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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Textbook Question
Chapter 3.4B, Problem 18A
ASSESSMENT
Simplify each of the following multiplications using properties of exponents. Leave answer as powers.
a.
c.
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Chapter 3 Solutions
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Ch. 3.1 - Mathematical Connections Explain why a number and...Ch. 3.1 - If a numeration system has place value, what does...Ch. 3.1 - Explain the difference between zero and nothingCh. 3.1 - What are the major drawbacks to each of the...Ch. 3.1 - Large numbers in the United States are written...Ch. 3.1 - In the Roman numeral system, explain a when you...Ch. 3.1 - Mathematical Connections Research an abacus and...Ch. 3.1 - Prob. 8MCCh. 3.1 - Mathematical Connections Research Adrian Treffers...Ch. 3.1 - Mathematical Connections Joanne asks if the year...
Ch. 3.1 - Betty asks how the two 3s in the numeral 32,356...Ch. 3.1 - A student claims that the Roman system is a...Ch. 3.1 - When using Roman numerals, a student asks whether...Ch. 3.1 - The School Book Page on page 88 shows place value...Ch. 3.1 - Which of the following numbers is represented by...Ch. 3.1 - Which number does the diagram above represent? a...Ch. 3.1 - Write a three-digit number using the digits 2,4...Ch. 3.1 - There are 153,685 people living in a city. What is...Ch. 3.1A - For each of the following pairs of numerals, tell...Ch. 3.1A - A cornerstone representing when a building was...Ch. 3.1A - Write each of the following numerals in Roman...Ch. 3.1A - Indicate which digit in 234,518 has place value....Ch. 3.1A - For each of the following base-ten numerals, give...Ch. 3.1A - Rewrite each of the following as base-ten numeral....Ch. 3.1A - Write the following numerals in words....Ch. 3.1A - How many digits are there in the Hindu-Arabic form...Ch. 3.1A - A certain three-digit natural number has the...Ch. 3.1A - In the counting frame, the value of each dot is...Ch. 3.1A - Write the base four numeral for the following...Ch. 3.1A - Prob. 13ACh. 3.1A - How many different digits are needed for the...Ch. 3.1A - Write 2032four in expanded notation and then...Ch. 3.1A - Determine the greatest three-digit number in each...Ch. 3.1A - Find the numeral preceding and succeeding each of...Ch. 3.1A - What, if anything, is wrong with the following...Ch. 3.1A - Draw base-five blocks to represent 231five.Ch. 3.1A - Without converting to base-ten, tell which is the...Ch. 3.1A - Recall that with base-ten blocks: 1long=10units,...Ch. 3.1A - Convert each of the following base-ten numerals to...Ch. 3.1A - Write each of the following numerals in base ten....Ch. 3.1A - Represent abcdsix, a base-six numeral, in expanded...Ch. 3.1A - In what base does 12b+26b=41b?Ch. 3.1A - You are asked to distribute 900 in prize money....Ch. 3.1A - For each of the following, find b if possible. If...Ch. 3.1A - Write the following numerals in the indicated base...Ch. 3.1A - Complete the following table. Base Ten Base Two...Ch. 3.1B - Prob. 1ACh. 3.1B - Prob. 2ACh. 3.1B - On the United States one-dollar bill, the number...Ch. 3.1B - Write each of the following numerals in Roman...Ch. 3.1B - Indicate which digit in 2,345,925 has place value....Ch. 3.1B - For each of the following base-ten numerals, give...Ch. 3.1B - Rewrite each of the following as a base-ten...Ch. 3.1B - Write the following in words. a. 253,243,810 b....Ch. 3.1B - How many digits are there in the Hindu-Arabic form...Ch. 3.1B - A two-digit number has the property that the units...Ch. 3.1B - Prob. 11ACh. 3.1B - Assessment Write the base-three numeral for