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nature of mathematics

Questions and Answers of Nature Of Mathematics

Santa Rosa Junior College enrolled 29,000 students in the fall of 2015. It was reported that of that number, 58% were female and 42% were male. In addition, 62% were over the age of 25. How many
The general Venn diagram for two sets has four regions (Figure 2.7), and the one for three sets has eight regions (Figure 2.10). Use patterns to develop a formula for the number of regions in a Venn
In Section 1.2, we used Euler circles to represent expressions such as “All Chevrolets are automobiles.” Rephrase this using set terminology.
In Section 1.2, we used Euler circles to represent expressions such as “Some people are nice.” Represent this relationship using Venn diagrams. Be sure to label the circles and the universe.
Each of the circles in Figure 2.12 is identified by a letter, each having a number value from 1 to 9. Where the circles overlap, the number is the sum of the values of the letters in the overlapping
Explain what is meant by the seven pattern.
Discuss the nature of inductive and deductive reasoning.
What do we mean by order of operations?
Explain inductive reasoning. Give an original example of an occasion when you have used inductive reasoning or heard it being used.
Does the B.C. cartoon illustrate inductive or deductive reasoning? Explain your answer. HOW CAN ANYONE PROVE THAT NO TWO SNOWFLAKES ARE ALIKE? Tust boida Hartuwe John Hart All ights reserved. ..IF
Explain deductive reasoning. Give an original example of an occasion when you have used deductive reasoning or heard it being used.
Does the news clip below illustrate inductive or deductive reasoning? Explain your answer. The old fellow in charge of the checkroom in a large hotel was noted for his memory. He never used checks
Problems 21–24 are modeled after Example 1. Find the requested pattern.Three patternData from Example 1Find the eight pattern.
Problems 21–24 are modeled after Example 1. Find the requested pattern.Four patternData from Example 1Find the eight pattern.
Problems 21–24 are modeled after Example 1. Find the requested pattern.Five patternData from Example 1Find the eight pattern.
Problems 21–24 are modeled after Example 1. Find the requested pattern.Six patternData from Example 1Find the eight pattern.
a. What is the sum of the first 25 consecutive odd numbers? 625b. What is the sum of the first 250 consecutive odd numbers? 62,500
a. What is the sum of the first 50 consecutive odd numbers?b. What is the sum of the first 1,000 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
Consider the square shown in Figure 1.11.Figure 1.11Is this a magic square? 10 14 13 15 7 8 11 12 10 11 11 12 13 11 15 14 16
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
Circle any number of the magic square in Figure 1.11. Cross out all the numbers in the same row and column. Then circle any remaining number and cross out all the numbers in the same row and column.
Complete the Sudoku puzzles in Problems 31–32. 3 دیا 8 2 4 3 نا 9 4 7 6 3 نیا 2 8 1 6 2 5 3 1 7 9 5 1 19 5 6 9 الا 6
Complete the Sudoku puzzles in Problems 31–32. 8 9 7 6 4 4 6 437 4 2 1 7 6 9 6 4 2 8 | | 8 00 | با 5 3 7 5 1 4 2 5 نیا 3
The following square of numbers consists of nine square numbers. Is this a magic square with nine distinct square numbers? 127² 2² 74² 46² 113² 82² 58² 94² 97²
The following square of numbers consists of nine square numbers. Is this a magic square with nine distinct square numbers? 3,495² 2,958² 1,785² 3,005² 35² 3,642² 2,125² 2,7752 2,058²
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.
Use Euler circles to check the validity of the arguments in Problems 35–46.All cats are animals.This is not an animal.Therefore, this is not a cat.
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 fatteningfood 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.
Use Euler circles to check the validity of the arguments in Problems 35–46.No professors are ignorant.All ignorant people are vain.Therefore, no professors are vain.
Use Euler circles to check the validity of the arguments in Problems 35–46.No monkeys are soldiers.All monkeys are mischievous.Therefore, some mischievous creatures are not soldiers.
Use Euler circles to check the validity of the arguments in Problems 35–46.All lions are fierce.Some lions do not drink coffee.Therefore, some fierce creatures do not drink coffee.
Refer to the lyrics of “By the Time I Get to Phoenix” on the next page. Tell whether each answer you give is arrived at inductively or deductively.a. In what basic direction (north, south, east,
Refer to the lyrics of “Ode to Billy Joe.” Tell whether each answer you give is arrived at inductively or deductively.a. How many people are involved in this story? List them by name and/or
Use Euler circles to check the validity of the arguments in Problems 35–46.All red hair is pretty.No pretty things are valuable.Therefore, no red hair is valuable.
Which direction is the bus traveling? Did you arrive at your answer using inductive or deductive reasoning? O O
Which is larger—the number of all seven-letter English words ending in ing, or the number of seven-letter words with “i” as the fifth letter? Did you arrive at your answer using inductive or
Consider the following pattern: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 9 × 987,654,321 - 1c. Use this
Consider the following pattern:123,456,789 × 9 = 1,111,111,101123,456,789 × 18 = 2,222,222,202123,456,789 × 27 = 3,333,333,303a. Use this pattern and inductive reasoning to find the next problem
What is the sum of the digits in 3333333342 Did you arrive at your answer using inductive or deductive reasoning?
Enter 999999 into your calculator, then divide it by seven.Now toss a die (or randomly pick a number from 1 through 6) and multiply this number by the displayed calculator number.Arrange the digits
How many squares are there in Figure 1.12?Figure 1.12
How many triangles are there in Figure 1.13?Figure 1.13
“Martin Gardner was one of the great intellects produced in this country in the 20th century,” said Douglas Hofstadtler. From 1956 to 1986, Gardner was the author of the “ Mathematical Games”
