The Heart of Mathematics: An Invitation to Effective Thinking
4th Edition
ISBN: 9781118156599
Author: Edward B. Burger, Michael Starbird
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 10.3, Problem 27MS
Facebank. Your roommates are developing some social networking software they expect to go big some day. They ask you to invest some money, promising you an annual return of 10%. If you believe their hype, how much of your money (or really, your parents’ money) should you invest if you want to have $50,000 after ten years? (Hint: Use the formula
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Amy invested $500 per month in a 401k that earned 6% annual return for 40 years. Hank invested $1,000 per month in a 401k that also earned 6% annual return, but for 20 years. Which of the following would be true?
Each time you get dimes or quarters for change, you throw them into a jar. You are hoping to save $50. Write a model that shows the different numbers of dimes and quarters that you could accumulate to reach your goal.
Suppose you start a company to make a phone application. You pay a developer
$4,048 to create the app. You pay a hosting company $45/month to host your users
data.
You sell the app at $2 per download.
How many downloads must you get to break even at the end of your first year of
business?
Your Answer:
Answer
Chapter 10 Solutions
The Heart of Mathematics: An Invitation to Effective Thinking
Ch. 10.1 - What do you expect? How do you compute an expected...Ch. 10.1 - The average bite. Your little sister loves visits...Ch. 10.1 - A tooth for a tooth? Suppose your cousins Tooth...Ch. 10.1 - Spinning wheel. Suppose the spinner shown is...Ch. 10.1 - Fair game. What does it mean for a game to be...Ch. 10.1 - Cross on the green (S). A standard roulette wheel...Ch. 10.1 - In the red. Given the bet from Mindscape 6, what...Ch. 10.1 - Free Lotto. For several years in Massachusetts,...Ch. 10.1 - Bank value. What is the expected value of keeping...Ch. 10.1 - Value of money. In Newcombs Paradox, first suppose...
Ch. 10.1 - Die roll. What is the expected value of each of...Ch. 10.1 - Dice roll (ExH). What is the expected value of...Ch. 10.1 - Fair is foul. Someone has a weighted coin that...Ch. 10.1 - Foul is fair (S). Someone has a weighted coin that...Ch. 10.1 - Cycle cycle (H). You live in an area where the...Ch. 10.1 - Whats your pleasure? You have three options for...Ch. 10.1 - Roulette expectation. A standard roulette wheel...Ch. 10.1 - Fair wheeling. You are at the roulette table and...Ch. 10.1 - High rolling (H). Here is a die game you play...Ch. 10.1 - Fair rolling. Suppose you are considering the game...Ch. 10.1 - Spinning wheel. You pay $5, pick one of the four...Ch. 10.1 - Dice (ExH). You place a bet and then roll two fair...Ch. 10.1 - Uncoverable bases. Show by a specific example how...Ch. 10.1 - Under the cap. A national soda company runs a...Ch. 10.1 - Two coins in a fountain. You pay Si for two coins...Ch. 10.1 - Three coins in a fountain. You pay $5 for three...Ch. 10.1 - Insure (S). You own a $9000 car and a $850...Ch. 10.1 - Get a job (H). You search for a job. Three...Ch. 10.1 - Take this job and... Given the employment scenario...Ch. 10.1 - Book value. Refer back to our analysis of the...Ch. 10.1 - In search of... A group of deep-sea divers...Ch. 10.1 - Solid gold. There is a 50% chance that the price...Ch. 10.1 - Four out of five. In Newcombs Paradox, suppose...Ch. 10.1 - Chevalier de Méré. Suppose that the Chevalier de...Ch. 10.1 - The St. Petersburg paradox. Here is an interesting...Ch. 10.1 - Coin or god. In Newcombs Paradox, first suppose...Ch. 10.1 - An investment. You wish to invest $1000, and you...Ch. 10.1 - Pap test (H). Assume that the insurance value of a...Ch. 10.1 - Prob. 40MSCh. 10.1 - Spin to win. To play a certain carnival game, you...Ch. 10.1 - Spinner winner. To play a different carnival game,...Ch. 10.1 - Insurance wagering (H). From the point of view of...Ch. 10.1 - Probable cause. Continuing the scenario from the...Ch. 10.1 - The bicycle thief. Some entrepreneurial classmates...Ch. 10.2 - Remarkably risky. List two activities that are...Ch. 10.2 - Surprisinly safe. List two activities that are...Ch. 10.2 - Infectious numbers (H). Suppose a disease is...Ch. 10.2 - SARS scars (S). Suppose a new vaccine that...Ch. 10.2 - A hairy pot. At a certain famous school of...Ch. 10.2 - Blonde, bleached blonde (H). You have high...Ch. 10.2 - Blonde again (S). Given the scenario in Mindscape...Ch. 10.2 - Bleached again. Given the scenario in Mindscape 6,...Ch. 10.2 - Safety first. Suppose a particular car is widely...Ch. 10.2 - Scholarship winner (ExH). You apply for a national...Ch. 10.2 - Less safe (ExH). Given the scenario in our air...Ch. 10.2 - Aw, nuts! Suppose that the loss of life expectancy...Ch. 10.2 - Dont cell! (H) Suppose you are a U.S. senator and...Ch. 10.2 - Buy low and cell high (H). The microwaves produced...Ch. 10.2 - Taxi blues (H). An eyewitness observes a...Ch. 10.2 - More taxi blues (S). An eyewitness observes a...Ch. 10.2 - Few blues. An eyewitness observes a hit-and-run...Ch. 10.2 - More safety. Given the scenario of our earlier air...Ch. 10.2 - Reduced safety. Given the scenario of our air...Ch. 10.2 - HIV tests. Recall that, in the United States,...Ch. 10.2 - More HIV tests. Given the tests described in the...Ch. 10.2 - Super sale. The bookstore is having a super sale...Ch. 10.2 - V.isk risk (H). You always sort your laundry into...Ch. 10.2 - Bag for life. An insurance company estimates that...Ch. 10.2 - Mooving sale. Plush toy versions of your college...Ch. 10.2 - Reweighing life expectancy An example in this...Ch. 10.3 - Simple interest (H). Suppose you deposit $500 into...Ch. 10.3 - Less simple interest. Suppose that at the...Ch. 10.3 - The power of powers (H). In this section we...Ch. 10.3 - Crafty compounding. Two thousand years ago, a...Ch. 10.3 - Keg costs. List some of the opportunity costs...Ch. 10.3 - You can bank on us (or them) (S). You wish to...Ch. 10.3 - The Kennedy compound. You wish to ivest $1000 for...Ch. 10.3 - Three times a lady. The Three-Timesa-Year Savings...Ch. 10.3 - Baker kneads dough (ExH). Your favorite baker,...Ch. 10.3 - I want my ATV! You want to purchase a cool, yellow...Ch. 10.3 - Lottery loot later? You have a big problem: Youve...Ch. 10.3 - Open sesame (S). Bert and Ernie each open a...Ch. 10.3 - Jelly-filled investments (H). Suppose you purchase...Ch. 10.3 - Taking stock. Suppose that a stock transaction...Ch. 10.3 - Making your pocketbook stocky. Suppose that a...Ch. 10.3 - Money-tree house. You decide you wish to build...Ch. 10.3 - Future vlaue (S). What is the future value of $...Ch. 10.3 - Present value (ExH). On the first day of your...Ch. 10.3 - Double or nothing (H). You decide you wish to...Ch. 10.3 - Triple or nothing. You decide you wish to triple...Ch. 10.3 - Power versus product (S). In this section we...Ch. 10.3 - Double vision. Suppose we have $P and we invest it...Ch. 10.3 - Adding up the bucks (H). You have a job every...Ch. 10.3 - Fiddling for dollars. As presented in the section...Ch. 10.3 - Facebank. Your roommates are developing some...Ch. 10.3 - Boatload o cash. At age 12 you dream of sailing...Ch. 10.3 - Houseload o cash. You want to buy a house by age...Ch. 10.4 - Landslide Lyndon. The two candidates in the 1948...Ch. 10.4 - Electoral college. Briefly outline a voting scheme...Ch. 10.4 - Voting for voting. What are some differences...Ch. 10.4 - Voting for sport. Given an example (ideally from...Ch. 10.4 - The point of the arrow (S). What does Arrows...Ch. 10.4 - Dictating an election through a dictator. Suppose...Ch. 10.4 - Pro- or Con-dorcet? (S) Consider the following...Ch. 10.4 - Where is Dr. Pepper? (S) Given the voting data...Ch. 10.4 - Approval drinking (H). Returning to the voting...Ch. 10.4 - Mindscapes 10 through 15 are based on the...Ch. 10.4 - Mindscapes 10 through 15 are based on the...Ch. 10.4 - Mindscapes 10 through 15 are based on the...Ch. 10.4 - Mindscapes 10 through 15 are based on the...Ch. 10.4 - Mindscapes 10 through 15 are based on the...Ch. 10.4 - Mindscapes 10 through 15 are based on the...Ch. 10.4 - Whats it all about, Ralphie? Many people believe...Ch. 10.4 - Two, too (ExH). Given an election between just two...Ch. 10.4 - Two, too II (ExH). Given an election between just...Ch. 10.4 - Instant runoffs. One way to avoid the lengthy...Ch. 10.4 - Run runoff. Given the method of instant runoff...Ch. 10.4 - Coin coupling. For this challenge, you will need...Ch. 10.4 - From money-mating to cupids arrow. Explain how the...Ch. 10.4 - Vote night. There are four candidates running for...Ch. 10.4 - Wroof recount. The election in the previous...Ch. 10.4 - Biggest loser? Who was the biggest loser in the...Ch. 10.4 - The X-act winner. Your schools math club has 73...Ch. 10.4 - Borda rules. Candidates A, B, and C are running...Ch. 10.5 - Prob. 1MSCh. 10.5 - Understanding icing (S). Suppose a person who had...Ch. 10.5 - Liquid gold. Suppose you and your two brothers are...Ch. 10.5 - East means West. Suppose you have a triangular...Ch. 10.5 - Two-bedroom bliss (H). Suppose you and a roommate...Ch. 10.5 - Your preference. Suppose the accompanying figure...Ch. 10.5 - Bulk. Suppose for you, bigger is better, so your...Ch. 10.5 - Dont move that knif. Give a specific scenario to...Ch. 10.5 - Prob. 9MSCh. 10.5 - Just do it. Get three people together and have...Ch. 10.5 - The real world. Give three real-world examples...Ch. 10.5 - Same tastes (H). If you are dividing a cake among...Ch. 10.5 - Crossing the line. In each triangle shown on the...Ch. 10.5 - Cutting up Mass (S). You, Joan, and John want to...Ch. 10.5 - Where to cut (H). The accompanying figure pictures...Ch. 10.5 - Land preference (ExH). Suppose you are preparing...Ch. 10.5 - Uneven pair (S). Suppose two people want to divide...Ch. 10.5 - Diversity pays. Explain why having differences of...Ch. 10.5 - Be fair. The moving-knife and yelling Stop method...Ch. 10.5 - Nuclear dump (ExH). Suppose there is a nuclear...Ch. 10.5 - Disarming (H). Two nuclear superpowers decide to...Ch. 10.5 - Cupcakes. Suppose you had 100 different cupcakes...Ch. 10.5 - Barely consistent. It is possible for Chris to...Ch. 10.5 - Your X. You and your ex-roommate happen to share a...Ch. 10.5 - Musical Xs. You play the violin in a chamber trio...Ch. 10.5 - Cake plot. Imagine a cake in the shape of a...Ch. 10.5 - Cake trisection. Imagine a cake in the shape of a...Ch. 10.5 - Roomate wrangling. You and a friend rent a...
Additional Math Textbook Solutions
Find more solutions based on key concepts
49-52: Percentage Comparisons. Complete the following sentences.
49. The life expectancy (at birth) of America...
Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
Suppose that X and Y have the following joint probability function:
Find the expected value of g(X, Y) = XY2.
...
Probability and Statistics for Engineers and Scientists
Find the additive inverse of each of the following integers. Write the answer in the simplest possible form. a....
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
In the following problem, we ask the reader to some of the details left out of the above discussion, to analys...
Differential Equations: An Introduction to Modern Methods and Applications
Solve each problem involving proportions. Price of Gasoline If 6 gallons of premium unleaded gasoline cost $17....
Mathematical Ideas (13th Edition) - Standalone book
Percentiles. The pth percentile of a sorted data set is a number xp such that p of the data fall at or below xp...