the...Ch. 3.1B - Write the first 10 counting numerals for each of...Ch. 3.1B - How many different digits are used in base...Ch. 3.1B - Write 2022three in expanded form and then convert...Ch. 3.1B - Determine the greatest three-digit number in each...Ch. 3.1B - Find the numeral preceding and succeeding each of...Ch. 3.1B - What, if anything, is wrong with the following? a....Ch. 3.1B - Draw base-two blocks to represent 1001two.Ch. 3.1B - Prob. 20ACh. 3.1B - Assessment What is the fewest number of multibase...Ch. 3.1B - Convert each of the following base-ten numerals to...Ch. 3.1B - Write each of the following numerals in base ten....Ch. 3.1B - Represent abcdeight as a base-ten numeral in...Ch. 3.1B - In what base does 54b+45b=132b?Ch. 3.1B - Who Wants the Money, a game show, distributes...Ch. 3.1B - For each of the following numerals, find digit b,...Ch. 3.1B - Using only the number keys on a calculator, fill...Ch. 3.1B - Assessment Complete the following table. Base Ten...Ch. 3.1B - Use fair trading to represent the base-three...Ch. 3.2 - In a survey of 52 students, 22 said they were...Ch. 3.2 - To find 9+7, a student says she thinks of 9+7 as...Ch. 3.2 - Explain in two different ways why if ab and c is a...Ch. 3.2 - Prob. 4MCCh. 3.2 - Describe any model not in this text that you could...Ch. 3.2 - a. Create a word problem in which the set model...Ch. 3.2 - Discuss the merit of the following expanded...Ch. 3.2 - Is the front-end estimate for addition before...Ch. 3.2 - In the new textbooks, there is an emphasis on...Ch. 3.2 - Search for or develop an algorithm for...Ch. 3.2 - Give several examples from real-world situations...Ch. 3.2 - a. Give a numerical example of when front-end...Ch. 3.2 - Zeke claims that he can get the same answer to the...Ch. 3.2 - A child is asked to compute 7+2+3+8+11 and writes...Ch. 3.2 - When Richie was asked to round 2568 to the nearest...Ch. 3.2 - When Ashley was asked to round 345 to the nearest...Ch. 3.2 - Making a ten with ten frames is also helpful in...Ch. 3.2 - The associative, commutative, and identity...Ch. 3.2 - Read the compensation algorithm for addition on...Ch. 3.2 - Page 115 shows adding from left and breaking up...Ch. 3.2 - Prob. 21MCCh. 3.2 - Prob. 22MCCh. 3.2 - Prob. 23MCCh. 3.2 - Prob. 24MCCh. 3.2 - Prob. 25MCCh. 3.2 - Prob. 1NAEPCh. 3.2 - Prob. 2NAEPCh. 3.2 - Prob. 3NAEPCh. 3.2 - Prob. 4NAEPCh. 3.2A - Prob. 1ACh. 3.2A - If n(A)=3, n(B)=5 and n(AB)=6, what do you know...Ch. 3.2A - Give an example to show why, in the definition of...Ch. 3.2A - If n(A)=3, n(AB)=6, answer the following...Ch. 3.2A - Use a number line to model 5+7.Ch. 3.2A - A student uses the counting on strategy for adding...Ch. 3.2A - Use doubles+1 to solve 7+8.Ch. 3.2A - Use ten frames to make a ten. Then complete the...Ch. 3.2A - Prob. 9ACh. 3.2A - Which of the following sets are closed under...Ch. 3.2A - Each of the following equations illustrates an...Ch. 3.2A - Each of the following illustrates a property of...Ch. 3.2A - Show that each of the following is true. Give a...Ch. 3.2A - Find the solution for x in the set W for each of...Ch. 3.2A - Prob. 15ACh. 3.2A - Make a drawing similar to the one in Figure 15 to...Ch. 3.2A - Janet worked her addition problems by placing the...Ch. 3.2A - Use the lattice algorithm to perform each of the...Ch. 3.2A - Use the column-addition algorithm to compute...Ch. 3.2A - Use the opposite-change algorithm to compute...Ch. 3.2A - Perform each of the following addition problems in...Ch. 3.2A - Determine what is wrong with the following...Ch. 3.2A - Use breaking up and bridging to compute each of...Ch. 3.2A - Use trading off to compute each of the following...Ch. 3.2A - Prob. 25ACh. 