR OWN WORDS Problems 11-60 are included to give a quick overview of what this text is about. Select five problems you would like to learn how to solve.In mathematics, is is important to read the directions before attempting to work any problems. You are NOT expected to able to work any problems. You are NOT expected to be able to work Problems 11-60 at this time. You ARE expected to be able to work those problems AFTER reading this text. So for now, just place each assigned question in one of the following categories: Yes. I know how to start this problem. No. I dont think I know how to start this problem. Hopeful. If someone shows me how to proceed, I think I could answer this question. Hopeless. I dont think Ill ever be able to answer this question. A long, straight fence having a pole every 8 ft is 1, 440 ft long. How many fence poles are needed for the fence?In mathematics, is is important to read the directions before attempting to work any problems. You are NOT expected to able to work any problems. You are NOT expected to be able to work Problems 11-60 at this time. You ARE expected to be able to work those problems AFTER reading this text. So for now, just place each assigned question in one of the following categories: Yes. I know how to start this problem. No. I dont think I know how to start this problem. Hopeful. If someone shows me how to proceed, I think I could answer this question. Hopeless. I dont think Ill ever be able to answer this question. How many cards must you from a deck of 52 playing cards to be sure that at least two are from the same suit?How many people must be in a room to be sure that at least four of them have the same birthday not necessarily the same year?In mathematics, is is important to read the directions before attempting to work any problems. You are NOT expected to able to work any problems. You are NOT expected to be able to work Problems 11-60 at this time. You ARE expected to be able to work those problems AFTER reading this text. So for now, just place each assigned question in one of the following categories: Yes. I know how to start this problem. No. I dont think I know how to start this problem. Hopeful. If someone shows me how to proceed, I think I could answer this question. Hopeless. I dont think Ill ever be able to answer this question. Find the units digit of 32015-22015.If a year had two consecutive months with a Friday the thirteenth, which months would they have to be?On Saturday evenings, a favourite pastime of the high school students in Santa Rosa, California, is to cruise certain streets. The selected routes are shown in the following illustration. Is it possible to choose a route so that all of the permitted streets are travelled exactly once?In mathematics, is is important to read the directions before attempting to work any problems. You are NOT expected to able to work any problems. You are NOT expected to be able to work Problems 11-60 at this time. You ARE expected to be able to work those problems AFTER reading this text. So for now, just place each assigned question in one of the following categories: Yes. I know how to start this problem. No. I dont think I know how to start this problem. Hopeful. If someone shows me how to proceed, I think I could answer this question. Hopeless. I dont think Ill ever be able to answer this question. What is the largest number that is the divisor of both 210 and 330?In mathematics, is is important to read the directions before attempting to work any problems. You are NOT expected to able to work any problems. You are NOT expected to be able to work Problems 11-60 at this time. You ARE expected to be able to work those problems AFTER reading this text. So for now, just place each assigned question in one of the following categories: Yes. I know how to start this problem. No. I dont think I know how to start this problem. Hopeful. If someone shows me how to proceed, I think I could answer this question. Hopeless. I dont think Ill ever be able to answer this question. The news print shows a letter printed in the Ask Marilyn column of Parade Magazine Sept. 27, 1992. How would you answer it?If the population of the world on October 12,2002, was 6.248 billion, when do you think the world population should have reached 7 billion? Calculate the date to the nearest month using the information that the world population reached 6 billion on October 12,1999. The world population actually reached 7 billion on October 31,2011. What does this say about your prediction?20PS In mathematics, is is important to read the directions before attempting to work any problems. You are NOT expected to able to work any problems. You are NOT expected to be able to work Problems 11-60 at this time. You ARE expected to be able