A Problem Solving Approach to Mathematics for Elementary School Teachers, Books a la Carte Edition plus NEW MyLab Math with Pearson eText - Access Card Package (12th Edition)
12th Edition
ISBN: 9780133865479
Author: Rick Billstein, Shlomo Libeskind, Johnny Lott
Publisher: PEARSON
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Chapter 10.4, Problem 17MC
Mathematical Connections
A student asks, “If the mean income of
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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.
Please 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.
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)…
Chapter 10 Solutions
A Problem Solving Approach to Mathematics for Elementary School Teachers, Books a la Carte Edition plus NEW MyLab Math with Pearson eText - Access Card Package (12th Edition)
Ch. 10.1 - Read about basic ideas of statistics in Common...Ch. 10.1 - Suggest how students at different grades might...Ch. 10.1 - Examine grade-school books to see what types of...Ch. 10.1 - Mathematical Connections What are the Nielsen...Ch. 10.1 - Prob. 7MCCh. 10.1 - National Assessment of Educational ProgressNAEP...Ch. 10.1 - Prob. 2NAEPCh. 10.1A - A second-grade class has a project to determine...Ch. 10.1A - Prob. 2ACh. 10.1A - Prob. 3A
Ch. 10.1A - To determine the most popular book among students...Ch. 10.1A - Prob. 5ACh. 10.1A - Prob. 6ACh. 10.1A - If a class were to investigate how many countries...Ch. 10.1A - Prob. 8ACh. 10.1A - In a set of student evaluations of their...Ch. 10.1A - Prob. 10ACh. 10.1A - If a bar graph like the one shown here were used...Ch. 10.1A - Prob. 12ACh. 10.1B - A second-grade class has a project to determine...Ch. 10.1B - An elementary school class decides to determine...Ch. 10.1B - Assessment To determine student computer use,...Ch. 10.1B - Prob. 7ACh. 10.1B - Prob. 8ACh. 10.1B - Assessment A university professor used a rating...Ch. 10.1B - Suppose a poll is to be conducted in an elementary...Ch. 10.1B - Prob. 11ACh. 10.1B - Determine the population and the sample in the...Ch. 10.2 - Mathematical Connections a. Discuss when a...Ch. 10.2 - Mathematical Connections Explain whether a circle...Ch. 10.2 - Mathematical Connections Explain why the sum of...Ch. 10.2 - Mathematical Connections The federal budget for...Ch. 10.2 - Prob. 5MCCh. 10.2 - Prob. 6MCCh. 10.2 - Mathematical Connections Find five examples of...Ch. 10.2 - Mathematical Connections A graph similar to the...Ch. 10.2 - Prob. 11MCCh. 10.2 - Prob. 12MCCh. 10.2 - Prob. 13MCCh. 10.2 - Prob. 14MCCh. 10.2 - Mathematical Connections Paul asks how to create a...Ch. 10.2 - National Assessment of Educational Progress NAEP...Ch. 10.2 - Prob. 2NAEPCh. 10.2 - National Assessment of Educational Progress NAEP...Ch. 10.2A - The following the pictograph shows the approximate...Ch. 10.2A - Prob. 2ACh. 10.2A - Sixth grade students reported the numbers of apps...Ch. 10.2A - Prob. 4ACh. 10.2A - Draw a histogram based on the stem and leaf plot...Ch. 10.2A - Prob. 6ACh. 10.2A - Prob. 7ACh. 10.2A - Prob. 8ACh. 10.2A - Prob. 9ACh. 10.2A - Prob. 10ACh. 10.2A - Seniors Sierra High were asked to about their...Ch. 10.2A - Prob. 12ACh. 10.2A - a. A 2-inch-long rectangle serves as a percentage...Ch. 10.2A - Prob. 14ACh. 10.2A - a. If the number of people reading mysteries in...Ch. 10.2A - Prob. 16ACh. 10.2A - Prob. 17ACh. 10.2A - Prob. 18ACh. 10.2A - Prob. 19ACh. 10.2B - The following pictograph shows the approximate...Ch. 10.2B - Display the following information