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 twopan
Now, a real $100 offer: Find a 3 × 3 magic square with nine distinct square numbers. If you find such a magic square, write to me and I will include it in the next edition and pay you a $100 reward.
Find a 5 × 5 magic square whose magic number is 44. That is, the sum of the rows, columns, and diagonals is 44. Furthermore, the square can be turned upside down without changing this property.
Ten full crates of walnuts weigh 410 pounds, whereas an empty crate weighs 10 pounds. How much do the walnuts alone weigh?
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
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.
In the chapter overview (did you read it?), it was pointed out that this text was written for people who think they don’t like mathematics, or people who think they can’t work math problems, or
In Example 1, we concluded that there were 6 different paths. List each of those paths.Data from Example 1In how many different ways could Melissa get from the YWCA (point A) to the St. Francis
At the beginning of this section, three hints for success were listed. Discuss each of these from your perspective. Are there any other hints that you might add to this list?
In Example 2, the solution was found by going 7 blocks down and 3 blocks over. Could the solution also have been obtained by going 3 blocks over and 7 blocks down? Would this solution end up in a
Describe the location of the numbers 1, 2, 3, 4, 5, . . . in Pascal’s triangle.
Describe the location of the numbers 1, 4, 10, 20, 35, . . . in Pascal’s triangle.
a. If a 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
In Problems 11–14, what is the number of direct routes from point A to point B? A B
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
In Problems 11–14, what is the number of direct routes from point A to point B? A B
In Problems 11–14, what is the number of direct routes from point A to point B? A B
In Problems 11–14, what is the number of direct routes from point A to point B? A 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.EFigure 1.6
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.FFigure 1.6
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.GFigure 1.6
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.HFigure 1.6
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
The ferry portion on the USS Nimitz houses 10 rows of parking spaces. Repeat Problem 19 for 10 rows instead of four.Data from Problem 19A car pulls onto the USS Nimitz, which is now a car ferry.As a
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
Jerry’s mother has three children. The oldest is a boy named Harry, who has brown eyes. Everyone says he is a math whiz. The next younger is a girl named Henrietta. Everyone calls her Mary because
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.JFigure 1.6
A deaf-mute walks into a stationery store and wants to purchase a pencil sharpener. To communicate this need, the customer pantomimes by sticking a finger in one ear and rotating the other hand
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.IFigure 1.6
a. What is the sum of the numbers in row 1 of Pascal’s triangle?b. What is the sum of the numbers in row 2 of Pascal’s triangle?c. What is the sum of the numbers in row 3 of Pascal’s
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.LFigure 1.6
What is the sum of the numbers in row n of Pascal’s 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.KFigure 1.6
How many 3-cent stamps are there in a dozen?
Which weighs more—a ton of coal or a ton of feathers?
If you take 7 cards from a deck of 52 cards, how many cards do you have?
Oak Park Cemetery in Oak Park, New Jersey, will not bury anyone living west of the Mississippi. Why?
If posts are spaced 10 feet apart, how many posts are needed for 100 feet of straight-line fence?
At six o’clock, the grandfather clock struck 6 times. If it was 30 seconds between the first and last strokes, how long will it take the same clock to strike noon?
A person arrives at home just in time to hear one chime from the grandfather clock. A half-hour later it strikes once. Another half-hour later it chimes once. Still another half-hour later it chimes
Two volumes of Newman’s The World of Mathematics stand side by side, in order, on a shelf. A bookworm starts at page i of Volume I and bores its way in a straight line to the last page of Volume
Two girls were born on the same day of the same month of the same year to the same parents, but they are not twins. Explain how this is possible.
How many outs are there in a baseball game that lasts the full 9 innings?
Two U.S. coins total $0.30, yet one of these coins is not a nickel. What are the coins?
A farmer has to get a fox, a goose, and a bag of corn across a river in a boat that is large enough only for him and one of these three items. If he leaves the fox alone with the goose, the fox will
Can you place ten lumps of sugar in three empty cups so that there is an odd number of lumps in each cup?
Six glasses are standing in a row. The first three are empty, and the last three are full of water. By handling and moving only one glass, it is possible to change this arrangement so that no empty
Suppose you have a long list of numbers to add, and you have misplaced your calculator. Discuss the different approaches that could be used for adding this column of numbers.
You are faced with a long division problem, and you have misplaced your calculator. You do not remember how to do long division. Discuss your alternatives to come up with the answer to your problem.
You have 10 items in your grocery cart. Six people are waiting in the express lane (10 items or less); one person is waiting in the first checkout stand and two people are waiting in another checkout
You drive up to your bank and see five cars in front of you waiting for two lanes of the drivethrough banking services. What additional information do you need in order to decide whether to drive

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