to work those problems AFTER reading this text. So for now, just place each assigned question in one of the following categories: Yes. I know how to start this problem. No. I dont think I know how to start this problem. Hopeful. If someone shows me how to proceed, I think I could answer this question. Hopeless. I dont think Ill ever be able to answer this question. If a,b=ab+a+b, what is the value of 1, 2,3, 4?22PS In mathematics, is is important to read the directions before attempting to work any problems. You are NOT expected to able to work any problems. You are NOT expected to be able to work Problems 11-60 at this time. You ARE expected to be able to work those problems AFTER reading this text. So for now, just place each assigned question in one of the following categories: Yes. I know how to start this problem. No. I dont think I know how to start this problem. Hopeful. If someone shows me how to proceed, I think I could answer this question. Hopeless. I dont think Ill ever be able to answer this question. If 1 is the first odd number, what is the 473 rd odd number?In mathematics, is is important to read the directions before attempting to work any problems. You are NOT expected to able to work any problems. You are NOT expected to be able to work Problems 11-60 at this time. You ARE expected to be able to work those problems AFTER reading this text. So for now, just place each assigned question in one of the following categories: Yes. I know how to start this problem. No. I dont think I know how to start this problem. Hopeful. If someone shows me how to proceed, I think I could answer this question. Hopeless. I dont think Ill ever be able to answer this question. If 1+2+3++n=nn+12, what is the sum of the first 100, 000 counting numbers beginning with 1?In mathematics, is is important to read the directions before attempting to work any problems. You are NOT expected to able to work any problems. You are NOT expected to be able to work Problems 11-60 at this time. You ARE expected to be able to work those problems AFTER reading this text. So for now, just place each assigned question in one of the following categories: Yes. I know how to start this problem. No. I dont think I know how to start this problem. Hopeful. If someone shows me how to proceed, I think I could answer this question. Hopeless. I dont think Ill ever be able to answer this question. A four-inch cube is painted red on all sides. It is cut into one-inch cubes. What fraction of all the one-inch cubes are painted on one side only?In mathematics, is is important to read the directions before attempting to work any problems. You are NOT expected to able to work any problems. You are NOT expected to be able to work Problems 11-60 at this time. You ARE expected to be able to work those problems AFTER reading this text. So for now, just place each assigned question in one of the following categories: Yes. I know how to start this problem. No. I dont think I know how to start this problem. Hopeful. If someone shows me how to proceed, I think I could answer this question. Hopeless. I dont think Ill ever be able to answer this question. If slot machines had two arms and people had one arm, then it is probable that our number system would be based on the digits 0,1,2,3, and 4 only. How would the number we know as 18 be written in such a number system?In mathematics, is is important to read the directions before attempting to work any problems. You are NOT expected to able to work any problems. You are NOT expected to be able to work Problems 11-60 at this time. You ARE expected to be able to work those problems AFTER reading this text. So for now, just place each assigned question in one of the following categories: Yes. I know how to start this problem. No. I dont think I know how to start this problem. Hopeful. If someone shows me how to proceed, I think I could answer this question. Hopeless. I dont think Ill ever be able to answer this question. If Ma,b stands for the larger number in the parentheses, and ma,b stands for the lesser number in the parentheses, what is the value of Mm1, 2,m2, 3?If a group of 50 persons consists of 20 males, 12 children and 25 women, how many men are in the group?In mathematics, is is important to read the directions before attempting to work any problems. You are NOT expected to able to work any problems. You are NOT expected to be able to work Problems 11-60 at this time. You ARE expected to be able to work those problems AFTER reading this text. So for now, just place each assigned question in one of the following categories: Yes. I know how to start this problem. No. I dont think I know how to start this problem. Hopeful. If someone shows me how to proceed, I think I could answer this question. Hopeless. I