A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
13th Edition
ISBN: 9780135183885
Author: Rick Billstein, Shlomo Libeskind, Johnny Lott, Barbara Boschmans
Publisher: PEARSON
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Chapter 4.CR, Problem 28CR
To determine
To prove:
That for all whole numbers
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3. Bayesian Inference – Updating Beliefs
A medical test for a rare disease has the following characteristics:
Sensitivity (true positive rate): 99%
Specificity (true negative rate): 98%
The disease occurs in 0.5% of the population.
A patient receives a positive test result.
Questions:
a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.
Chapter 4 Solutions
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Ch. 4.1 - Prob. 1MCCh. 4.1 - A customer wants to mail a package. The postal...Ch. 4.1 - Prob. 4MCCh. 4.1 - Prob. 5MCCh. 4.1 - A number in which each digit except 0 appears...Ch. 4.1 - Prob. 7MCCh. 4.1 - Three tiles marked x, yandz need three different...Ch. 4.1 - Prob. 10MCCh. 4.1 - Prob. 11MCCh. 4.1 - Jamila claims 10 is both even and odd because it...
Ch. 4.1 - Sabine claimed that a whole number is divisible by...Ch. 4.1 - Your seventh-grade class has just completed a unit...Ch. 4.1 - A student claims that a number is divisible by 24...Ch. 4.1 - Alejandro claims zero is neither even nor odd...Ch. 4.1 - Prob. 17MCCh. 4.1 - Andy has three cards, A, B, and C. Each card has...Ch. 4.1 - Prob. 2NAEPCh. 4.1A - If you multiply an even number by 2 and add 1, is...Ch. 4.1A - Classify each of the following statements as true...Ch. 4.1A - Use the divisibility test to test each of the...Ch. 4.1A - Using divisibility test, solve each of the...Ch. 4.1A - Find all possible single digits that can be placed...Ch. 4.1A - Find in the following blanks with the greatest...Ch. 4.1A - Prob. 7ACh. 4.1A - Without using Calculator, classify each of the...Ch. 4.1A - Classify each of the following statements as true...Ch. 4.1A - Find if possible a whole number solution that...Ch. 4.1A - Classify each of the following statements as true...Ch. 4.1A - An archery target consists of five concentric...Ch. 4.1A - To find the remainder when a number is divided by...Ch. 4.1A - If 45|n, what other whole numbers divide n? Why?Ch. 4.1A - Devise a test for divisibility by 16.Ch. 4.1A - A palindrome is a number that reads the same...Ch. 4.1A - Prove the test for divisibility by 9 for any...Ch. 4.1A - If the five-digit number aa248 is divisible by 9,...Ch. 4.1B - If you multiply an odd number by 2 and add 1, is...Ch. 4.1B - Without using a calculator, test each of the...Ch. 4.1B - Using divisibility test, solve each of the...Ch. 4.1B - Find all possible single digits that can be placed...Ch. 4.1B - Without using a calculator, classify each of the...Ch. 4.1B - Prob. 7ACh. 4.1B - Prob. 8ACh. 4.1B - Prob. 9ACh. 4.1B - Prob. 10ACh. 4.1B - The bookstore marked some notepads down from 2.00...Ch. 4.1B - Classify each of the following statements as true...Ch. 4.1B - In a football game, a touchdown with an extra...Ch. 4.1B - Classify each of the following statements as true...Ch. 4.1B - Compete the following table where n is the given...Ch. 4.1B - If 28|n, what other whole numbers divide n? Why?Ch. 4.1B - Devise a test for divisibility by 25.Ch. 4.1B - Use the casting out nines approach outlined in...Ch. 4.1B - Prob. 19ACh. 4.1B - Prove the test for divisibility by 9 for any...Ch. 4.1B - For what digit a is the five-digit number a6a14...Ch. 4.2 - Mathematical Connections Explain why the product...Ch. 4.2 - Mathematical Connections Explain why the product...Ch. 4.2 - Mathematical Connections In the Sieve of...Ch. 4.2 - Mathematical Connections Let M=2357+11131719,...Ch. 4.2 - Prob. 5MCCh. 4.2 - Prob. 6MCCh. 4.2 - Prob. 7MCCh. 4.2 - A perfect square is a number that can be written...Ch. 4.2 - Prob. 9MCCh. 4.2 - Prob. 10MCCh. 4.2 - Prob. 11MCCh. 4.2 - Mathematical Connections When students asked their...Ch. 4.2 - Mathematical Connections a. In which of the...Ch. 4.2 - To test for divisibility by 12, one student...Ch. 4.2 - Prob. 15MCCh. 4.2 - Prob. 16MCCh. 4.2 - Prob. 17MCCh. 4.2 - Prob. 18MCCh. 4.2 - Prob. 19MCCh. 4.2 - Prob. 20MCCh. 4.2 - Prob. 21MCCh. 4.2 - Prob. 22MCCh. 4.2 - Prob. 23MCCh. 4.2 - Prove that if a number is divisible by 45, then it...Ch. 4.2 - Prob. 1NAEPCh. 4.2 - Prob. 2NAEPCh. 4.2A - a. Fill in the missing numbers in the following...Ch. 4.2A - Prob. 2ACh. 4.2A - Find the prime factorization of the following...Ch. 4.2A - What is the greatest prime that must be considered...Ch. 4.2A - Question. Determine which of the following Number...Ch. 4.2A - Find the least natural number that is divisible by...Ch. 4.2A - Find the least three-digit whole number that has...Ch. 4.2A - Prob. 8ACh. 4.2A - Prob. 9ACh. 4.2A - Explain why 2332253 is not a prime factorization...Ch. 4.2A - Is it possible to find non-zero whole numbers...Ch. 4.2A - If 32n=26355473117, explain why 2357116 is a...Ch. 4.2A - Is 74113 a factor of 75113? Explain why or why...Ch. 4.2A - Prob. 14ACh. 4.2A - Prob. 15ACh. 4.2A - Briah and Emma are on the same swim team for the...Ch. 4.2A - A women with a basket of eggs finds that if she...Ch. 4.2A - A band of 17 pirates stole a sack of golden coins....Ch. 4.2A - A license plate is in two parts, a two-digit...Ch. 4.2A - The prime numbers 11 and 13 are twin primes...Ch. 4.2A - A whole number is a perfect number if the sum of...Ch. 4.2B - a. Fill in the missing numbers in the following...Ch. 4.2B - Use a factor tree to find the prime factorization...Ch. 4.2B - Find the prime factorization of the following...Ch. 4.2B - What is the greatest prime that must be considered...Ch. 4.2B - Determine which of the following numbers are...Ch. 4.2B - Find the least natural number that is divisible by...Ch. 4.2B - Find the greatest four-digit whole number that has...Ch. 4.2B - Prob. 8ACh. 4.2B - Find the prime factorization of each of the...Ch. 4.2B - Explain why 225392 is not a prime factorization...Ch. 4.2B - Is it possible to find non-zero whole numbers...Ch. 4.2B - If 2n=26355473117 explain why 2357116 is a factor...Ch. 4.2B - Prob. 13ACh. 4.2B - Prob. 14ACh. 4.2B - Mr. Wong wants to build a new rectangular patio....Ch. 4.2B - Prob. 16ACh. 4.2B - Jose has fewer than 100 baseball cards. If he puts...Ch. 4.2B - Isabelle, Noelle, and Juliette acquired a pile of...Ch. 4.2B - For a collection of red, green and blue beads,...Ch. 4.2B - A prime such as 7331 is a magic prime because any...Ch. 4.2B - A whole number is an abundant number if the sum of...Ch. 4.3 - Can two non-zero whole numbers have a greatest...Ch. 4.3 - Prob. 2MCCh. 4.3 - Prob. 3MCCh. 4.3 - Prob. 4MCCh. 4.3 - Is it true that every common divisor of two...Ch. 4.3 - Prob. 6MCCh. 4.3 - Prob. 7MCCh. 4.3 - Prob. 8MCCh. 4.3 - Prob. 9MCCh. 4.3 - Prob. 10MCCh. 4.3 - Explain why GCD(a,b) is always a divisor of...Ch. 4.3 - Prob. 12MCCh. 4.3 - Eleanor claims that the GCD(0,a)=0. Is she...Ch. 4.3 - A student claims the GCD(0,0) does not exist. Is...Ch. 4.3 - Prob. 15MCCh. 4.3 - Prob. 16MCCh. 4.3 - Prob. 17MCCh. 4.3 - Prob. 18MCCh. 4.3 - Prob. 19MCCh. 4.3 - Prob. 20MCCh. 4.3 - Prob. 21MCCh. 4.3 - Prob. 22MCCh. 4.3 - Prob. 1NAEPCh. 4.3A - Use colored rods to find the GCD and the LCM of 6...Ch. 4.3A - Prob. 2ACh. 4.3A - Find the GCD and the LCM for each of the following...Ch. 4.3A - Find the GCD for each pair of numbers using the...Ch. 4.3A - Find the LCM for each of the following groups of...Ch. 4.3A - The product of two numbers is 1734 and their GCD...Ch. 4.3A - The GCD of two numbers is 19 and their LCM is 228....Ch. 4.3A - Prob. 8ACh. 4.3A - Prob. 9ACh. 4.3A - To find GCD24, 20, 12, it is possible to find...Ch. 4.3A - Show that 97, 219, 988, 751 and 4 are relatively...Ch. 4.3A - Draw Venn diagrams to show the prime factors for...Ch. 4.3A - Find three pairs (a,b) such that LCM(a,b)=48.Ch. 4.3A - Find all whole numbers x such that GCD(49,x)=1 and...Ch. 4.3A - In Quinns dormitory room, there are three...Ch. 4.3A - A company is running a promotion on Facebook....Ch. 4.3A - If there were to be 9 boys and 6 girls at a party...Ch. 4.3A - Three motorcyclists ride around a circular course...Ch. 4.3A - Anna has made 42 chocolate chip cookies and 54...Ch. 4.3A - The front wheel of a tricycle has a circumference...Ch. 4.3A - Jazz has 72 yd of red ribbon and 42 yd of blue...Ch. 4.3B - Use colored rods to find the GCD and the LCM of 4...Ch. 4.3B - Find the GCD and LCM for each of the following...Ch. 4.3B - Find the GCD and LCM for each of the following...Ch. 4.3B - Find the GCD and LCM for each of the following...Ch. 4.3B - Find the LCM for each of the following groups of...Ch. 4.3B - The product of two numbers is 5880 and their GCD...Ch. 4.3B - The GCD of two numbers is 11 and their LCM is 330....Ch. 4.3B - Assume a and b are natural numbers and answer the...Ch. 4.3B - Classify each of the following statements as true...Ch. 4.3B - To find GCD 24, 20, 12, it is possible to find GCD...Ch. 4.3B - Show that 181, 345, 913 and 11 are relatively...Ch. 4.3B - Draw Venn diagrams to show the prime factors for...Ch. 4.3B - Find three pairs (a,b) such that LCM(a,b)=60.Ch. 4.3B - Find all whole numbers x such that GCD(25,x)=1 and...Ch. 4.3B - A light display has colored lights, each of which...Ch. 4.3B - A movie rental store gave a free popcorn to every...Ch. 4.3B - Bonita purchases 245 white bouncy balls, 238...Ch. 4.3B - A college runs two different bus routes starting...Ch. 4.3B - By selling cookies at 24c each, Cheng made enough...Ch. 4.3B - Gina runs every 4 days, cycles every 16 days, and...Ch. 4.3B - Kobe has collected 300 football card and 264...Ch. 4.CR - Classify each of the following statements as true...Ch. 4.CR - Test each of the following numbers for...Ch. 4.CR - Find the greatest digit if possible, that makes...Ch. 4.CR - Prob. 4CRCh. 4.CR - How can you tell whether a number is divisible by...Ch. 4.CR - Prob. 6CRCh. 4.CR - Find all the positive divisors of 144.Ch. 4.CR - Prob. 8CRCh. 4.CR - Prob. 9CRCh. 4.CR - Determine whether each of the following numbers is...Ch. 4.CR - Prob. 11CRCh. 4.CR - Prob. 12CRCh. 4.CR - Find the prime factorization of each of the...Ch. 4.CR - Prob. 14CRCh. 4.CR - Prob. 15CRCh. 4.CR - Find the GCD for each of the following pairs of...Ch. 4.CR - Find the LCM of each of the following gropus of...Ch. 4.CR - Prob. 19CRCh. 4.CR - Prob. 20CRCh. 4.CR - Prob. 21CRCh. 4.CR - Prob. 22CRCh. 4.CR - Two bells ring at 8:00A.M for the remainder of the...Ch. 4.CR - Midas has 120 gold coins and 144 silver coins. He...Ch. 4.CR - Jane and Ramon are running laps on a track. If...Ch. 4.CR - Prob. 26CRCh. 4.CR - Prob. 27CRCh. 4.CR - Prob. 28CRCh. 4 - NOW TRY THIS For any whole numbers aandb,...Ch. 4 - NOW TRY THIS If d(x+y+z) and dz, why d(x+y)?Ch. 4 - Prob. 3NTCh. 4 - NOW TRY THIS 4 Colored rods are used in the...Ch. 4 - Prob. 5NTCh. 4 - Prob. 6NT
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