The Heart of Mathematics: An Invitation to Effective Thinking, WileyPLUS NextGen Card with Loose-leaf Set Single Semester: An Invitation to Effective Thinking (Key Curriculum Press)
4th Edition
ISBN: 9781119760054
Author: Burger, Edward B. , Starbird, Michael
Publisher: Wiley (WileyPLUS Products)
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 2.3, Problem 39MS
A small factor. Prove that if a number greater than 1 is not a prime number, then it must have a prime factor less than or equal to its square root. (Hint: Suppose that all the factors are greater than its square root, and show that the product of any two of them must be larger than the original number.) This Mindscape shows that, to determine if a number is a prime, we have only to check divisibility of the primes up to the square root of the number.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Complete solutions need handwriting. For all only sure experts solve it correct complete solutions
The graph below shows the U.S. federal expenses for 2012.
A) estimate the fraction of the total expenses that were spent on Medicare. Write your answer as the
closest fraction whose denominator is 100.
B) estimate the fraction of the total expenses that were spent on Medicare and Medicaid. Write your
answer as the closest fraction, whose denominator is 100.
Starting with the finished version of Example 6.2, attached, change the decision criterion to "maximize expected utility," using an exponential utility function with risk tolerance $5,000,000. Display certainty equivalents on the tree.
a. Keep doubling the risk tolerance until the company's best strategy is the same as with the EMV criterion—continue with development and then market if successful.
The risk tolerance must reach $ ____________ before the risk averse company acts the same as the EMV-maximizing company.
b. With a risk tolerance of $320,000,000, the company views the optimal strategy as equivalent to receiving a sure $____________ , even though the EMV from the original strategy (with no risk tolerance) is $ ___________ .
Chapter 2 Solutions
The Heart of Mathematics: An Invitation to Effective Thinking, WileyPLUS NextGen Card with Loose-leaf Set Single Semester: An Invitation to Effective Thinking (Key Curriculum Press)
Ch. 2.1 - Muchos mangos. You inherit a large crate of...Ch. 2.1 - Packing balk. Your best friend is about to turn 21...Ch. 2.1 - Alternative rock. You have an empty CD rack...Ch. 2.1 - The Byrds. You have 16 new CDs to put on your...Ch. 2.1 - For the birds. Explain the Pigeonhole principle.Ch. 2.1 - Treasure chest (ExH). Someone offers to give you a...Ch. 2.1 - Order please. Order the following numbers from...Ch. 2.1 - Penny for your thoughts (H). Two thousand years...Ch. 2.1 - Twenty-nine is hat. Find the most interesting...Ch. 2.1 - Perfect numbers. The only natural numbers that...
Ch. 2.1 - Many fold (S). Suppose you were able to take a...Ch. 2.1 - Only one cake. Suppose we had a room filled with...Ch. 2.1 - For the birds. Years ago, before overnight...Ch. 2.1 - Sock hop (ExH). You have 10 pain of socks, five...Ch. 2.1 - The last one. Here is a game to be played with...Ch. 2.1 - See the three. What proportion of the first 1000...Ch. 2.1 - See the three II (H). What proportion of the first...Ch. 2.1 - See the three III. Explain why almost all...Ch. 2.1 - Commuting. One hundred people in your neighborhood...Ch. 2.1 - RIP (S). The Earth has more than 6.8 billion...Ch. 2.1 - Say the sequence. The following are the first few...Ch. 2.1 - Lemonade. You want to buy a new car, and you know...Ch. 2.1 - With a group of folks. In a small group, discuss...Ch. 2.1 - Ramanujan noodles (H). Ramanujan tells you that...Ch. 2.1 - Bird count. You want to know how many pigeons you...Ch. 2.1 - Many pennies. Suppose you have a 33 checkerboard...Ch. 2.1 - Wheres the birdie? One of your pigeons decides to...Ch. 2.2 - Fifteen Fibonaccis. List the first 15 Fibonacci...Ch. 2.2 - Born . What is the precise number that the symbol ...Ch. 2.2 - Tons of ones. Verify that 1+11+11 equals 3/2.Ch. 2.2 - Twos and threes. Simplify the quantities 2+22+22...Ch. 2.2 - The amity of . Solve the following equations for...Ch. 2.2 - Baby bunnies. This question gave the Fibonacci...Ch. 2.2 - Discovering Fibonacci relationships (S). By...Ch. 2.2 - Discovering more Fibonacci relationships, By...Ch. 2.2 - Late bloomers (ExH). Suppose we start with one...Ch. 2.2 - A new start. Suppose we build a sequence of...Ch. 2.2 - Discovering Lucas relationships. By experimenting...Ch. 2.2 - Still more Fibonacci relationships. By...Ch. 2.2 - Even more Fibonacci relationships. By...Ch. 2.2 - Discovering Fibonacci and Lucas relationships. By...Ch. 2.2 - The enlarging area paradox (S). The square shown...Ch. 2.2 - Sum of Fibonacci (H). Express each of the...Ch. 2.2 - Some more sums. Express each of the following...Ch. 2.2 - Fibonacci nim: The first move. Suppose you are...Ch. 2.2 - Fibonacci nim: The first move II. Suppose you are...Ch. 2.2 - Fibonacci nim: The first move III. Suppose you are...Ch. 2.2 - Fibonacci nim: The next move. Suppose you are...Ch. 2.2 - Fibonacci nim: The next move II. Suppose you are...Ch. 2.2 - Prob. 23MSCh. 2.2 - Beat your friend. Play Fibonacci nim with a...Ch. 2.2 - Beat another friend. Play Fibonacci nim with...Ch. 2.2 - Discovering still more Fibonacci relationships. By...Ch. 2.2 - Finding factors (S). By experimenting with...Ch. 2.2 - The rabbits rest. Suppose we have a pair of baby...Ch. 2.2 - Digging up Fibonacci roots. Using the square root...Ch. 2.2 - Tribonacci. Lets start with the numbers 0, 0, 1,...Ch. 2.2 - Prob. 31MSCh. 2.2 - Prob. 32MSCh. 2.2 - Prob. 33MSCh. 2.2 - A big fib (ExH). Suppose we have a natural number...Ch. 2.2 - Decomposing naturals (H). Use the result of...Ch. 2.2 - How big is it? Is it possible for a Fibonacci...Ch. 2.2 - Too small. Suppose we have a natural number that...Ch. 2.2 - Beyond Fibonacci. Suppose we create a new sequence...Ch. 2.2 - Generalized sums. Let Gn be the generalized...Ch. 2.2 - Its hip to be square (H). Adapt the methods of...Ch. 2.2 - Personal perspectives. Write a short essay...Ch. 2.2 - With a group of folks. In a small group, discuss...Ch. 2.2 - Here we celebrate the power of algebra as a...Ch. 2.2 - Finding x(H). Solve for x:x=1+6x.Ch. 2.2 - Appropriate address. Fibonaccis house number is...Ch. 2.2 - Zen bunnies. Your rabbits do yoga every morning in...Ch. 2.2 - The power of gold (H). In 1843 Jacques Binet (not...Ch. 2.3 - PrimaI Instincts. List the first 15 prime numbers.Ch. 2.3 - Fear factor. Express each of the following numbers...Ch. 2.3 - Odd couple. If n is an odd number greater than or...Ch. 2.3 - Tower of power. The first four powers of 3 are...Ch. 2.3 - Compose a list. Give an infinite list of natural...Ch. 2.3 - A silly start. What is the smallest number that...Ch. 2.3 - Waking for a nonprime. What is the smallest...Ch. 2.3 - Always, sometimes, never. Does a prime multiplied...Ch. 2.3 - The dividing line. Does a nonprime divided by a...Ch. 2.3 - Prime power. Is it possible for an extremely large...Ch. 2.3 - Nonprimes (ExH). Are there infinitely many natural...Ch. 2.3 - Prime test. Suppose you are given a number n and...Ch. 2.3 - Twin primes. Find the first 15 pairs of twin...Ch. 2.3 - Goldbach. Express the first 15 even numbers...Ch. 2.3 - Odd Goldbach (H). Can every odd number greater...Ch. 2.3 - Still the 1 (S). Consider the following sequence...Ch. 2.3 - Zeros and ones. Consider the following sequence of...Ch. 2.3 - Zeros, ones, and threes. Consider the following...Ch. 2.3 - A rough count. Using results discussed in this...Ch. 2.3 - Generating primes (H). Consider the list of...Ch. 2.3 - Generating primes II. Consider the list of...Ch. 2.3 - Floating in factors. What is the smallest natural...Ch. 2.3 - Lucky 13 factor. Suppose a certain number when...Ch. 2.3 - Remainder reminder (S). Suppose a certain number...Ch. 2.3 - Remainder roundup. Suppose a certain number when...Ch. 2.3 - Related remainders (H). Suppose we have two...Ch. 2.3 - Prime differences. Write out the first 15 primes...Ch. 2.3 - Minus two. Suppose we take a prime number greater...Ch. 2.3 - Prime neighbors. Does there exist a number n such...Ch. 2.3 - Perfect squares. A perfect square is a number that...Ch. 2.3 - Perfect squares versus primes. Using a calculator...Ch. 2.3 - Prime pairs. Suppose that p is a prime number...Ch. 2.3 - Remainder addition. Let A and B be two natural...Ch. 2.3 - Remainder multiplication. Let A and B be two...Ch. 2.3 - A prime-free gap (S). Find a run of six...Ch. 2.3 - Prime-free gaps. Using Mindscape 35, show that,...Ch. 2.3 - Three primes (ExH). Prove that it is impossible to...Ch. 2.3 - Prime plus three. Prove that if you take any prime...Ch. 2.3 - A small factor. Prove that if a number greater...Ch. 2.3 - Prime products (H). Suppose we make a number by...Ch. 2.3 - Seldom prime. Suppose that x is a natural number...Ch. 2.3 - A special pair of twins. A composite number x is...Ch. 2.3 - Special K p. A prime p satisfies the equation...Ch. 2.3 - Prob. 48MSCh. 2.3 - One real root (H). Find one value of x for which...Ch. 2.4 - A flashy timepiece. You own a very expensive watch...Ch. 2.4 - Living in the past. Your watch currently reads...Ch. 2.4 - Mod prods. Which number from 0 to 6 is equivalent...Ch. 2.4 - Prob. 4MSCh. 2.4 - A tower of mod power. Reduce 13 mod 11. Reduce 132...Ch. 2.4 - Hours and hours. The clock now reads 10:45. What...Ch. 2.4 - Days and days. Today is Saturday. What day of the...Ch. 2.4 - Months and months (H). It is now July. What month...Ch. 2.4 - Celestial seasonings (S). Which of the following...Ch. 2.4 - SpaghettiOs. Which of the following is the correct...Ch. 2.4 - Prob. 11MSCh. 2.4 - Tonic water. Which of the following is the correct...Ch. 2.4 - Real mayo (H). The following is the UPC for...Ch. 2.4 - Applesauce. The following is the UPC for Lucky...Ch. 2.4 - Grand Cru. The following is the UPC for Celis Ale...Ch. 2.4 - Mixed nuts. The following is the UPC for Planters...Ch. 2.4 - Blue chips. The following is the UPC for Garden of...Ch. 2.4 - Lemon. The following is the UPC for RealLemon...Ch. 2.4 - Decoding (S). A friend with lousy handwriting...Ch. 2.4 - Check your check. Find the bank code on your...Ch. 2.4 - Prob. 21MSCh. 2.4 - More bank checks (ExH). Determine the check digits...Ch. 2.4 - UPC your friends. Have a friend find a product...Ch. 2.4 - Whoops. A UPC for a product is Explain why the...Ch. 2.4 - Whoops again. A bank code is Explain why the...Ch. 2.4 - Mod remainders (S). Where would 129 be on a mod 13...Ch. 2.4 - More mod remainders. Where would 2015 be on a mod...Ch. 2.4 - Money orders. U.S. Postal Money Orders have a...Ch. 2.4 - Airline tickets. An airline ticket identification...Ch. 2.4 - UPS. United Parcel Service uses the same check...Ch. 2.4 - Check a code. U.S. Postal Money Order serial...Ch. 2.4 - ISBN-13. The 13-digit book identification number,...Ch. 2.4 - ISBN-13 check (H). Find the check digits for the...Ch. 2.4 - ISBN-13 error. The ISBN-13 978-4-1165-9105-4 is...Ch. 2.4 - Brush up your Shakespeare. Find a book containing...Ch. 2.4 - Mods and remainders. Use the Division Algorithm...Ch. 2.4 - Catching errors (H). Give some examples in which...Ch. 2.4 - Why three? In the UPC, why is 3 the number every...Ch. 2.4 - A mod surprise. For each number n from 1 to 4,...Ch. 2.4 - A prime magic trick. Pick a prime number and call...Ch. 2.4 - One congruence, two solutions. Find two different...Ch. 2.4 - Chinese remainder. Find one natural number x that...Ch. 2.4 - More remainders. Find one natural number z that...Ch. 2.4 - Quotient coincidence. Suppose x is a natural...Ch. 2.4 - Prob. 49MSCh. 2.5 - What did you say? The message below was encoded...Ch. 2.5 - Secret admirer. Use the scheme on page 99 to...Ch. 2.5 - Setting up secrets. Let p=7 and q=17. Are p and q...Ch. 2.5 - Second secret setup. Let p=5 and q=19. Are p and q...Ch. 2.5 - Secret squares. Reduce the following quantities:...Ch. 2.5 - Petit Fermat 5. Compute 24 (mod 5). Compute 44...Ch. 2.5 - Petit Fermat 7. Compute 46 (mod 7). Compute 56...Ch. 2.5 - Top secret (ExH). In our discussion, the two...Ch. 2.5 - Middle secret (H). In our discussion, the two...Ch. 2.5 - Prob. 10MSCh. 2.5 - Creating your code (S). Suppose you wish to devise...Ch. 2.5 - Using your code. Given the coding scheme you...Ch. 2.5 - Public secrecy. Using the List in Mindscape 12,...Ch. 2.5 - Going public. Using the list in Mindscape 12, with...Ch. 2.5 - Secret says (H). Using the list in Mindscape 12,...Ch. 2.5 - Big Fermat (S). Compute 5600 (mod 7). (Hint:...Ch. 2.5 - Big and powerful Fermat (ExH). Recall how...Ch. 2.5 - The value of information. How large should the...Ch. 2.5 - Something in common. Suppose that p is a prime...Ch. 2.5 - Faux pas Fermat. Compute 15 mod 6, 25 mod 6, 35...Ch. 2.5 - Breaking the code. If you could factor a large...Ch. 2.5 - Signing your name. Suppose you get a message that...Ch. 2.5 - Prob. 27MSCh. 2.5 - FOILed! FOIL the expression (a1)(q1). Suppose you...Ch. 2.5 - FOILed again! FOIL the expression (x1)(y1)....Ch. 2.5 - Secret primes. You know that p and q are primes...Ch. 2.5 - Prob. 31MSCh. 2.6 - A rational being. What is the definition of a...Ch. 2.6 - Fattened tractions. Reduce these overweight...Ch. 2.6 - Prob. 3MSCh. 2.6 - Decoding decimals. Show that each of the decimal...Ch. 2.6 - Odds and ends. Square the numbers from 1 to 12. Do...Ch. 2.6 - Irrational rationalization. We know that 2 ¡s...Ch. 2.6 - Rational rationalization. We know 2/5 and 7/3 are...Ch. 2.6 - Rational or not (ExH). For each of the following...Ch. 2.6 - Irrational or not. Determine if each of the...Ch. 2.6 - In Mindscapes 10-16, show that the value given is...Ch. 2.6 - In Mindscapes 10-16, show that the value given is...Ch. 2.6 - In Mindscapes 10-16, show that the value given is...Ch. 2.6 - In Mindscapes 10-16, show that the value given is...Ch. 2.6 - In Mindscapes 10-16, show that the value given is...Ch. 2.6 - In Mindscapes 10-16, show that the value given is...Ch. 2.6 - In Mindscapes 10-16, show that the value given is...Ch. 2.6 - An irrational exponent (H). Suppose that E is the...Ch. 2.6 - Another irrational exponent. Suppose that E is the...Ch. 2.6 - Still another exponent (ExH). Suppose that E is...Ch. 2.6 - Another rational exponent. Suppose that E is the...Ch. 2.6 - Rational exponent. Suppose that E is the number...Ch. 2.6 - Rational sums. Show that the sum of any two...Ch. 2.6 - Rational products. Show that the product of any...Ch. 2.6 - Root of a rational Show that (1/2) is irrational.Ch. 2.6 - Root of a rational (S). Show that (2/3) is...Ch. 2.6 - . Using the fact that is irrational, show that +3...Ch. 2.6 - 2. Using the fact that is irrational, show that 2...Ch. 2.6 - 2. Suppose that we know only that 2 is irrational....Ch. 2.6 - A rational in disguise. Show that the number (22)2...Ch. 2.6 - Prob. 30MSCh. 2.6 - More cube roots. Show that 33 is irrational.Ch. 2.6 - One-fourth root. Show that the fourth root of...Ch. 2.6 - Irrational sums (S). Does an irrational number...Ch. 2.6 - Irrational products (H). Does an irrational number...Ch. 2.6 - Irrational plus rational. Does an irrational...Ch. 2.6 - p. Show that for any prime number p,p ¡s an...Ch. 2.6 - pq. Show that, for any two different prime numbers...Ch. 2.6 - p+q. Show that, for any prime numbers p and q,p+q...Ch. 2.6 - 4. The square root of 4 is equal to 2, which is a...Ch. 2.6 - Sum or difference (H). Let a and b be any two...Ch. 2.6 - Rational x. Simplify the following expressions to...Ch. 2.6 - High 5. Suppose that x is a positive number...Ch. 2.6 - Dont be scared (H). Consider the scary equation....Ch. 2.6 - A hunt for irrationals. Find all solutions to the...Ch. 2.6 - A hunt for rationales. For any number x, the...Ch. 2.7 - X marks the X-act spot. On the number tine above,...Ch. 2.7 - Moving the point. Simplify each of the...Ch. 2.7 - Watch out for ones! Express 1/9 in decimal form....Ch. 2.7 - Real redundancy Suppose M=0.4999.... Then what...Ch. 2.7 - Being irrational. Explain what it means for a...Ch. 2.7 - Always, sometimes, never. A number with an...Ch. 2.7 - Square root of 5. The 5 has an unending decimal...Ch. 2.7 - A rational search (ExH). Find a rational number...Ch. 2.7 - Another rational search. Find a rational number...Ch. 2.7 - An Irrational search (H). Describe an irrational...Ch. 2.7 - Another irrational search. Describe an irrational...Ch. 2.7 - Your neighborhood. Suppose we tell you that we are...Ch. 2.7 - Another neighborhood. Suppose we tell you that we...Ch. 2.7 - In Mindscapes 14-16, express each fraction in its...Ch. 2.7 - In Mindscapes 14-16, express each fraction in its...Ch. 2.7 - In Mindscapes 14-16, express each fraction in its...Ch. 2.7 - In Mindscapes 17-25, express each number as a...Ch. 2.7 - In Mindscapes 17-25, express each number as a...Ch. 2.7 - In Mindscapes 17-25, express each number as a...Ch. 2.7 - In Mindscapes 17-25, express each number as a...Ch. 2.7 - In Mindscapes 17-25, express each number as a...Ch. 2.7 - In Mindscapes 17-25, express each number as a...Ch. 2.7 - In Mindscapes 17-25, express each number as a...Ch. 2.7 - In Mindscapes 17-25, express each number as a...Ch. 2.7 - In Mindscapes 17-25, express each number as a...Ch. 2.7 - Farey fractions. Let F be the collection of all...Ch. 2.7 - Even irrational. Show that the number...Ch. 2.7 - Odd irrational (H). Show that the number...Ch. 2.7 - A proof for . Suppose we look at the first one...Ch. 2.7 - Irrationals and zero. Is there an irrational...Ch. 2.7 - Irrational with 1s and 2s (S). Is it possible to...Ch. 2.7 - Irrational with 1s and some 2s. Is it possible to...Ch. 2.7 - Half steps. Suppose you are just a point and are...Ch. 2.7 - Half steps again (ExH). Suppose now that you are a...Ch. 2.7 - Cutting . Is it possible to cut up the interval...Ch. 2.7 - From infinite to finite. Find a real number that...Ch. 2.7 - Rationals (H). Show that, between any two...Ch. 2.7 - Irrationals. Show that, between any two different...Ch. 2.7 - Terminator. Show that if a rational number has a...Ch. 2.7 - Terminator II. Show that if the denominator of a...Ch. 2.7 - An unknown digit. Let x be a digit satisfying the...Ch. 2.7 - Prob. 46MSCh. 2.7 - Is y irrational? You decide to create the digits...Ch. 2.7 - Is z irrational? Follow the same construction as...Ch. 2.7 - Triple digits (H). Suppose a, b, and c are digits...
Additional Math Textbook Solutions
Find more solutions based on key concepts
A categorical variable has three categories, with the following frequencies of occurrence: a. Compute the perce...
Basic Business Statistics, Student Value Edition
Assessment 1-1A Cookies are sold singly or in packages of 2 or 6. With this packaging, how many ways can you bu...
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
9. Grading Exams Your professor has just collected eight different statistics exams. If these exams are graded ...
Elementary Statistics (13th Edition)
Sampling Method. In Exercises 9-12, determine whether the sampling method appears to be sound or is flawed.
9. ...
Elementary Statistics
1. combination of numbers, variables, and operation symbols is called an algebraic______.
Algebra and Trigonometry (6th Edition)
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)
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
- 2.8.1arrow_forwardDo not use the Residue Theorem. Thank you.arrow_forwardA television network earns an average of $14 million each season from a hit program and loses an average of $8 million each season on a program that turns out to be a flop. Of all programs picked up by this network in recent years, 25% turn out to be hits and 75% turn out to be flops. At a cost of C dollars, a market research firm will analyze a pilot episode of a prospective program and issue a report predicting whether the given program will end up being a hit. If the program is actually going to be a hit, there is a 75% chance that the market researchers will predict the program to be a hit. If the program is actually going to be a flop, there is only a 30% chance that the market researchers will predict the program to be a hit. What is the maximum value of C that the network should be willing to pay the market research firm? Enter your answer in dollars, not in million dollars. $ __________ Calculate EVPI for this decision problem. Enter your answer in dollars, not in million…arrow_forward
- Evaluate the line integral sin z dz, So sin where C is the portion of the curve y = x² from 0 to −1 + i.arrow_forwardLet f(z) be complex differentiable everywhere in C. Fix two distinct complex numbers a and b and a circle C of radius R with |a| < R,|b| < R traversed in the counter-clockwise direction. Evaluate the integral Sc − f(z)dz (z - a)(z – b) in terms of a, b and the values of f at those points.arrow_forward| Let C be a circle (with a positive radius) such that z = 1 lies in its interior. Evaluate the contour integral So Tz zez (z - 1)³ = where C is traversed in the clockwise direction. dzarrow_forward
- question 8arrow_forwardTwo construction companies are bidding against one another for the right to construct a new community center building. The first construction company, Fine Line Homes, believes that its competitor, Buffalo Valley Construction, will place a bid for this project according to the distribution shown in this table: Buffalo Valley's Bid Bid Probability $160,000 0.2 $165,000 0.5 $170,000 0.2 $175,000 0.1 Furthermore, Fine Line Homes estimates that it will cost $160,000 for its own company to construct this building. Given its fine reputation and long-standing service within the local community, Fine Line Homes believes that it will likely be awarded the project in the event that it and Buffalo Valley Construction submit exactly the same bids. Find the bid that maximizes Fine Line’s expected profit. Max expected profit $ ________ . Bid that maximizes profit $ ________ .arrow_forwardFind the area of the surface obtained by rotating the circle x² + y² = r² about the line y = r.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
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
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Elements Of Modern Algebra
Algebra
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Cengage Learning,
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
What is a Relation? | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=hV1_wvsdJCE;License: Standard YouTube License, CC-BY
RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY