Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
6th Edition
ISBN: 9780321914620
Author: Jeffrey O. Bennett, William L. Briggs
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 11.B, Problem 28E
To determine
Make the tiling from the given triangle using translations as mentioned in the question.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
29% of all college students major in STEM (Science, Technology, Engineering, and Math). If 46 college students are randomly selected, find the probability thata. Exactly 11 of them major in STEM. b. At most 12 of them major in STEM. c. At least 11 of them major in STEM. d. Between 11 and 15 (including 11 and 15) of them major in STEM.
4. Assume that a risk-free money market account is added to the market described in Q3.
The continuously compounded rate of return on the money market account is log (1.1).
(i) For each given μ, use Lagrange multipliers to determine the proportions (as a
function of μ) of wealth invested in the three assets available for the minimum
variance portfolio with expected return μ.
(ii) Determine the market portfolio in this market and calculate its Sharp ratio.
3. A market consists of two risky assets with rates of return R₁ and R2 and no risk-free
asset. From market data the following have been estimated: ER₁ = 0.25, ER2 = 0.05,
Var R₁ = 0.01, Var R2 = 0.04 and the correlation between R1 and R2 is p = -0.75.
(i) Given that an investor is targeting a total expected return of μ = 0.2. What
portfolio weights should they choose to meet this goal with minimum portfolio
variance? Correct all your calculations up to 4 decimal points.
(ii) Determine the global minimum-variance portfolio and the expected return and
variance of return of this portfolio (4 d.p.).
(iii) Sketch the minimum-variance frontier in the μ-σ² plane and indicate the efficient
frontier.
(iv) Without further calculation, explain how the minimum variance of the investor's
portfolio return will change if the two risky assets were independent.
Chapter 11 Solutions
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Ch. 11.A - Prob. 1QQCh. 11.A - Prob. 2QQCh. 11.A - Prob. 3QQCh. 11.A - Prob. 4QQCh. 11.A - Prob. 5QQCh. 11.A - Prob. 6QQCh. 11.A - Prob. 7QQCh. 11.A - Prob. 8QQCh. 11.A - Prob. 9QQCh. 11.A - Prob. 10QQ
Ch. 11.A - Prob. 1ECh. 11.A - 2. Define fundamental frequency, harmonic, and...Ch. 11.A - 3. What is a 12-tone scale? How are the...Ch. 11.A - 4. Explain how the notes of the scale are...Ch. 11.A - Prob. 5ECh. 11.A - Prob. 6ECh. 11.A - Prob. 7ECh. 11.A - Prob. 8ECh. 11.A - Prob. 9ECh. 11.A - Prob. 10ECh. 11.A - Prob. 11ECh. 11.A - Prob. 12ECh. 11.A - Octaves. Starting with a tone having a frequency...Ch. 11.A - Notes of a Scale. Find the frequencies of the 12...Ch. 11.A - Prob. 15ECh. 11.A - 16. The Dilemma of Temperament. Start at middle A,...Ch. 11.A - Exponential Growth and Scales. Starting at middle...Ch. 11.A - 18. Exponential Growth and Scales. Starting at...Ch. 11.A - 19. Exponential Decay and Scales. What is the...Ch. 11.A - Prob. 20ECh. 11.A - Prob. 21ECh. 11.A - Prob. 22ECh. 11.A - Mathematics and Music. Visit a website devoted to...Ch. 11.A - Mathematics and Composers. Many musical composers,...Ch. 11.A - Prob. 25ECh. 11.A - Prob. 26ECh. 11.A - Digital