The Heart of Mathematics: An Invitation to Effective Thinking

4th Edition

ISBN: 9781118156599

Author: Edward B. Burger, Michael Starbird

Publisher: Wiley, John & Sons, Incorporated

See similar textbooks

Videos

Textbook Question

Chapter 7.4, Problem 6MS

Arithmetic. Compute the following sums and products of complex numbers: ( 2 + 3 i ) + ( 3 − 7 i ) ; ( − 2 + 5 i ) + ( 4 + 6 i ) ; ( 1 − 2 i ) ( 2 + 3 i ) ; ( − i ) ( 4 − 2 i ) ; ( 3 − 2 i ) 2 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.4, Problem 5MS

Chapter 7.4, Problem 7MS

Students have asked these similar questions

Please conduct a step by step of these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points. 1. One Sample T-Test: Determine whether the average satisfaction rating of customers for a product is significantly different from a hypothetical mean of 75. (Hints: The null can be about maintaining status-quo or no difference; If your alternative hypothesis is non-directional (e.g., μ≠75), you should use the two-tailed p-value from excel file to make a decision about rejecting or not rejecting null. If alternative is directional (e.g., μ < 75), you should use the lower-tailed p-value. For alternative hypothesis μ > 75, you should use the upper-tailed p-value.) H0 = H1= Conclusion: The p value from one sample t-test is _______. Since the two-tailed p-value is _______ 2. Two-Sample T-Test:…

Please conduct a step by step of these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points. What is one sample T-test? Give an example of business application of this test? What is Two-Sample T-Test. Give an example of business application of this test? .What is paired T-test. Give an example of business application of this test? What is one way ANOVA test. Give an example of business application of this test? 1. One Sample T-Test: Determine whether the average satisfaction rating of customers for a product is significantly different from a hypothetical mean of 75. (Hints: The null can be about maintaining status-quo or no difference; If your alternative hypothesis is non-directional (e.g., μ≠75), you should use the two-tailed p-value from excel file to make a decision about rejecting or not…

A professor gives two types of quizzes, objective and recall. He plans to give at least 15 quizzes this quarter. The student preparation time for an objective quiz is 15 minutes and for a recall quiz 30 minutes. The professor would like a student to spend at least 5 hours total (300 minutes) preparing for these quizzes. It takes the professor 1 minute to grade an objective quiz, and 1.5 minutes to grade a recall type quiz. How many of each type of quiz should the professor give in order to minimize his grading time (why still meeting the other requirements outlined)?

Chapter 7 Solutions

The Heart of Mathematics: An Invitation to Effective Thinking

Ch. 7.1 - The incredible shrinking duck. On the Quacked...Ch. 7.1 - Multiplicity (S). In the Sierpinski Triangle,...Ch. 7.1 - Different sizes. In the fern, find three reduced...Ch. 7.1 - Blooming broccoli. In the bunch of broccoli, find...Ch. 7.1 - Prob. 5MS Ch. 7.1 - Prob. 6MS Ch. 7.1 - Maybe moon. What features of the fractal forgeries...Ch. 7.1 - Exposing forgeries. What features of the fractal...Ch. 7.1 - Natures way. Find some examples of self-similarity...Ch. 7.1 - Do it yourself (H). Draw a figure that contains...

Ch. 7.1 - With a group of folks. In a small group, discuss...Ch. 7.1 - Prob. 12MS Ch. 7.2 - A search for self. What does self-similarity mean?Ch. 7.2 - Desperately seeking similarity. Which of these...Ch. 7.2 - Too many triangles? At stage 0, the Sierpinski...Ch. 7.2 - Counting Koch. Look at the early stages of the...Ch. 7.2 - Argyle art. Take four line segments and place them...Ch. 7.2 - Natures way. Find several examples of objects in...Ch. 7.2 - Whos the fairest? Can you position three mirrors...Ch. 7.2 - Billiards and mirrors. On an idealized, square...Ch. 7.2 - MTV. Youve become a rock star and consequently...Ch. 7.2 - Photo op. Suppose you arrange two mirrors facing...Ch. 7.2 - How many mes? Arrange mirrors and camera as in...Ch. 7.2 - Quacker, Quacker, Quacker. Suppose you had the job...Ch. 7.2 - Sierpinski hexed (S). Take an equilateral triangle...Ch. 7.2 - The Kinks (ExH). Kochs kinky curve is created by...Ch. 7.2 - Four times (H). Draw a picture on a square piece...Ch. 7.2 - Burger heaven (S). Sketch a picture of a...Ch. 7.2 - Ice cream cones. Draw a picture of an ice cream...Ch. 7.2 - Sierpinski boundary. Take the boundary of a...Ch. 7.2 - Catching Zs (H). Take a Z. Put in nine smaller Zs,...Ch. 7.2 - Replacement pinwheel. Take a 1,2,2 right triangle....Ch. 7.2 - Koch Stool (ExH). Start with a line segment, mark...Ch. 7.2 - Koch collage stool. Given the Koch Stool described...Ch. 7.2 - Sierpinski shooting. Suppose that you were playing...Ch. 7.2 - Sierpinski target practice (H). What sequence of...Ch. 7.2 - Cantor Set. Start with the interval [0, 1]. Build...Ch. 7.2 - Cantor luck (H). Start with the point 0. Flip a...Ch. 7.2 - Cantor Square (S). Take a square. Make four...Ch. 7.2 - Cantor Square shrunk. Take the Cantor Square....Ch. 7.2 - Cantor Squared. Draw the four corners of a square,...Ch. 7.2 - Hexed again. Suppose you start with the three...Ch. 7.2 - Prob. 31MS Ch. 7.2 - Antoines necklace. Antoines necklace is a delicate...Ch. 7.2 - Menger jacks. For the game of jacks, lets imagine...Ch. 7.2 - A tighter weave. Look back at the Tight Weave...Ch. 7.2 - A looser weave. Lets modify the carpet-designing...Ch. 7.2 - From where? Look at this fractal. What collage...Ch. 7.2 - Treed. Describe collage-making instructions that...Ch. 7.2 - Flaky (H). Describe collage making instructions...Ch. 7.2 - How big a hole? In the Tighter weave (34) and...Ch. 7.2 - 4D fractal. Describe a fractal in 4-dimensional...Ch. 7.2 - Personal perspectives. Write a short essay...Ch. 7.2 - With a group of folks. In a small group, discuss...Ch. 7.2 - Graphing Koch. Plot the following points in the...Ch. 7.2 - Koch adds life. Look at the points given in the...Ch. 7.2 - White out. Each stage of the Sierpinski triangle...Ch. 7.2 - Measuring the length of your Koch. The Koch stool...Ch. 7.2 - Counting Koch segments (H). Suppose you start with...Ch. 7.3 - Parallel grams. At right we see a parallelogram....Ch. 7.3 - Moving on up. Heres a triangle along with some...Ch. 7.3 - Bigger rug. Heres a picture of the Sierpinski...Ch. 7.3 - Dimension connection. What equation relates the...Ch. 7.3 - Divining dimension. If a fractal object requires...Ch. 7.3 - Stay inbounds. Give two consecutive integers that...Ch. 7.3 - Regular things (H). Find the fractal dimension of...Ch. 7.3 - More regular things. Find the fractal dimension of...Ch. 7.3 - Any right triangle. Take any right triangle. It...Ch. 7.3 - Sierpinski carpet (S). Compute the fractal...Ch. 7.3 - Koch Stool. Compute the fractal dimension of the...Ch. 7.3 - Cantor Set (H). The Cantor Set was constructed by...Ch. 7.3 - Cantor reduced. Suppose you take a unit interval,...Ch. 7.3 - Long Koch (ExH). The first stage in the...Ch. 7.3 - Pius (H). This fractal plus sign is self-similar...Ch. 7.3 - Tiniler triangles (S). Suppose you make something...Ch. 7.3 - Menger Sponge (ExH). Compute the fractal dimension...Ch. 7.3 - Thinning. Take a square. Make two copies, each...Ch. 7.3 - Not much. What is the fractal dimension of the...Ch. 7.3 - Koched (H). Create a Koch-like curve with fractal...Ch. 7.3 - Find a fractal. Describe a fractal having...Ch. 7.3 - Prob. 22MS Ch. 7.3 - Personal perspectives. Write a short essay...Ch. 7.3 - With a group of folks. In a small group, discuss...Ch. 7.3 - Prob. 25MS Ch. 7.3 - Power beyond the mathematics. Provide several...Ch. 7.3 - Varying dimensions. Using any method, including...Ch. 7.3 - Dimensional thinking. The text defines the...Ch. 7.3 - Power play (H). Using any method, including...Ch. 7.3 - Marching madness. The marching band wants to...Ch. 7.3 - More marching madness. For the second drill in the...Ch. 7.4 - Not Raul. Who was Gaston Julia?Ch. 7.4 - Use your imagination. What does the number i...Ch. 7.4 - Complex plots. The complex number 3+2i is plotted...Ch. 7.4 - Prob. 4MS Ch. 7.4 - Outie or innie? If you use the point a+bi to build...Ch. 7.4 - Arithmetic. Compute the following sums and...Ch. 7.4 - More arithmetic (ExH). Compute the following sums...Ch. 7.4 - Quick draw. Two complex numbers are marked and...Ch. 7.4 - III iterate I (12:S). Feeling queasy? Then compute...Ch. 7.4 - III iterate I (12:S). Feeling queasy? Then compute...Ch. 7.4 - III iterate I (12:S). Feeling queasy? Then compute...Ch. 7.4 - III iterate I (12:S). Feeling queasy? Then compute...Ch. 7.4 - III iterate II (18:S). Compute the first three...Ch. 7.4 - III iterate II (18:S). Compute the first three...Ch. 7.4 - III iterate II (18:S). Compute the first three...Ch. 7.4 - III iterate II (18:S). Compute the first three...Ch. 7.4 - 1III iterate III. Compute the first three iterates...Ch. 7.4 - III iterate III. Compute the first three iterates...Ch. 7.4 - III iterate III. Compute the first three iterates...Ch. 7.4 - III iterate III. Compute the first three iterates...Ch. 7.4 - Orange Julias. Pictured here are some Julia Sets...Ch. 7.4 - Julia Webbed. Visit the Heart of Mathematics Web...Ch. 7.4 - Great escape? For each of the complex...Ch. 7.4 - Great escape? For each of the complex numbers...Ch. 7.4 - Great escape? For each of the complex numbers...Ch. 7.4 - Mandelbrot or not? (H). The images on the...Ch. 7.4 - Mandelbrot or not? (H). The images on the...Ch. 7.4 - Zero in (S). For each picture of the Julia Sets in...Ch. 7.4 - Zero in (S). For each picture of the Julia Sets in...Ch. 7.4 - Zero in (S). For each picture of the Julia Sets in...Ch. 7.4 - Zero in (S). For each picture of the Julia Sets in...Ch. 7.4 - Mandelbrot origins. Using your insights from...Ch. 7.4 - Prob. 36MS Ch. 7.4 - Bounded Julia (ExH). Why is no Julia Set...Ch. 7.4 - Prisoner. Find a complex number a+bi that is fixed...Ch. 7.4 - Mandelbrot connections. Can every two points on...Ch. 7.4 - Personal perspectives. Write a short essay...Ch. 7.4 - With a group of folks. In a small group, discuss...Ch. 7.4 - Power beyond the mathematics. Provide several...Ch. 7.4 - Quadratic complexity (H). The quadratic formula...Ch. 7.4 - Special products. Compute the following products...Ch. 7.4 - Somethings fishy. The treasurer of the Marine...Ch. 7.4 - On the line. In the xy-plane, sketch the graph of...Ch. 7.4 - A line with a complex. Plot the points in the...Ch. 7.5 - Any interest? Suppose you put $1000 in a bank...Ch. 7.5 - Urban expansion. In the year 2004 the village of...Ch. 7.5 - Pre-sushi. Suppose a pond can sustain a maximum of...Ch. 7.5 - A booby trap. A small landmass off the Galapagos...Ch. 7.5 - Too many. The island of Birdburg has an area of...Ch. 7.5 - Call your shots. For each picture below, trace the...Ch. 7.5 - Getting cornered. Starting from the spot indicated...Ch. 7.5 - Double your money (H). Suppose you I deposit $1000...Ch. 7.5 - Too many(S). Earths surface is approximately...Ch. 7.5 - Rice bowl (H). One day long ago, the Emperor of...Ch. 7.5 - Natures way. Find some examples, other than those...Ch. 7.5 - The Game of Life (12:S). For each initial...Ch. 7.5 - The Game of Life (12:S). For each initial...Ch. 7.5 - The Game of Life (12:S). For each initial...Ch. 7.5 - The Game of Life (12:S). For each initial...Ch. 7.5 - Life cycles. For each initial population in the...Ch. 7.5 - Life cycles. For each initial population in the...Ch. 7.5 - Life cycles. For each initial population in the...Ch. 7.5 - Life cycles. For each initial population in the...Ch. 7.5 - Explosion. Devise a new initial population in the...Ch. 7.5 - Extinction. Construct a new initial population in...Ch. 7.5 - Periodic population (H). Construct a new initial...Ch. 7.5 - Programmed population. On a computer or...Ch. 7.5 - Programmed population: the next generation. Using...Ch. 7.5 - How many now? Suppose that a population is modeled...Ch. 7.5 - Fibonacci. Fibonacci numbers are constructed using...Ch. 7.5 - Fibonacci again. For each of the two columns you...Ch. 7.5 - Prob. 29MS Ch. 7.5 - Cobweb plots (ExH). Here we visualize the...Ch. 7.5 - More spiders (S). Here is the graph of...Ch. 7.5 - Arachnids. Here is the graph of y=4x(1x). Start on...Ch. 7.5 - Making dough. Many delicious French desserts, such...Ch. 7.5 - Making dough. Many delicious French desserts, such...Ch. 7.5 - Making dough. Many delicious French desserts, such...Ch. 7.5 - More cobwebs (H). Consider the inverted V graph...Ch. 7.5 - Yet more cobwebs. Given the inverted V graph...Ch. 7.5 - Cantors cuts. Start with the unit interval [0, 1]....Ch. 7.5 - How much Â¡s gone? In the construction of the...Ch. 7.5 - How much remains? Consider numbers that are not in...Ch. 7.5 - Personal perspectives. Write a short essay...Ch. 7.5 - With a group of folks. In a small group, discuss...Ch. 7.5 - Prob. 43MS Ch. 7.5 - Power beyond the mathematics. Provide several...Ch. 7.5 - Life happens. A particular starting configuration...Ch. 7.5 - Perplexing population predictions. Verhulst model...Ch. 7.5 - More prediction peril. Consider the previous...Ch. 7.5 - Cobweb parabola. Mindscapes 3032 describe cobweb...Ch. 7.5 - Two sad and one happy parabolas. Building on your...Ch. 7.6 - Does this thing come with a warranty? If you use...Ch. 7.6 - Root repeater. Find a calculator with a square...Ch. 7.6 - Transforming experience. The equation y=4x(1x) is...Ch. 7.6 - Up and over. In this graph, we see a red diagonal...Ch. 7.6 - Over and up. Here is a simpler version of the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - Too high. Consider a tent function that got too...Ch. 7.6 - More gone. In the too high tent function in the...Ch. 7.6 - Too short. Consider a short tent function. Will...Ch. 7.6 - Where to? Using the transformation y=3.5x(1x),...Ch. 7.6 - Calculator slips. Using the logistic...Ch. 7.6 - Take stock. Pick a stock. Some Web sites will...Ch. 7.6 - Repulsive. If you take the number 1 and square it,...Ch. 7.6 - Attractive. Again consider the process of repeated...Ch. 7.6 - Sierpinski attractor. Remember how the Sierpinski...Ch. 7.6 - Two step. Consider the transformation that takes...Ch. 7.6 - Periodic attraction (S). Again consider the...Ch. 7.6 - Periodic attraction. Again consider the...Ch. 7.6 - Four-peat (H). Consider the equation y=3.5x(1x)....Ch. 7.6 - Nearly fourly. Consider the equation y=3.5x(1x)....Ch. 7.6 - Tent attraction? Consider the point 0.4, which is...Ch. 7.6 - Becoming periodic. The point 0.4 is of period 2 in...Ch. 7.6 - The Earth moved (ExH). Consider a transformation...Ch. 7.6 - Poles apart. Consider the same transformation as...Ch. 7.6 - Logistic cobwebs. Lets explore the relatively...Ch. 7.6 - Logistic cobwebs. Lets explore the relatively...Ch. 7.6 - Logistic cobwebs. Lets explore the relatively...Ch. 7.6 - With a group of folks. In a small group, discuss...Ch. 7.6 - Power beyond the mathematics. Provide several...Ch. 7.6 - V-quation. Look at the graph for Mindscape 4. The...Ch. 7.6 - Meeting up. Look at the graph for Mindscape 38....Ch. 7.6 - We meet again. Look at the graph for Mindscape 39....Ch. 7.6 - Calculating percentages (H). Return to Table 1 on...Ch. 7.6 - Calculating percentages II. Repeat Mindscape 48...

Additional Math Textbook Solutions

Find more solutions based on key concepts

Fill in each blank so that the resulting statement is true. If n is a counting number, bn, read ______, indicat...

College Algebra (7th Edition)

Arc length calculations Find the arc length of the following curves on the given interval by integrating with r...

Calculus: Early Transcendentals (2nd Edition)

A Bloomberg Businessweek subscriber study asked, In the past 12 months, when travelling for business, what type...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Matching In Exercises 17–20, match the level of confidence c with the appropriate confidence interval. Assume e...

Elementary Statistics: Picturing the World (7th Edition)

Solve each formula for the given letter . [2.3] What percent of 60 is 42? [2.4]

Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)

In an experiment, die is rolled continually until a 6 appears, at which point the experiment stops. What is the...

A First Course in Probability (10th 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.