about the status...Ch. 10.2B - Prob. 3ACh. 10.2B - The heights reached by 15 model rockets launched...Ch. 10.2B - Prob. 5ACh. 10.2B - Prob. 6ACh. 10.2B - Given the following bar graph, estimate the length...Ch. 10.2B - Prob. 8ACh. 10.2B - Prob. 9ACh. 10.2B - Prob. 10ACh. 10.2B - Draw a circle graph for the data in exercise 10....Ch. 10.2B - Use the circle graph to answer the following...Ch. 10.2B - a. In a circle graph, a sector containing 82...Ch. 10.2B - Prob. 14ACh. 10.2B - A list of presidents, with the number of children...Ch. 10.2B - Prob. 16ACh. 10.2B - The histogram below shows the number of books read...Ch. 10.3 - Explain the concept of association as it is...Ch. 10.3 - Jacquie argued that scatterplots had little value...Ch. 10.3 - The Smith family drew a circle graph of their...Ch. 10.3 - Prob. 9MCCh. 10.3 - Prob. 10MCCh. 10.3 - Prob. 1NAEPCh. 10.3A - Assessment The graph below shows the population of...Ch. 10.3A - Prob. 3ACh. 10.3A - Prob. 4ACh. 10.3A - Prob. 5ACh. 10.3A - Prob. 6ACh. 10.3A - Assessment Consider an arithmetic sequence with...Ch. 10.3A - Prob. 8ACh. 10.3A - Assessment In the following scatterplots, find an...Ch. 10.3A - The following data show the cost of various...Ch. 10.3A - Assessment If a trend line has equation...Ch. 10.3A - Assessment If a trend line has equation y=150.8x,...Ch. 10.3B - The graph below shows the average age at which...Ch. 10.3B - Answer the following questions based on the line...Ch. 10.3B - The graph below shows line graphs for...Ch. 10.3B - The graph depicts the spelling result from Mr....Ch. 10.3B - Prob. 5ACh. 10.3B - Prob. 6ACh. 10.3B - Prob. 7ACh. 10.3B - Use the scatterplots shown to answer the...Ch. 10.3B - In the following scatterplots, find an equation of...Ch. 10.3B - Prob. 10ACh. 10.3B - Prob. 11ACh. 10.3B - Prob. 12ACh. 10.3B - Assessment If a trend line has equation...Ch. 10.3B - For each of the following pairs of variables,...Ch. 10.4 - Carl had scores of 90,95,85, and 90 on his first...Ch. 10.4 - The mean of the five numbers given is 50: 20 35 50...Ch. 10.4 - Sue drives 5 mi at 30 mph and ten 5 mi at 50 mph....Ch. 10.4 - Mathematical Connections Explain why the mode...Ch. 10.4 - Prob. 9MCCh. 10.4 - Mathematical Connections The mean of 5,7,9 is 7....Ch. 10.4 - Prob. 11MCCh. 10.4 - Mathematical Connections What does a large...Ch. 10.4 - Mathematical Connections In each pair of variables...Ch. 10.4 - Prob. 14MCCh. 10.4 - Mathematical Connections A student asks, If the...Ch. 10.4 - Mathematical Connections Jose asks, Why can a...Ch. 10.4 - Mathematical Connections Suppose the class takes a...Ch. 10.4 - Mathematical Connections A student asks if it is...Ch. 10.4 - Prob. 21MCCh. 10.4 - Mathematical Connections A student asks if it is...Ch. 10.4 - Mathematical Connections Mels mean on 10 tests for...Ch. 10.4 - Prob. 24MCCh. 10.4 - Mathematical Connections Given the bar graph...Ch. 10.4 - Mathematical Connections Following are raw test...Ch. 10.4 - National Assessment of Educational Progress NAEP...Ch. 10.4 - National Assessment of Educational Progress NAEP...Ch. 10.4 - Prob. 3NAEPCh. 10.4A - Assessment Calculate the mean, the median, and the...Ch. 10.4A - Prob. 2ACh. 10.4A - Assessment a. If three students scored 75 on a...Ch. 10.4A - Prob. 4ACh. 10.4A - Assessment Suppose in Selinas class there were...Ch. 10.4A - Prob. 6ACh. 10.4A - Prob. 7ACh. 10.4A - Prob. 8ACh. 10.4A - Prob. 9ACh. 10.4A - Prob. 10ACh. 10.4A - Prob. 11ACh. 10.4A - Prob. 12ACh. 10.4A - Prob. 13ACh. 10.4A - Prob. 14ACh. 10.4A - Assessment Following are box plots comparing the...Ch. 10.4A - Prob. 16ACh. 10.4A - Prob. 17ACh. 10.4A - Assessment What is the standard deviation of the...Ch. 10.4A - Prob. 19ACh. 10.4A - Prob. 20ACh. 10.4A - Assume a normal distribution and that the average...Ch. 10.4A - Prob. 22ACh. 10.4A - Prob. 23ACh. 10.4A - Prob. 24ACh. 10.4A - Prob. 25ACh. 10.4A - Prob. 26ACh. 10.4A - Prob. 27ACh. 10.4B - Calculate the mean, the median, and the mode for...Ch. 10.4B - Prob. 2ACh. 10.4B - Prob. 3ACh. 10.4B - Prob. 4ACh. 10.4B - Prob. 5ACh. 10.4B - Prob. 6ACh. 10.4B - a. Mr. Alberto wanted to count the score on a term...Ch. 10.4B - Prob. 9ACh. 10.4B - Prob. 10ACh. 10.4B - Prob. 11ACh. 10.4B - Prob. 12ACh. 10.4B - Prob. 13ACh. 10.4B - Ginnys median score on three tests was 90. Her...Ch. 10.4B - Prob. 15ACh. 10.4B - Prob. 16ACh. 10.4B - a. If all the numbers in a set are equal, what is...Ch. 10.4B - In a school system, teachers start at a salary of...Ch. 10.4B - Prob. 20ACh. 10.4B - Prob. 21ACh. 10.4B - Prob. 22ACh. 10.4B - The weights of newborn babies in a certain country...Ch. 10.4B - Prob. 24ACh. 10.4B - Prob. 25ACh. 10.4B - Prob. 26ACh. 10.4B - Prob. 27ACh. 10.5 - Discuss the effect on the appearance of a graph...Ch. 10.5 - Words such as may as in may help with reading...Ch. 10.5 - Prob. 3MCCh. 10.5 - Prob. 4MCCh. 10.5 - Prob. 5MCCh. 10.5 - Prob. 6MCCh. 10.5 - Following are the record swimming times of the...Ch. 10.5 - National Assessment of Educational Progress NAEP...Ch. 10.5 - Richard wants to estimate the average mean monthly...Ch. 10.5 - Prob. 3NAEPCh. 10.5A - Assessment The city of Podunk advertised itself as...Ch. 10.5A - Prob. 3ACh. 10.5A - Prob. 4ACh. 10.5A - Prob. 5ACh. 10.5A - Mathematical Connections Refer to the following...Ch. 10.5A - Prob. 9ACh. 10.5A - Prob. 10ACh. 10.5A - Prob. 11ACh. 10.5A - Prob. 12ACh. 10.5A - Prob. 14ACh. 10.5A - Prob. 15ACh. 10.5A - Prob. 16ACh. 10.5B - Prob. 4ACh. 10.5B - Prob. 10ACh. 10.5B - Prob. 11ACh. 10.5B - Prob. 12ACh. 10.5B - Prob. 13ACh. 10.5B - Prob. 14ACh. 10.5B - What are the characteristics that you think a...Ch. 10.5B - Prob. 16ACh. 10.5B - Prob. 17ACh. 10.5B - Prob. 18ACh. 10.5B - In the figure shown, monthly sales of three...Ch. 10.5B - Prob. 20ACh. 10.CR - Suppose you read that the average family in...Ch. 10.CR - Prob. 2CRCh. 10.CR - Prob. 3CRCh. 10.CR - Prob. 5CRCh. 10.CR - Prob. 6CRCh. 10.CR - The budget for the Wegetem Crime Co. is 2,000,000....Ch. 10.CR - Prob. 8CRCh. 10.CR - Prob. 9CRCh. 10.CR - Prob. 10CRCh. 10.CR - The life expectancies at birth for males and...Ch. 10.CR - Prob. 12CRCh. 10.CR - Prob. 13CRCh. 10.CR - Prob. 14CRCh. 10.CR - Prob. 15CRCh. 10.CR - Prob. 16CRCh. 10.CR - Prob. 17CRCh. 10.CR - Prob. 18CRCh. 10.CR - Prob. 20CRCh. 10.CR - Prob. 21CRCh. 10.CR - Prob. 22CRCh. 10.CR - Prob. 23CRCh. 10.CR - Prob. 24CRCh. 10.CR - Prob. 26CRCh. 10.CR - CHAPTER 10 REVIEW Give examples of several ways to...Ch. 10.CR - Prob. 28CRCh. 10.CR - Prob. 29CRCh. 10.CR - Prob. 30CRCh. 10.CR - Prob. 31CRCh. 10.CR - Prob. 32CRCh. 10 - NOW TRY THIS On the student page shown below, work...Ch. 10 - Prob. 2NTCh. 10 - Prob. 3NTCh. 10 - Prob. 4NTCh. 10 - Prob. 5NTCh. 10 - Prob. 7NTCh. 10 - Prob. 8NTCh. 10 - Prob. 9NTCh. 10 - Prob. 10NTCh. 10 - Prob. 12NTCh. 10 - Prob. 13NT
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- 5. [-/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_forwardPractice 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_forward
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