- Construct a Koch snowflake by beginning with an equilateral triangle and replacing each side with a . Repeat this process twice.
- Develop a fractal by beginning with a square and replacing each sidewith a . Repeat this process twice.
- Determine the ratio of the length to width of various photographs and compare these ratios to Ф.
- Determine the ratio of the length to the width of your cell phone screen and compare this ratio to Φ.
- Using the Internet, determine the current 10 highest-paid athletes in each of the following sports organizations: Major League Baseball, the National Football League, the National Basketball
- Do research and write a report on the Huntington–Hill method, the current method used to apportion the representatives in the House of Representatives. Include historical background and describe
- Research and write a report on how voting is conducted on one of the following events: (a) Academy Awards (b) Grammy Awards (e) Pulitzer Prize (c) Heisman Trophy Award (d) Nobel Prizes Include in
- Do research and write a report on the apportionment method used in the House of Representatives in 1872. Include in your report a description of the method used.
- Construct a preference table showing 12 votes for 3 candidates, A, B, and C, where candidates A and B both have 5 first-place votes.
- Write a research paper on the history of voting methods. Include how the flaws in the voting methods discussed in this section were uncovered.
- Choose a country other than the United States and write a research paper on how the president or prime minister is chosen. Describe in detail the voting method used. Include the strengths and
- Construct a preference table with four candidates and three rankings of the candidates, similar to the preference table in Exercise 29, such that the pairwise comparison method violates the
- Construct a preference table with three candidates and four rankings of the candidates, similar to the preference table in Exercise 10, such that the plurality with elimination method violates the
- Construct a preference table with three candidates and three rankings of the candidates, similar to the preference table in Exercise 9, such that the Borda count method violates the majority
- Construct a preference table with four candidates and four rankings of the candidates, similar to the preference table in Exercise 11, such that the plurality method violates the head-to-head
- Write a paper on which apportionment method you think is the best. Include reasons to support your choice, including the advantages and disadvantages of the method you have selected.
- Write a paper on the history and development of the branch of mathematics known as knot theory. Include a discussion on its applications to science and technology.
- Choose a continent other than North America or Australia and create a graph showing the common boundaries between countries. Be sure to use a current map.
- Use a graph to represent (a) The floor plan of your home. (b) The streets in your neighborhood within 1/2 mile from your home in all directions.
- Poll your entire class to determine which students knew each other prior to taking this course. Draw a graph that shows this relationship.
- Write a paper on traveling salesman problems. Include a brief history of the problems. Also include advances made toward reducing the computational time of deter-mining the optimal solution as well
- Write a research paper on the life and work of Joseph Kruskal, who developed Kruskal’s algorithm.
- Create a minimum-cost spanning tree that would serve as the least expensive way to provide sheltered sidewalks between major buildings on your college campus. Assume that the cost per foot is the
- Create a tree that shows the administrative structure at your college or university. Start with the highest-ranking officer (that is, president, chancellor, provost) and work down to the department
- Come up with a list of five cities you would like to visit. Use the Internet to search for airline prices between these five cities. Make sure to include the city with the airport nearest your home
- Create a minimum-cost spanning tree that would serve as the least expensive way to create a computer network among the five largest cities in your state. Assume that the cost per mile is the same
- In this project, you actually become the statistician.(a) Select a project of interest to you in which data must be collected.(b) Write a proposal and submit it to your instructor for approval. In
- Ask your instructor for the class mean and class standard deviation for one of the exams taken by your class. For that exam, calculate the z-score for your exam grade. How many standard deviations is
- Obtain a set of test scores from your instructor.(a) Determine the mean, median, mode, and midrange of the test scores.(b) Determine the range and standard deviation of the set of scores. (You may
- List three populations other than those given in the text that may not be normally distributed.
- List three populations other than those given in the text that may be normally distributed.
- Two other measures of location that we did not mention in this section are stanines and deciles. Use statistics books, books on educational testing and measurements, and Internet websites to write a
- (a) Calculate the mean, median, mode, and midrange of your exam grades in your mathematics course.(b) Which measure of central tendency best represents your average grade? (c) Which measure of
- Find a scatter diagram in a newspaper or magazine and write a paper on what the diagram indicates. Indicate whether you believe that the bivariate data show a positive correlation, a negative
- Use the following list which shows the names of the 43 U.S. presidents and the number of children in their families. Is this set of data representative of the U.S. population? Explain. W. H.
- (a) Obtain a set of bivariate data from a newspaper or magazine.(b) Plot the information on a scatter diagram.(c) Indicate whether you believe that the data show a positive correlation, a negative
- Use the following list which shows the names of the 43 U.S. presidents and the number of children in their families. Do you think the number of children per family in the United States is a normal
- (a) Select a category of bivariate data that you think has a strong positive correlation. Designate the independent variable and the dependent variable. Explain why you believe that the bivariate
- Read the book How to Lie with Statistics by Darrell Huff and write a book report on it. Select three illustrations from the book that show how people manipulate statistics.
- (a) Do you believe that a correlation exists between a person?s height and the length of a person?s arm? (b) Select 10 people from your class and measure (in inches) their height and the length of
- Select one type of sampling technique and write a report on how statisticians obtain that type of sample. Also indicate when that type of sampling technique may be preferred. List two examples of
- (a) Select and indicate a topic and population of interest to which a random sampling technique can be applied to obtain data.(b) Explain how you or your group would obtain a random sample for your
- Find five advertisements or commercials that may be statistically misleading. Explain why each may be misleading.
- Repeat Exercise 37 for the last digit of the students’ Social Security numbers. Include classes for the digits 0–9.Data from Exercise 37:What do you believe a histogram of the months in which the
- (a) Birthdays What do you believe a histogram of the months in which the students in your mathematics class were born (January is month 1 and December is month 12) would look like? Explain. (b)
- Calculate the range and standard deviation of your exam grades in this mathematics course. Round the mean to the nearest tenth to calculate the standard deviation.
- Can you think of any situations in which a small standard deviation may be desirable?
- Can you think of any situations in which a large standard deviation may be desirable?
- Consider the following illustrations of two bank-customer waiting systems. (a) How would you expect the mean waiting time in Bank A to compare with the mean waiting time in Bank B? (b) How would
- Girolamo Cardano (1501–1576) wrote Liber de Ludo Aleae, which is considered to be the first book on probability. Cardano had a number of different vocations. Do research and write a paper on the
- We briefly discuss Jacob Bernoulli. The Bernoulli family produced several prominent mathematicians, including Jacob I, Johann I, and Daniel. Write a paper on the Bernoulli family, indicating some of
- Write a paper on how insurance companies use empirical probabilities in determining insurance premiums. An insurance agent may be able to direct you to a source of information.
- Can people selected at random distinguish Coke from Pepsi? Which do they prefer?(a) Design an experiment to determine the empirical prob-ability that a person selected at random can select Coke when
- When a book is published, it is assigned a 10-digit code number called the International Standard Book Number (ISBN). Do research and write a report on how this coding system works.
- There are many types of games of chance to choose from at casinos. The house has the advantage in each game, but the advantages differ according to the game. Do research and write a paper
- Determine whether your state has a lottery. If so, do research and write a paper indicating(a) The probability of winning the grand prize.(b) The odds against winning the grand prize.(c) Explain,
- The area of mathematics called combinatorics is the science of counting. Do research and write a paper on combinatorics and its many applications.
- Flip two coins 50 times and record the number of times exactly one head was obtained. Determine the empirical probability of flipping exactly one head.
- Roll a die 50 times and record the results. Determine the empirical probability of rolling(a) a 1. (b) a 4.(c) Does the probability of rolling a 1 appear to be the same as the probability of
- Roll a pair of dice 60 times and record the sums. Determine the empirical probability of rolling a sum of(a) 2. (b) 7. (c) Does the probability of rolling a sum of 2 appear to be the same
- Flip a coin 50 times and record the results. Determine the empirical probability of flipping(a) A head. (b) A tail. (c) Does the probability of flipping a head appear to be the same as
- Select a card from a deck of cards 40 times with replacement and compute the empirical probability of selecting a heart.
- Find two circle graphs in newspapers, in magazines, or on the Internet whose data are not given in percents. Redraw the graphs and label them with percents.
- Consider the following places where a loan may be obtained: banks, savings and loans, credit unions, and pawnshops. Write a report that includes the following information:(a) Describe the ownership
- Write a paper on the history of simple interest and com-pound interest. Answer the questions: When was simple interest first charged on loans? When was compound interest first given on investments?
- Imagine you have $4000 to invest and you need this money to grow to $5000 by investing in a CD. Contact a local bank or credit union to obtain the following CD information: the interest rate, the
- Suppose your family currently does not own a washer and dryer and you do not have the money needed to purchase the appliances. Do research to determine if it would be less expensive to borrow money
- Write a brief report giving the advantages and disadvantages of leasing a car. Determine all the individual costs involved with leasing a car. Indicate why you would prefer to lease or purchase a car
- Suppose you purchase a new wardrobe for $1000 with a credit card. You decide to pay for your new wardrobe by making the minimum monthly payment each month. You do not charge anything else to this
- The closing of a house involves many additional costs for the both the buyer and the seller. Select a home that is for sale and note the asking price. Do research and use this asking price to
- Search in your area to find your “dream home” that is for sale and note the asking price. Next, search the websites of local lenders to find the best interest rates for both a 15-year fixed
- Annuities, IRAs, 401k plans, 403b plans, SEP accounts, and Keogh accounts are all types of investments that can be used to save for retirement. Inter-view a financial advisor to discuss each of these
- Write a paper on investing in mutual funds. Include in your paper a description of the following terms: net asset value (NAV),portfolio manager,and expense ratios.
- Write a paper on investing in bonds. Include in your paper a description of the following terms: Treasury bonds, corporate bonds, and municipal bonds.
- Write a paper on investing in stocks (see the Did You Know? on page 619). Include in your paper a description of the following terms: New York Stock Exchange, National Association of Securities
- The concept and notation for modular systems were introduced by Carl Friedrich Gauss in 1801. Write a paper on Gauss’s contribution to modular systems.
- Do research on the Enigma ciphering machine. Write a paper on the role the machine played prior to and during World War II.
- The study of encoding and decoding mes-sages is called cryptography. Write a paper on how matrices and matrix multiplication are currently used in cryptography.
- Find an example from a magazine, a newspaper, or the Internet that displays information using a matrix. Write a paper explaining how to interpret the information provided by the matrix.
- We solved systems of linear equations algebraically. Systems of linear equations may also be solved using matrix multiplication. Do research and show how the system of equations3x + 2y = 54x - 3y =
- There are other classifications of mathematical systems besides groups. For example, there are rings and fields. Determine the requirements that must be met for a mathematical system to be(a) A
- Create a mathematical system with two binary operations. Select a set of elements and two binary operations so that one binary operation with the set of elements meets the requirements for a group
- Research the geometric constructions that use a straight-edge and a compass only. Prepare a poster demonstrating five of these basic constructions.
- Write a research paper on the three classic geometry problems of Greek antiquity.
- Write a research paper on Euclid’s contributions to geometry.
- Use a straightedge and a compass to construct a triangle with sides of equal length (an equilateral triangle) by doing the following: (a) Use the straightedge to draw a line segment of any length and
- Write a paper on the use of geometry in the photographic process. Include discussions on the use of similar figures.
- Write a paper on the history and use of the theodolite, a surveying instrument.
- Construct cardboard models of one or more of the platonic solids. Search the Internet for patterns to follow.
- Write a paper on the contributions of Heron of Alexandria to geometry.
- Pappus of Alexandria (ca. A.D. 350) was the last of the well-known ancient Greek mathematicians. Write a paper on his life and his contributions to mathematics.
- The early Babylonians and Egyptians did not know about π and had to devise techniques to approximate the area of a circle. Write a paper on the techniques these societies used to approximate the
- Calculate the volume of the room in which you sleep or study. Go to a store that sells room air conditioners and find out how many cubic feet can be cooled by the different models available. Describe
- Research the proof of the Pythagorean theorem provided by President James Garfield. Write a brief paper and make a poster of this proof and the associated diagrams.
- In the movie The Wizard of Oz, once the scarecrow gets his diploma he states the following: “In an isosceles triangle, the sum of the square roots of the two equal sides is equal to the square root
- Research the official dimensions of the playing surface of your favorite sport and determine the area of the playing surface in both square feet and square yards.
- Write a paper on the mathematics displayed in the artwork of M. C. Escher. Include such topics as tessellations, optical illusions, perspective, and non-Euclidean geometry.
- In the study of biology, reflective symmetry is called bi-lateral symmetry and rotational symmetry is called radial symmetry. Write a report on the role symmetry plays in the study of biology.
- Using the method, create a unique tessellation using a regular hexagon like the one shown below. Be creative, using color and sketches to complete your tessellation.
- Create a unique tessellation from a square piece of cardboard by using the method. Be creative, using color and sketches to complete your tessellation.