Excursions in Modern Mathematics (9th 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
- In the situation of the example, how long could you keep the car if your expense account allowed 242?arrow_forwardLast year, at Haven's Pond Car Dealership, for a particular model of BMW, Jeep, and Toyota, one could purchase all three cars for a total of $140,000. This year, due to inflation, the same cars would cost $151,830. The cost of the BMW increased by 8%, the Jeep by 5%, and the Toyota by 12%. If the price of last year's Jeep was $7,000 less than the price of last year's BMW, what was the price of each of the three cars last year?arrow_forwardForrest's Nursery owns 7000 white pine trees. Each year, they plan to sell 12% of the trees. Write an explicit formula to model this situation.arrow_forward
- In February, Apple stock rose from $120.69 to $164.85, while Tesla stock increased from $675.50 a share to $809.87. You've invested $1500 in Feb 2021 and sold them for $2802.83 in Feb 2022. How many shares of each stock did you purchase? Apple A 29.78% (1Y) T Tesla Buy Sell a 12.73% (1Y) S182.00 Buy Sell $1.230.00 $149.00 TW TY SY 10Y se97.00 Position Overview Transactions News TW TY SY 10Y Personal portfolio Value 0 $498.29 (a +27.10%) $106.24 Position Overview Transactions News Amount invested 0 $392.05 Share price O $809.87 % of portfolio 0 4% Today's change O A 1.14% Average price O $129.70 View more v Shares 0 3.02268arrow_forwardEd Moura has $34000 invested in stocks paying 8%. How much additional money should he invest in certificates of deposit paying 2% so that the average return on the two investments is 3%? He should invest $___ in certificates of deposit.arrow_forwardSuppose you save $5 each week. At the end of one year, how much money will you have saved?arrow_forward
- Suppose you have a choice between receiving $5,000 today or $10,000 in five years. You believeyou can earn 10% on the $5,000 today, but want to know what the $5,000 will be worth in fiveyearsarrow_forwardGeorgia McBeal is trying to save for her retirement. She believes she can earn 10% on average each year on her retirement fund. Assume that at the beginning of each of the next 40 years, Georgia will allocate x dollars to her retirement fund. If at the beginning ofa year Georgia has y dollars in her fund, by the end of the year, it will grow to 1.1y dollars. How much should Georgia allocate to her retirement fund each year to ensure that she will have $1 million at the end of 40 years? What key factors are being ignored in this analysis of the amount saved for retirement?arrow_forwardJeff Bezos, who owns Amazon, has a net worth of approximately $143.1 billion (as of mid-2018). An employee in the Amazon distribution center earns about $13 an hour. The estimated lifespan of the employee is 71 years. If the employee worked 24 hours a day, every day of the year from the moment of his birth, how many lifespans would it take for him to earn wages equivalent to Jeff Bezos' net worth? Round the answer to the nearest whole number.arrow_forward
- Two cars with the same purchase price are not worth the same amount at the end of the year. Some cars depreciate faster than others. A truck depreciates at 45%45% and a Jeep depreciates at 25%25% per year. Assume the initial purchase price is $19,000.$19,000. Use a spreadsheet to determine how much more the Jeep is worth in three years.arrow_forwardA company made one of the largest single purchases of long-distance telephone time in history. It purchased A company made one of the largest single purchases of long-distance telephone time in history. It purchased 43 million minutes at a total cost of $1,720,000. If the company resells the phone time at an average of 7 cents per minute, how much profit will it make on the purchase? million minutes at a total cost of $1,720,000. If the company resells the phone time at an average of 7 cents per minute, how much profit will it make on the purchase?arrow_forwarddvisor estimates that the money-market fund will return 5% over the next year, the blue-chip fund 9%, and the high-tech fund 16%. Jason wants a total of first-year return of $4000. To avoid excessive risk, he decides to invest three times as much money in the money-market fund as in the high-tech stock fund. How much should he invest in each fund? 4. Let A=5, -31 -2 3 a. Find the inverse of matrix A, if it exists. Write out all work. b. Use your answer from part a. to solve the system of linear equations below. (Note: You must use part a. in order to get full credit for this question.) 5x-3y 10 -2x+3y 15 %3D %3D DII DD F10 F7 F8arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
What is a Linear Equation in One Variable?; Author: Don't Memorise;https://www.youtube.com/watch?v=lDOYdBgtnjY;License: Standard YouTube License, CC-BY
Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY