HEART OF MATHEMATICS
4th Edition
ISBN: 9781119760061
Author: Burger
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 6.2, Problem 33MS
Tell the truth. Someone said that she made a two-holed torus by gluing 60 triangles together along their edges. Once it was all glued, this person claimed that there were 30 vertices on the object. Is she telling the truth? Explain why or why not.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Part i
Part ii
2. In each case below, state whether the statement is true or false. Justify your answer in
each case.
(i) Suppose A and B are sets. Then, AnB = 6 ⇒ AUB = A
(ii) Suppose A and B are sets. Then, AUB = B ⇒ ACB
(iii) Suppose A and B are sets. Then, AUB = B ⇒ B C A
Chapter 6 Solutions
HEART OF MATHEMATICS
Ch. 6.1 - Map maker, map maker make me a graph. Represent...Ch. 6.1 - Unabridged list. Represent cach landmass from...Ch. 6.1 - Will the walk work? Does your graph from...Ch. 6.1 - Walk around the house. Is it possibel to traverse...Ch. 6.1 - Walk the line. Does this graph above have an Euler...Ch. 6.1 - Walkabout. Does this graph have an Euler circuit?...Ch. 6.1 - Linking the loops. In this map, the following...Ch. 6.1 - Scenic drive. (S) Here is a map of Rockystone...Ch. 6.1 - Under-edged. (H) Does this graph have an Euler...Ch. 6.1 - No man is an island. The country of Pelago...
Ch. 6.1 - Path-o-rama. For each graph below, determine if...Ch. 6.1 - Walk around the block. Create a graph of the...Ch. 6.1 - Walking the dogs. Your dogs, Abbey and Bear, love...Ch. 6.1 - Delivery query. The next time you see a postal...Ch. 6.1 - Snow job. (ExH) Shown here is a map of the tiny...Ch. 6.1 - Special delivery. (ExH) Julia is the letter...Ch. 6.1 - Draw this old house. Suppose you wanted to trace...Ch. 6.1 - Path of no return. Consider this map showing a...Ch. 6.1 - Without a trace. Is it possibel to trace out...Ch. 6.1 - New Euler. In the three previous Mindscapes, you...Ch. 6.1 - New edge—new circuit. Look at the graph for...Ch. 6.1 - New edge—new path. Review your work for...Ch. 6.1 - Path to proof. Suppose you have a connected graph...Ch. 6.1 - No Euler no how. Look at graph (a) for Mindscape...Ch. 6.1 - Degree day. (S) For cach graph below, determine...Ch. 6.1 - degrees of proof. Review your work for Mindscape...Ch. 6.1 - Degrees in sequence. Can you draw a graph that has...Ch. 6.1 - Even Steven. Review your work in Mindscape 28 to...Ch. 6.1 - Little League lesson. (H) You are in charge of...Ch. 6.1 - With a group of folks. In a small group, discuss...Ch. 6.1 - Power beyond the mathematics. Provide several...Ch. 6.1 - Here we celebrate the power of algebra as a...Ch. 6.1 - Here we celebrate the power of algebra as a...Ch. 6.1 - Here we celebrate the power of algebra as a...Ch. 6.1 - Here we celebrate the power of algebra as a...Ch. 6.1 - Here we celebrate the power of algebra as a...Ch. 6.2 - What a character! What expression gives the Euler...Ch. 6.2 - Count, then verify. What are the values of V, E,...Ch. 6.2 - Sneeze, then verify. Look at an unopened tissue...Ch. 6.2 - Blow, then verify. Inflate a ballon and use a...Ch. 6.2 - Add one. Find the values V, E, and F for the graph...Ch. 6.2 - Bowling. What is the Euler Characteristic of the...Ch. 6.2 - Making change. We begin with the graph pictured at...Ch. 6.2 - Making a point. Take a connected graph and add a...Ch. 6.2 - On the edge (H). Is it possible to add an edge to...Ch. 6.2 - Soap films. Consider the following sequence of...Ch. 6.2 - Dualing. What is the relationship between the...Ch. 6.2 - Prob. 12MSCh. 6.2 - Lots of separation. Suppose we are told that a...Ch. 6.2 - Prob. 14MSCh. 6.2 - Psychic readings. Someone is thinking of a...Ch. 6.2 - Prob. 16MSCh. 6.2 - Prob. 17MSCh. 6.2 - Circular reasoning. Create a connected graph as...Ch. 6.2 - Prob. 19MSCh. 6.2 - More circles. Consider the sphere described in...Ch. 6.2 - In the rough (S). Count the number of facets,...Ch. 6.2 - Cutting corners (H). The following collection of...Ch. 6.2 - Stellar. The following collection of pictures...Ch. 6.2 - A torus graph (ExH). The Euler Characteristic...Ch. 6.2 - Regular unfolding. Each graph below represents...Ch. 6.2 - A tale of two graphs. Suppose we draw a graph that...Ch. 6.2 - Two graph conjectures (S). Can you conjecture a...Ch. 6.2 - Lots of graphs conjecture. Can you conjecture a...Ch. 6.2 - Torus count. Three hollowed, triangular prisms...Ch. 6.2 - Torus two count (H). Carefully count the number of...Ch. 6.2 - Torus many count. Using the preceding calculations...Ch. 6.2 - Prob. 32MSCh. 6.2 - Tell the truth. Someone said that she made a...Ch. 6.2 - No sphere. Suppose we have a sphere built out of...Ch. 6.2 - Soccer ball. A soccer ball is made of pentagons...Ch. 6.2 - Klein bottle. Using the diagram here for building...Ch. 6.2 - Not many neighbors. Show that every map has at...Ch. 6.2 - Infinite edges. Suppose we consider a conn ected...Ch. 6.2 - Here we celebrate the power of algebra as a...Ch. 6.2 - Prob. 44MSCh. 6.2 - Prob. 45MSCh. 6.2 - Here we celebrate the power of algebra as a...Ch. 6.2 - Here we celebrate the power of algebra as a...Ch. 6.3 - Dont be cross. Here is a drawing of a graph with...Ch. 6.3 - De Plane! De Plane! (S) Is the graph given in...Ch. 6.3 - Countdown (H). For the graph drawing shown, count...Ch. 6.3 - Prob. 4MSCh. 6.3 - Criss-Cross. Is it possible to redraw the graph...Ch. 6.3 - Dont cross in the edge. Each of the graphs drawn...Ch. 6.3 - Hot crossed buns. Each of the graphs drawn below...Ch. 6.3 - Prob. 8MSCh. 6.3 - Spider on a mirror. Is it possible to redraw the...Ch. 6.3 - One more vertex. The graph here is drawn to show...Ch. 6.3 - Yet one more vertex (H). The graph shown is drawn...Ch. 6.3 - Familiar freckles. Is it possible to redraw the...Ch. 6.3 - Remind you of anyone you know? Is it possible to...Ch. 6.3 - Final countdown. For this graph drawing, count the...Ch. 6.3 - Euler check-up. Use your answer to the previous...Ch. 6.3 - Euler second opinion. For the graph drawing shown...Ch. 6.3 - Prob. 17MSCh. 6.3 - Prob. 18MSCh. 6.3 - A colorful museum. This figure shows the floor...Ch. 6.3 - Limit of 5. Start drawing a planar graph. Keep...Ch. 6.3 - Starring the hexagon. Is it possible to redraw...Ch. 6.3 - Prob. 22MSCh. 6.3 - Prob. 23MSCh. 6.3 - Getting greedy. (H) Suppose you are asked to color...Ch. 6.3 - Stingy rather than greedy. By coloring the...Ch. 6.3 - Getting more colorful. Graphs dont have to be...Ch. 6.3 - Prob. 27MSCh. 6.3 - Prob. 28MSCh. 6.3 - Chromatically applied. There are eight radio...Ch. 6.3 - Prob. 30MSCh. 6.3 - Personal perspectives. Write a short essay...Ch. 6.3 - Here we celebrate the power of algebra as a...Ch. 6.3 - Here we celebrate the power of algebra as a...Ch. 6.3 - Prob. 37MSCh. 6.3 - Here we celebrate the power of algebra as a...Ch. 6.3 - Here we celebrate the power of algebra as a...Ch. 6.4 - Up close and personal. Create a graph to model...Ch. 6.4 - Network lookout. Find an examle of a network...Ch. 6.4 - Prob. 3MSCh. 6.4 - Hamiltonian holiday (S). You are interning for a...Ch. 6.4 - Home style. Create a graph to model the rooms in...Ch. 6.4 - Six degrees or less. Suppose this graph is a model...Ch. 6.4 - Degrees of you. Find ten willing friends or...Ch. 6.4 - Campus shortcut. Find a map of your campus and...Ch. 6.4 - Arborist lesson. Which of the graphs below are...Ch. 6.4 - Prob. 10MSCh. 6.4 - Prob. 11MSCh. 6.4 - Prob. 12MSCh. 6.4 - Prob. 13MSCh. 6.4 - Prob. 14MSCh. 6.4 - Prob. 15MSCh. 6.4 - Hamilton Study. Look at the graph you drew to...Ch. 6.4 - Business trip redux. Look back in the section and...Ch. 6.4 - Handling Hamiltons. For each graph below, find a...Ch. 6.4 - Road trip. You are checking out gradua te programs...Ch. 6.4 - Back to Hatties trip. Look back in this section...Ch. 6.4 - Solve the Icosian Game. Find a Hamiltonian circuit...Ch. 6.4 - Hunt for Hamilton (S). A large island country has...Ch. 6.4 - Has no Hamilton. Give some characteristics that...Ch. 6.4 - Cubing Hamilton (ExH). Can you find a Hamihonian...Ch. 6.4 - Hamiltonian path. A Hamiltonian path is a path in...Ch. 6.4 - Sorry, no path. Give some characteristics that...Ch. 6.4 - Prob. 27MSCh. 6.4 - Prob. 28MSCh. 6.4 - Prob. 29MSCh. 6.4 - Prob. 30MSCh. 6.4 - Edge count. Look at all the trees you drew in the...Ch. 6.4 - Personal perspecthes. Write a short essay...Ch. 6.4 - Prob. 33MSCh. 6.4 - Prob. 34MSCh. 6.4 - Dollars and cents. Your spanning tree has three...Ch. 6.4 - Adding up. Your spanning tree has four edges with...Ch. 6.4 - Prob. 38MSCh. 6.4 - Vertex search (H). Your graph has a Hamiltonian...Ch. 6.4 - Binary gossip tree. You told a secret to two of...
Additional Math Textbook Solutions
Find more solutions based on key concepts
The given expression
Pre-Algebra Student Edition
1. How many solutions are there to ax + b = 0 with ?
College Algebra with Modeling & Visualization (5th Edition)
CHECK POINT I You deposit $3000 in s savings account at Yourtown Bank, which has rate of 5%. Find the interest ...
Thinking Mathematically (6th Edition)
Fill in each blank so that the resulting statement is true. Any set of ordered pairs is called a/an ____.The se...
Algebra and Trigonometry (6th Edition)
For a population containing N=902 individual, what code number would you assign for a. the first person on the ...
Basic Business Statistics, Student Value Edition
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- 5arrow_forwardNo chatgpt pls will upvotearrow_forward1. Find the mean of the x-values (x-bar) and the mean of the y-values (y-bar) and write/label each here: 2. Label the second row in the table using proper notation; then, complete the table. In the fifth and sixth columns, show the 'products' of what you're multiplying, as well as the answers. X y x minus x-bar y minus y-bar (x minus x-bar)(y minus y-bar) (x minus x-bar)^2 xy 16 20 34 4-2 5 2 3. Write the sums that represents Sxx and Sxy in the table, at the bottom of their respective columns. 4. Find the slope of the Regression line: bi = (simplify your answer) 5. Find the y-intercept of the Regression line, and then write the equation of the Regression line. Show your work. Then, BOX your final answer. Express your line as "y-hat equals...arrow_forward
- Apply STATA commands & submit the output for each question only when indicated below i. Generate the log of birthweight and family income of children. Name these new variables Ibwght & Ifaminc. Include the output of this code. ii. Apply the command sum with the detail option to the variable faminc. Note: you should find the 25th percentile value, the 50th percentile and the 75th percentile value of faminc from the output - you will need it to answer the next question Include the output of this code. iii. iv. Use the output from part ii of this question to Generate a variable called "high_faminc" that takes a value 1 if faminc is less than or equal to the 25th percentile, it takes the value 2 if faminc is greater than 25th percentile but less than or equal to the 50th percentile, it takes the value 3 if faminc is greater than 50th percentile but less than or equal to the 75th percentile, it takes the value 4 if faminc is greater than the 75th percentile. Include the outcome of this code…arrow_forwardsolve this on paperarrow_forwardFor each given function f(x) find f'(x) using the rules learned in section 9.5. 1. f(x)=x32 32x 2. f(x)=7x+13 3. f(x) = x4 4. f(x) = √√x³ 5. f(x) = 3x²+ 3 x2arrow_forward
- Apply STATA commands & submit the output for each question only when indicated below i. Apply the command egen to create a variable called "wyd" which is the rowtotal function on variables bwght & faminc. ii. Apply the list command for the first 10 observations to show that the code in part i worked. Include the outcome of this code iii. Apply the egen command to create a new variable called "bwghtsum" using the sum function on variable bwght by the variable high_faminc (Note: need to apply the bysort' statement) iv. Apply the "by high_faminc" statement to find the V. descriptive statistics of bwght and bwghtsum Include the output of this code. Why is there a difference between the standard deviations of bwght and bwghtsum from part iv of this question?arrow_forwardAccording to a health information website, the distribution of adults’ diastolic blood pressure (in millimeters of mercury, mmHg) can be modeled by a normal distribution with mean 70 mmHg and standard deviation 20 mmHg. b. Above what diastolic pressure would classify someone in the highest 1% of blood pressures? Show all calculations used.arrow_forwardWrite STATA codes which will generate the outcomes in the questions & submit the output for each question only when indicated below i. ii. iii. iv. V. Write a code which will allow STATA to go to your favorite folder to access your files. Load the birthweight1.dta dataset from your favorite folder and save it under a different filename to protect data integrity. Call the new dataset babywt.dta (make sure to use the replace option). Verify that it contains 2,998 observations and 8 variables. Include the output of this code. Are there missing observations for variable(s) for the variables called bwght, faminc, cigs? How would you know? (You may use more than one code to show your answer(s)) Include the output of your code (s). Write the definitions of these variables: bwght, faminc, male, white, motheduc,cigs; which of these variables are categorical? [Hint: use the labels of the variables & the browse command] Who is this dataset about? Who can use this dataset to answer what kind of…arrow_forward
- Apply STATA commands & submit the output for each question only when indicated below İ. ii. iii. iv. V. Apply the command summarize on variables bwght and faminc. What is the average birthweight of babies and family income of the respondents? Include the output of this code. Apply the tab command on the variable called male. How many of the babies and what share of babies are male? Include the output of this code. Find the summary statistics (i.e. use the sum command) of the variables bwght and faminc if the babies are white. Include the output of this code. Find the summary statistics (i.e. use the sum command) of the variables bwght and faminc if the babies are male but not white. Include the output of this code. Using your answers to previous subparts of this question: What is the difference between the average birthweight of a baby who is male and a baby who is male but not white? What can you say anything about the difference in family income of the babies that are male and male…arrow_forwardnot use ai pleasearrow_forwardPidgeonhole 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…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
Intermediate AlgebraAlgebraISBN:9781285195728Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Intermediate Algebra
Algebra
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
Finding the length of an arc; Author: Maths Genie;https://www.youtube.com/watch?v=fWGPf5peCc8;License: Standard YouTube License, CC-BY
Circles, Angle Measures, Arcs, Central & Inscribed Angles, Tangents, Secants & Chords - Geometry; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=nd46bA9DKE0;License: Standard Youtube License