dont think Ill ever be able to answer this question. There are only five regular polyhedra, and Figure 7 shows the patterns that give those polyhedra. Name the polyhedron obtained from each of the patterns shown.30PS What is the 1,000th positive integer that is not divisible by 3?In mathematics, is is important to read the directions before attempting to work any problems. You are NOT expected to able to work any problems. You are NOT expected to be able to work Problems 11-60 at this time. You ARE expected to be able to work those problems AFTER reading this text. So for now, just place each assigned question in one of the following categories: Yes. I know how to start this problem. No. I dont think I know how to start this problem. Hopeful. If someone shows me how to proceed, I think I could answer this question. Hopeless. I dont think Ill ever be able to answer this question. A frugal man allows himself a glass of wine before dinner on every third day, an after-dinner chocolate every fifth day, and a steak dinner once a week. If it happens that he enjoys all three luxuries on March 31, what will be the date of the next steak dinner that is preceded by wine and followed by an after-dinner chocolate?How many trees must be cut to make a trillion one-dollar bills? To answer this question, you need to make some assumptions. Assume that a pound of paper is equal to a pound of wood and also assume that a dollar bill weighs about one gram. This implies that a pound of wood yields about 450 dollar bills. Furthermore, estimate that an average tree has a height of 50ft and a diameter of 12 inches. Finally, assume that wood yields about 50lb/ft3.34PS Critique the statement given in the news clip.In mathematics, is is important to read the directions before attempting to work any problems. You are NOT expected to able to work any problems. You are NOT expected to be able to work Problems 11-60 at this time. You ARE expected to be able to work those problems AFTER reading this text. So for now, just place each assigned question in one of the following categories: Yes. I know how to start this problem. No. I dont think I know how to start this problem. Hopeful. If someone shows me how to proceed, I think I could answer this question. Hopeless. I dont think Ill ever be able to answer this question. The two small circles have radii of 2 and 3. Find the ratio of the area of the smallest circle to the area of the shaded region.37PS The map shows the percent of children ages 19-35 months who are immunized by the state. What conclusion can you draw from this map?39PS Find limn(1+1n)n.41PS 42PS Suppose the percentage of alcohol in the blood t hours after consumption is given by C(t)=0.3et/2. What is the rate at which the percentage of alcohol is changing with respect to time?44PS A map of small village is shown in Figure 8. To walk from A to B, Sarah obviously must walk at least 7 blocks all the blocks are the same length. What is the number of shortest paths from A to B? FIGURE 8 A village map A hospital wishes to provide for its patients a diet that has a minimum of 100 g of carbohydrates, 60 g of protein, and 40 g of fats per day. These requirements can be met with two foods: Food Carbohydrates Protein Fats A 6g/oz 3g/oz 1g/oz B 2g/oz 2g/oz 2g/oz It is also important to minimize costs; food A costs 0.14 per ounce and food B costs 0.06 per ounce. How many ounces of each food should be bought for each patient per day to meet the minimum daily requirements at the lowest cost?47PS Find the smallest number of operations needed to build up to the number 100 if you start at 0 and use only two operations: doubling or increasing by 1. Challenge: Answer the same question if you want to build up any positive integer n.If log2x+log4x=logbx, what is b?Supply the missing number in the following sequence: 10,11,12,13,14,15,16,17,20,22,24,_,100,121,10,000.51PS Answer the question asked in the news clip from Ask Marilyn column of Parade Magazine July 16, 1995.Five cards are drawn at random from a pack of cards that have been numbered consecutively from 1 to 104 and have been thoroughly shuffled. What is the probability that the numbers on the cards as they are drawn are in increasing order of magnitude?What is the sum of the counting numbers from 1 to 104?The Kabbalah is a body of mystical teaching from the Torah. One medieval inscription is shown on the left: The inscription on the left shows Hebrew characters that can be translated into numbers, as shown at the right. What can you say about this pattern of numbers?What is the maximum number of points of intersection of n distinct lines?The equation P=153,000e0.05t represents the population of a city t years after 2000. What is the population of the city in the year 2000? Show a graph of the citys population for the next 20 years.The Egyptians had an interesting, pictorial numeration system. Here is how you would count using Egyptian numerals: ,,,,,,,,,,,,,. Write down your age using Egyptian numerals. The symbol | is called a stroke, and is called a heel bone. The Egyptians used a scroll for 100, a lotus flower for 1,000, a pointing finger for 10,000, a polliwog for 100,000, and an astonished man for the number 1,000,000. Without doing any research, write what you think todays date would look like using Egyptian numerals.If you start with 1 and double the amount received on the previous day, how much money will you have in 30 days?Consider two experiments and events defined as follows: Experiment A: Roll one die 4 times and keep a record of how many times you obtain at least one 6. Event E={obtainatleastone6in4rollsofasingledie} Experiment B: Roll a pair of dice 24 times and keep a record of how many times you obtain at least one 12. Event F={obtainatleastone12in24rollsofapairofdice} Do you think event E or event F is more likely? You might whish to experiment by rolling dice.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.IN YOUR OWN WORDS What do you think the primary goal of mathematics education should be? What do you think it is in the United States? Discuss the differences between what it is and what you think it should be.3PS 4PS IN YOUR OWN WORDS In Example 1, we concluded that there were 6 different paths. List each of those paths. Example 1 Problem solving-from here to there In how many different ways could Melissa get from the YWCA point A to the St. Francis Hotel point C in Figure 1.1, using the method of Figure 1.3?6PS Describe the location of the numbers 1, 2,3, 4,5, in Pascals triangle.Describe the location of the numbers 1,4,10,20,35, in Pascals triangle.a.If family has 5 children, in how many ways could the parents have 2 boys and 3 girls as children? b.If a family has 6 children, in how many ways could the parents have 3 boys and 3 girls as children?a. If a family has 7 children, in how many ways could the parents have 4 boys and 3 girls as children? b. If a family has 8 children, in how many ways could the parents have 3 boys and 5 girls as children?In Problems 11-14, what is the number of direct routes from point A to point B?In Problems 11-14, what is the number of direct routes from point A to point B?In Problems 11-14, what is the number of direct routes from point A to point B?In Problems 1114, what is the number of direct routes from point A to point B?Use the map in Figure 1.6 to determine the number of different paths from point A to the point indicated in Problems 15-18. Remember, no backtracking is allowed. E 16PS 17PS 18PS A car pulls onto the USS Nimitz, which is now a car ferry. As a car enters the ferry, there are four rows of traffic directors arranged in a triangular pattern, such that one director is in the first row, two in the second, three in the third, and four in the fourth row. They are directing traffic into five parking spots, labelled A through E in Figure 1.7 FIGURE 1.7 Traffiic directors lead cars to spaces. Given that cars must proceed according to the traffic arrows, how many different paths are there into each of the parking spots?The ferry portion on the USS Nimitz, houses 10 rows of parking spaces. Repeat Problem 19 for 10 rows instead of four. Problem 19: A car pulls onto the USS Nimitz, which is now a car ferry. As a car enters the ferry, there are four rows of traffic directors arranged in a triangular pattern, such that one director is in the first row, two in the second, three in the third, and four in the fourth row. They are directing traffic into five parking spots, labelled A through E in Figure 1.7 FIGURE 1.7 Traffiic directors lead cars to spaces. Given that cars must proceed according to the traffic arrows, how many different paths are there into each of the parking spots?Ten full crates of walnuts weith 410 pounds, whereas an empty create withgs 10 pounds. How much do the walnuts alone weigh?There are three separate, equal-size boxes, and inside each box there are two separate small boxes, and inside each of the small boxes there are three even smaller boxes. How many boxes are there all together?23PS 24PS a. What is the sum of the numbers in row 1 of Pacals triangle? b.What is the sum of the numbers in row 2 of Pascals triangle? c.What is the sum of the numbers in row 3 of Pascals triangle? d.What is the sum of the numbers in row 4 of Pascals triangle?What is the sum of the numbers in row n of Pascals triangle?Use the map in Figure 1.6 to determine the number of different paths from point A to the point indicated in Problems 27-30. Remember, no backtracking is allowed. J 28PS 29PS Use the map in Figure 1.6 to determine the number of different paths from point A to the point indicated in Problems 27-30. Remember, no backtracking is allowed. K Problems 31-44 are not typical math problems but are problems that require only common sense and sometimes creative thinking How many 3-cent stamps are there in a dozen?Problems 31-44 are not typical math problems but are problems that require only common sense and sometimes creative thinking Which weighs morea ton of coal or a ton of feathers?Problems 31-44 are not typical math problems but are problems that require only common sense and sometimes creative thinking If you take 7 cards from a deck of 52 cards, how many cards do you have?Problems 31-44 are not typical math problems but are problems that require only common sense and sometimes creative thinking Oak Park Cementry in Oak Park, New Jersey, will not bury anyone living west of the Missisippi. Why?35PS 36PS 37PS 38PS Problems 31-44 are not typical math problems but are problems that require only common sense and sometimes creative thinking How many outs are there in a baseball game that lasts the full 9 innings?40PS 41PS Problems 31-44 are not typical math problems but are problems that require only common sense and sometimes creative thinking A farmer has to get a fox, a goose, and a bag of corn across a river in a boat that is large enoughonly for him and one of these three items. If he leaves the fox alone with the goose, the fox will eat the goose. If he leaves the goose alone with the corn, the goose will eat the corn. How does he get all the items across the river?Problems 31-44 are not typical math problems but are problems that require only common sense and sometimes creative thinking Can you place ten lumps of sugar in three empty cups so that there is an odd number of lumps in each cup?44PS 45PS 46PS 47PS 48PS A boy cyclist and a girl cyclist are 10 miles apart and pedaling toward each other. The boys rate is 6 miles per hour, and the girls rate is 4 miles per hour. There is also a friendly fly zooming continuously back and forth from one bike to other. If the flys rate is 20 miles per hour, by the time the cyclists reach each other, how far does the fly fly?50PS Alex, Beverly, and Cal live on the same straight road. Alex lives 10 miles from Beverly, and Cal lives 2 miles from Beverly. How far does Alex live from Cal?In a different language, liro cas means red tomato. The meaning of dum cas dan is big red barn and xer dan means big horse. What are the words for red barn in this language?53PS 54PS 55PS The number 6 has four divisorsnamely, 1,2,3, and 6. List all numbers less than 20 that have exactly four divisors.Consider the routes from A to B and notice that there is now a barricade blocking the path. Work out a general solution for the number of paths with a blockade, and then illustrate your general solution by giving the number of paths for each of the following street patterns.HISTORICAL QUEST Thoth, an ancient Egyptian god of wisdom and learning, has abducted Ahmes, a famous Egyptian scribe, in order to assess his intellectual prowess. Thoth places Ahmes before a large funnel set in the ground see Figure 1.8 on the nest page. It has a circular opening 1,000 ft in diameter, and its walls are quite slippery. If Ahmes attempts to enter the funnel, he will slip down the wall. At the bottom of the funnel is a sleep-inducing liquid that will instantly put Ahmes to sleep for eight hours if he touches it. Thoth hands Ahmes two objects: a rope 1, 006.28 ft in length and the skull of a chicken. Thoth says to Ahmes, If you are able to get to the central tower and touch it, we will live in harmony for the next millennium. If not, I will detain you for further testing. Please note that with each passing hour, I will decrease the ropes length by a foot. How can Ahmes reach the central ankh tower and touch it? Note that there are two ankh-shaped towers. One stands on a cylindrical platform in the center of the funnel. The platforms surface is at ground level. The distance from the surface to the liquid is 500 ft. The other ankh tower is on the land, at the edge of the funnel.A magician divides a deck of cards into two equal piles, counts down from the top of the first pile to the seventh card, and shows it to the audience without looking at it herself. These seven cards are replaced face down in the same order on top of the first pile. She then picks up the other pile and deals the top three cards up in a row in front of her. If the first card is a six, then she starts counting with six and counts to ten, thus placing four more cards on this pile as shown. In turn, the magician does the same for the next two cards. If the card is a ten or a face card, then no additional cards are added. The remainder of this pile is placed on top of the first pile. Next, the magician adds the values of the three face-ups cards 6107 for this illustration and counts down in the first deck this number of cards. That card is the card that was originally shown to the audience. Explain why this trick works.60PS IN YOUR OWN WORDS Discuss the nature of inductive and deductive reasoning.IN YOUR OWN WORDS Explain what is meant by the seven pattern.IN YOUR OWN WORDS What do you mean by order of operations?IN YOUR OWN WORDS What is the scientific method?IN YOUR OWN WORDS Explain inductive reasoning. Give an original example of an occasion when you have used inductive reasoning or heard it being used.IN YOUR OWN WORDS Explain deductive reasoning. Give an original example of an occasion when you have used deductive reasoning or heard it being used.Perform the operations in Problems 7-18. a. 5+26 b. 7+32 Perform the operations in Problems 7-18. a. 14+63 b. 3052 Perform the operations in Problems 7-18. a. 38+37 b. 3(8+7)Perform the operations in Problems 7-18. a. (8+6)2 b. 8+62 11PS 12PS 13PS 14PS 15PS 16PS 17PS Perform the operations in Problems 7-18. a. 3+[(93)2]+[(26)3] b. [(3+9)(32)]+[(26)3]Does the B.C. cartoon illustrate inductive or deductive reasoning? Explain your answer.Does the news clip below illustrate inductive or deductive reasoning? Explain your answer.Problems 21-24 are modelled after Example 1. Find the requested pattern. three pattern Problems 21-24 are modelled after Example 1. Find the requested pattern. four pattern Problems 21-24 are modelled after Example 1. Find the requested pattern. five pattern Problems 21-24 are modelled after Example 1. Find the requested pattern. six pattern a. What is the sum of the first 25 consecutive odd numbers? b. What is the sum of the first 250 consecutive odd numbers?a. What is the sum of the first 50 consecutive odd numbers? b. What is the sum of the first 1000 consecutive odd numbers?The first known example of a magic square comes from China. Legend tells us that around the year 200 B.C. the emperor Yu of the Shang dynasty received the following magic square etched on the back of a tortoises shell: The incident supposedly took place along the Lo River, so this magic square has come to be known as the Lo-shu magic square. The even numbers are black female numbers and the odd numbers are white male numbers. Translate this magic square into modern symbols. This same magic square called wafq in Arabic appears in Islamic literature in the 10th century A.D. and is attributed to Jabir ibn Hayyan.HISTORICAL QUEST The Lo-shu magic square in problem 27 has the even numbers in black yin numbers and the odd numbers in white yang. What is the relationship between the yin and the yang numbers in this magic square? Do you think this is a coincidence, a special property of the Lo-shu square, or is it something else?Consider the square shown in Figure 1.11. 10 7 8 11 14 11 12 15 13 10 11 14 15 12 13 16 Figure 1.11 Magic square? Is this a magic square?30PS HISTORICAL QUEST Magic squares remind us of Sudoku number puzzles. Sudoku or su doku is a number puzzle, usually consisting of a 99 grid divided into nine 33 boxes, into which numbers already appear in a few cells. You may have seen such a puzzle online or in your newspaper, but would you believe that Sudoku was invented by a 74-year-old Indianapolis man who never received credit for his invention of this type of puzzle problem? In May 1979, a puzzle created by Howard Gams was published, but few paid attention. Then, in April 1984, Japans puzzle group Nikoli discovered Garnss puzzle, invented the word SudokuSu = number, Doku = singletrademarked the name, and published new versions of the puzzle. At that time, and with this new name, the puzzle became a worldwide phenomenon. The object of the puzzle is to complete all the remaining cells with the numbers from 1 to 9, so that: each row contains all the numbers from 1 to 9 each column contains all the numbers from 1 to 9 each 33 box contains all the numbers from 1 to 9 Complete the Sudoku puzzles in Problems 31-32.HISTORICAL QUEST Magic squares remind us of Sudoku number puzzles. Sudoku or su doku is a number puzzle, usually consisting of a 99 grid divided into nine 33 boxes, into which numbers already appear in a few cells. You may have seen such a puzzle online or in your newspaper, but would you believe that Sudoku was invented by a 74-year-old Indianapolis man who never received credit for his invention of this type of puzzle problem? In May 1979, a puzzle created by Howard Gams was published, but few paid attention. Then, in April 1984, Japans puzzle group Nikoli discovered Garnss puzzle, invented the word SudokuSu = number, Doku = singletrademarked the name, and published new versions of the puzzle. At that time, and with this new name, the puzzle became a worldwide phenomenon. The object of the puzzle is to complete all the remaining cells with the numbers from 1 to 9, so that: each row contains all the numbers from 1 to 9 each column contains all the numbers from 1 to 9 each 33 box contains all the numbers from 1 to 9 Complete the Sudoku puzzles in Problems 31-32.33PS 34PS Use Euler circles to check the validity of the arguments in Problems 35-46. All mathematicians are eccentrics. All eccentrics are rich. Therefore, all mathematicians are rich.Use Euler circles to check the validity of the arguments in Problems 35-46. All snarks are fribbles. All fribbles are ugly. Therefore, all snarks are ugly.37PS Use Euler circles to check the validity of the arguments in Problems 35-46. All bachelors are handsome. Some bachelors do not drink lemonade. Therefore, some handsome men do not drink lemonade.Use Euler circles to check the validity of the arguments in Problems 35-46. No students are enthusiastic. You are enthusiastic. Therefore, you are not a student.Use Euler circles to check the validity of the arguments in Problems 35-46. No politicians are honest. Some dishonest people are found out. Therefore, some politicians are found out.Use Euler circles to check the validity of the arguments in Problems 35-46. All candy is fattening. All candy is delicious. Therefore, all fattening food is delicious.Use Euler circles to check the validity of the arguments in Problems 35-46. All parallelograms are rectangles. All rectangles are polygons. Therefore, all parallelograms are polygons.43PS 44PS 45PS 46PS 47PS 48PS Which direction is the bus travelling? Did you arrive at your answer using inductive or deductive reasoning?50PS Consider the following pattern: 911=89211=18893211=2888943211=38888 a. Use this pattern and inductive reasoning to find the next problem and the next answer in the sequence. b. Use this pattern to find 99876543211 c. Use this pattern to find 910,9876543211 Consider the following pattern: 1234567899=111111110112345678918=222222220212345678927=3333333303 a. Use this pattern and inductive reasoning to find the next problem and the next answer in the sequence. b. Use this pattern to find 1234567899000 c. Use this pattern to find 12345678981000 What is the sum of the digits in 3333333342. Did you arrive at your answer using inductive or deductive reasoning?54PS How many squares are there in Figure 1.11? FIGURE 1.12 How many squares?How many triangles are there in Figure 1.12? FIGURE 1.13 How many triangles?You have 9 coins, but you are told that one of the coins is counterfeit and weighs just a little more than an authentic coin. How can you determine the counterfeit with 2 weighings on a two-pan balance scale? This problem is discussed in Chapter 2.58PS 59PS 60PS Level 1 IN YOUR OWN WORDS What do we mean by exponent?Level 1 IN YOUR OWN WORDS Define scientific notation and discuss why it is useful.Level 1 IN YOUR OWN WORDS Do you plan to use a calculator for working in this text? If so, what type of logic does it use?Level 1 4. IN YOUR OWN WORDS Describe differences in evaluating exponents and using scientific notation on a calculator.Level 1 IN YOUR OWN WORDS What is the largest number whose name you know? Describe the size of this number.Level 1 IN YOUR OWN WORDS What is a trillion? Do not simply define this number, but discuss its magnitude size in terms that are easy to understand.Level 1 Write each of the numbers in Problems 7-10 in scientific notation and in floating-point notation as on calculator. a. 3, 200 b. 0.0004 c. 64, 000, 000, 000 Level 1 Write each of the numbers in Problems 7-10 in scientific notation and in floating-point notation as on calculator. a. 23.79 b. 0.000001 c. 35, 000, 000, 000 Level 1 Write each of the numbers in Problems 7-10 in scientific notation and in floating-point notation as on calculator. a. 5, 629 b. 630, 000 c. 0.00000 0034 Level 1 Write each of the numbers in Problems 7-10 in scientific notation and in floating-point notation as on calculator. a. googol b. 1, 200, 300 c. 0.00000 123 11PS 12PS 13PS 14PS 15PS Level 1 Write each of the numbers in Problemc15-18 in scientific notation. The velocity of light in a vacuum is about 30, 000, 000, 000 cm/sec.Level 1 Write each of the numbers in Problemc15-18 in scientific notation. The distance between earth and Mars 220, 000, 000 miles when drawn to scale is 0.0000025 in.18PS 19PS 20PS 21PS 22PS 23PS 24PS 25PS 26PS 27PS 28PS Level 1 In problems 25-30, first estimate your answer and then calculate the exact answer. In the musical Rent, there is a song called Seasons of Love that uses the number 525, 600 minutes. How long is this?30PS 31PS 32PS 33PS Level 2 Compute the results in Problems 31-36. Leave your answers in scientific notation. a. (2xy2)(21x1y4)x2y2 b. x2y(2x3y5)22x4y8 35PS Level 2 Compute the results in Problems 31-36. Leave your answers in scientific notation. a. 4,500,000,000,0000.00001500.0003 b. 0.03480.0000000000000020.0000580.03 37PS 38PS 39PS 40PS 41PS 42PS 43PS 44PS 45PS Level 2 In Problems 41-48, you need to make some assumptions before you estimate your answer. State your assumptions and then calculate the exact answer. The San Francisco Examiner February 6, 2000, Travel Section reported that David Phillips, a civil engineer at University of California, Davis, was pushing his shopping cart when he noticed a promotion of Healthy Choice. He could earn 1, 000 airline miles for every 10 bar codes from Healthy Choice products he sent to the company by the end of the month. Frozen entries are about 2 apiece, but with a little work he found individual servings of chocolate pudding for 25 cents each. He was able to accumulate 1, 215, 000 airline miles. How much did it cost him?47PS 49PS Level 3 HISTORICAL QUEST Zerah Colburn 1804-1840 toured America when he was 6 years old to display his calculating ability. He could instantaneously give the square and cube roots of large numbers. It is reported that it took him only a few Seconds to find 816. Use your calculator to help you find this number exactly not in scientific notation.51PS 52PS Level 3 The Library of Congress contains about 35 million books, and this is about 10 terabytes. A recent study by IBM estimates that humanity creates about 2.5 quintillion bytes of data every day. Compare this amount of daily data creation photos, videos, social-media posts, word-processing files, phone-call records, financial records, and so on with the data stored in the Library of Congress. Which do you think is larger? Now, calculate the exact answer by converting 2.5 quintillion bytes to terabytes. What is the number of exabytes of worldwide data generated each year?Level 3 A sheet of notebook paper is approximately 0.003 in. thick. Tear the sheet in half so that there are 2 sheets. Repeat so that there are 4 sheets. If you repeat again, there will be a pile of 8 sheets. Continue in this fashion until the paper has been halved 50 times. If it were possible to complete the process, how high would you guess the final pile would be? After you have guessed, compute the height.55PS Problem Solving Level 3 If it takes one second to write down each digit, how long will it take to write down all the numbers from 1 to 1, 000, 000?57PS 58PS 59PS Problem Solving Level 3 It is known that a persons body has about one gallon of blood in it, and that a cubic foot will hold about 7.5 gallons of liquid. It is also known that Central Park in New York has an area of 840 acres. If walls were built around the park, how tall would those walls need to be to contain the blood of all 7, 350, 000, 000 people in the world?In your own words Compare and contrast the following news clip and the fable in the chapter opening on page 2 with your own experiences in learning mathematics.IN YOUR OWN WORDS Describe Polyas problem-solving model.3CR Compute 111,111,111111,111,111. Do not use direct multiplication; show all your work.5CR 6CR 7CR 8CR 9CR 10CR 11CR 12CR Rearrange the cards in the formation shown here so that each horizontal, vertical, and diagonal line of three adds up to 15.15CR 16CR 17CR 18CR 19CR 20CR 1PS IN YOUR OWN WORDS Distinguish between equal and equivalent sets.3PS 4PS Tell whether each set in Problems 5-8 is well defined. If it is not well defined, change it so that it is well defined. a. The set of students attending the University of California b. Grains of sand on earth 6PS Tell whether each set in Problems 5-8 is well defined. If it is not well defined, change it so that it is well defined. a. Good bets on the next race at Hialeah b. Years that will be bumper years for growing corn in Iowa Tell whether each set in Problems 5-8 is well defined. If it is not well defined, change it so that it is well defined. a. Counting number less than 0 b. The set of people with pointed ears Specify the sets in Problems 9-14 by roster. a. Distinct letters in the word mathematics b. Current U.S. president Specify the sets in Problems 9-14 by roster. a. Odd counting numbers less than 11 b. Positive multiples of 3 11PS 12PS Specify the sets in Problems 9-14 by roster. a. Distinct letters in the word pipe b. Counting numbers greater than 150 Specify the sets in Problems 9-14 by roster. a. Counting numbers containing only 1s b. Even counting numbers between 5 and 15 15PS 16PS 17PS 18PS 19PS 20PS 21PS 22PS 23PS 24PS 25PS 26PS 27PS 28PS 29PS 30PS 31PS 32PS 33PS 34PS 35PS 36PS 37PS 38PS 39PS 40PS 41PS 42PS

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