Processing. A variety of apps and software...Ch. 11.A - Prob. 28ECh. 11.B - Prob. 1QQCh. 11.B - 2. All lines that are parallel in a real scene...Ch. 11.B - 3. The Last Supper in Figure 11.6. Which of the...Ch. 11.B - Prob. 4QQCh. 11.B - Prob. 5QQCh. 11.B - Prob. 6QQCh. 11.B - Prob. 7QQCh. 11.B - Prob. 8QQCh. 11.B - Prob. 9QQCh. 11.B - Prob. 10QQCh. 11.B - Prob. 1ECh. 11.B - Prob. 2ECh. 11.B - Prob. 3ECh. 11.B - Prob. 4ECh. 11.B - Prob. 5ECh. 11.B - 6. Briefly explain why there are only three...Ch. 11.B - 7. Briefly explain why more tilings are possible...Ch. 11.B - 8. What is the difference between periodic and...Ch. 11.B - Prob. 9ECh. 11.B - Prob. 10ECh. 11.B - Prob. 11ECh. 11.B - Prob. 12ECh. 11.B - Prob. 13ECh. 11.B - Prob. 14ECh. 11.B - Vanishing Points. Consider the simple drawing of a...Ch. 11.B - Correct Perspective. Consider the two boxes shown...Ch. 11.B - Drawing with Perspective. Make the square, circle,...Ch. 11.B - Drawing MATH with Perspective. Make the letters M,...Ch. 11.B - 19. The drawing in Figure 11.34 shows two poles...Ch. 11.B - Two Vanishing Points. Figure 11.35 shows a road...Ch. 11.B - Prob. 21ECh. 11.B - Prob. 22ECh. 11.B - Prob. 23ECh. 11.B - Prob. 24ECh. 11.B - Prob. 25ECh. 11.B - Prob. 26ECh. 11.B - Prob. 27ECh. 11.B - Prob. 28ECh. 11.B - Prob. 29ECh. 11.B - Prob. 30ECh. 11.B - 30-31 : Tilings from Translating and Reflecting...Ch. 11.B - 32-33: Tilings from Quadrilaterals. Make a tiling...Ch. 11.B - Tilings from Quadrilaterals. Make a tiling from...Ch. 11.B - Prob. 34ECh. 11.B - Prob. 35ECh. 11.B - Prob. 36ECh. 11.B - Prob. 37ECh. 11.B - Prob. 38ECh. 11.B - Art and Mathematics. Visit a website devoted to...Ch. 11.B - 40. Art Museums. Choose an art museum, and study...Ch. 11.B - Prob. 41ECh. 11.B - Penrose Tilings. Learn more about the nature and...Ch. 11.B - Prob. 43ECh. 11.C - Prob. 1QQCh. 11.C - 2. Which of the following is not a characteristic...Ch. 11.C - 3. If a 1-foot line segment is divided according...Ch. 11.C - 4. To make a golden rectangle, you should
a. a...Ch. 11.C - Prob. 5QQCh. 11.C - Prob. 6QQCh. 11.C - Suppose you start with a golden rectangle and cut...Ch. 11.C - Prob. 8QQCh. 11.C - Prob. 9QQCh. 11.C - Prob. 10QQCh. 11.C - Prob. 1ECh. 11.C - How is a golden rectangle formed?Ch. 11.C - What evidence suggests that the golden ratio and...Ch. 11.C - Prob. 4ECh. 11.C - 5. What is the Fibonacci sequence?
Ch. 11.C - 6. What is the connection between the Fibonacci...Ch. 11.C - 7. Maria cut her 4-foot walking stick into two...Ch. 11.C - Prob. 8ECh. 11.C - Prob. 9ECh. 11.C - Prob. 10ECh. 11.C - Prob. 11ECh. 11.C - Prob. 12ECh. 11.C - Prob. 13ECh. 11.C - Prob. 14ECh. 11.C - Prob. 15ECh. 11.C - Prob. 16ECh. 11.C - Prob. 17ECh. 11.C - 18. Everyday Golden Rectangles. Find at least...Ch. 11.C - 19. Finding . The property that defines the golden...Ch. 11.C - 20. Properties of
a. Enter into your calculator....Ch. 11.C - Prob. 21ECh. 11.C - The Lucas Sequence. A sequence called the Lucas...Ch. 11.C - Prob. 23ECh. 11.C - The Golden Navel. An Old theory claims that, on...Ch. 11.C - Prob. 25ECh. 11.C - Prob. 26ECh. 11.C - Prob. 27ECh. 11.C - Prob. 28ECh. 11.C - Golden Controversies. Many websites are devoted to...Ch. 11.C - 30. Fibonacci Numbers. Learn more about Fibonacci...
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
- 2. A landlord is about to write a rental contract for a tenant which lasts T months. The landlord first decides the length T > 0 (need not be an integer) of the contract, the tenant then signs it and pays an initial handling fee of £100 before moving in. The landlord collects the total amount of rent erT at the end of the contract at a continuously compounded rate r> 0, but the contract stipulates that the tenant may leave before T, in which case the landlord only collects the total rent up until the tenant's departure time 7. Assume that 7 is exponentially distributed with rate > 0, λ‡r. (i) Calculate the expected total payment EW the landlord will receive in terms of T. (ii) Assume that the landlord has logarithmic utility U(w) = log(w - 100) and decides that the rental rate r should depend on the contract length T by r(T) = λ √T 1 For each given λ, what T (as a function of X) should the landlord choose so as to maximise their expected utility? Justify your answer. Hint. It might be…arrow_forwardPlease solving problem2 Problem1 We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. (This model is the same as in Prob. 1 of HW#2).We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.arrow_forwardPlease ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.arrow_forward
- This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. A B A B at some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 2 cos(3πt) and y= 2 sin(3t) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot(3πt) sin(3лt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411- 4 -2 sin (3лt) (d)…arrow_forward5. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.AE.003. y y= ex² 0 Video Example x EXAMPLE 3 (a) Use the Midpoint Rule with n = 10 to approximate the integral कर L'ex² dx. (b) Give an upper bound for the error involved in this approximation. SOLUTION 8+2 1 L'ex² d (a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.) dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)] 0.1 [0.0025 +0.0225 + + e0.0625 + 0.1225 e0.3025 + e0.4225 + e0.2025 + + e0.5625 €0.7225 +0.9025] The figure illustrates this approximation. (b) Since f(x) = ex², we have f'(x) = 0 ≤ f'(x) = < 6e. ASK YOUR TEACHER and f'(x) = Also, since 0 ≤ x ≤ 1 we have x² ≤ and so Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final answer to five decimal places.) 6e(1)3 e 24( = ≈arrow_forward1. Consider the following preference ballots: Number of voters Rankings 6 5 4 2 1st choice A DCB DC 2nd choice B B D 3rd choice DCBD 4th choice CA AAA For each of the four voting systems we have studied, determine who would win the election in each case. (Remember: For plurality with runoff, all but the top two vote-getters are simultaneously eliminated at the end of round 1.)arrow_forward
- Practice k Help ises A 96 Anewer The probability that you get a sum of at least 10 is Determine the number of ways that the specified event can occur when two number cubes are rolled. 1. Getting a sum of 9 or 10 3. Getting a sum less than 5 2. Getting a sum of 6 or 7 4. Getting a sum that is odd Tell whether you would use the addition principle or the multiplication principle to determine the total number of possible outcomes for the situation described. 5. Rolling three number cubes 6. Getting a sum of 10 or 12 after rolling three number cubes A set of playing cards contains four groups of cards designated by color (black, red, yellow, and green) with cards numbered from 1 to 14 in each group. Determine the number of ways that the specified event can occur when a card is drawn from the set. 7. Drawing a 13 or 14 9. Drawing a number less than 4 8. Drawing a yellow or green card 10. Drawing a black, red, or green car The spinner is divided into equal parts. Find the specified…arrow_forwardProblem 1.We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.(d) We assume that you sell the American put to a market participant A for the pricefound in (b). Explain how you act on the market…arrow_forwardWhat is the standard scores associated to the left of z is 0.1446arrow_forward
- 2. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.015. Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) ASK YOUR TEACHER 3 1 3 + dy, n = 6 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule Need Help? Read It Watch Itarrow_forwardThis question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. B A B at some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 2 cos(3πt) and y= 2 sin(3πt) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot (3πt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +41/1 (d) Express the slope of the rod…arrow_forwardConsider the proof below: Proposition: If m is an even integer, then 5m +4 is an even integer. Proof: We see that |5m+4=10n+4 = 2(5n+2). Therefore, 5m+4 is an even integer. **Note: you may assume the proof is valid, just poorly written. Based upon the Section 1.3 screencast and the reading assignment, select all writing guidelines that are missing in the proof. Proof begins by stating assumptions ✓ Proof has an invitational tone/uses collective pronouns Proof is written in complete sentences Each step is justified ☐ Proof has a clear conclusionarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSON
Discrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
Sequences and Series Introduction; Author: Mario's Math Tutoring;https://www.youtube.com/watch?v=m5Yn4BdpOV0;License: Standard YouTube License, CC-BY
Introduction to sequences; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=VG9ft4_dK24;License: Standard YouTube License, CC-BY