3.2A - Estimate each answer by rounding. a. 878+2340 b....Ch. 3.2A - Use front-end estimation with adjustment to...Ch. 3.2A - Use the range strategy to estimate each of the...Ch. 3.2A - Suppose you had a balance of 3287 in your checking...Ch. 3.2A - Prob. 31ACh. 3.2A - 32. Complete the following magic square using the...Ch. 3.2A - If A, B, and C each stand for a different single...Ch. 3.2A - A special domino set contains all number pairs...Ch. 3.2A - Find the missing digits in each of the following...Ch. 3.2A - Place the digits 7, 6, 8, 3, 5, and 2 in the boxes...Ch. 3.2A - In the following problem, the sum is correct but...Ch. 3.2A - The following is a supermagic square....Ch. 3.2A - a. Place the numbers 1 through 9 in the following...Ch. 3.2A - Use scratch addition to perform the following...Ch. 3.2B - Prob. 1ACh. 3.2B - Prob. 2ACh. 3.2B - If n(B)=4, and n(AB)=6, answer the following. a....Ch. 3.2B - Use a number line to model 3+9.Ch. 3.2B - A student uses the counting on strategy for adding...Ch. 3.2B - Use the doubles plus strategy for adding the...Ch. 3.2B - Explain whether the following sets are closed...Ch. 3.2B - Prob. 8ACh. 3.2B - Use ten frames to make a ten. Then complete the...Ch. 3.2B - Each of the following equations is an example of...Ch. 3.2B - Each of the following illustrates a properties of...Ch. 3.2B - Prob. 12ACh. 3.2B - Prob. 13ACh. 3.2B - Prob. 14ACh. 3.2B - Make an appropriate drawing like the one in figure...Ch. 3.2B - Hector computed his addition problems by placing...Ch. 3.2B - Use the lattice algorithm to perform each of the...Ch. 3.2B - Use the column-addition algorithm to compute...Ch. 3.2B - Use the opposite-change algorithm to compute...Ch. 3.2B - Perform each of the following addition problems in...Ch. 3.2B - Determine what is wrong with the following...Ch. 3.2B - Prob. 22ACh. 3.2B - Estimate each answer by rounding. a. 937+28 b....Ch. 3.2B - Use front-end estimation with adjustment to...Ch. 3.2B - a. Would the clustering strategy of estimation be...Ch. 3.2B - Use the range strategy to estimate each of the...Ch. 3.2B - The attendance at a Country Fair for six days...Ch. 3.2B - Complete the following magic square using the...Ch. 3.2B - If A,B,C, and D each represent a different single...Ch. 3.2B - George is cooking a meal for Thanksgiving. He can...Ch. 3.2B - Use scratch addition to perform the following...Ch. 3.2B - What is the greatest possible addend that can be...Ch. 3.2B - In the following problem, the sum is correct but...Ch. 3.2B - The following is a super magic square taken from...Ch. 3.2B - a. Place the numbers 24 through 32 in the...Ch. 3.3 - When subtraction and addition appear in an...Ch. 3.3 - Explain whether it is important for elementary...Ch. 3.3 - Prob. 3MCCh. 3.3 - Explain how the model shown can be used to...Ch. 3.3 - Prob. 5MCCh. 3.3 - Prob. 6MCCh. 3.3 - Prob. 7MCCh. 3.3 - Prob. 8MCCh. 3.3 - Prob. 9MCCh. 3.3 - Prob. 10MCCh. 3.3 - Prob. 11MCCh. 3.3 - A student says asks why we use subtraction to...Ch. 3.3 - Prob. 13MCCh. 3.3 - Prob. 14MCCh. 3.3 - A first grader claims that 24=2 because you just...Ch. 3.3 - Ashton claims that if he has 8 cookies and eats 3...Ch. 3.3 - Jordan and Maksim started with the same number of...Ch. 3.3 - Prob. 18MCCh. 3.3 - To find 6819, Joe began by finding 61 and then 98...Ch. 3.3 - Mairead subtracted 415212 by writing 42=2 and...Ch. 3.3 - Olinda found 51849=469. She was not sure she was...Ch. 3.3 - Pauli subtracted 549 from 5004 as follows. How...Ch. 3.3 - Molly computed 26148 by first subtracting 50 from...Ch. 3.3 - Prob. 24MCCh. 3.3 - Prob. 25MCCh. 3.3 - Prob. 26MCCh. 3.3 - Prob. 27MCCh. 3.3 - Prob. 28MCCh. 3.3 - The trading-off strategy for mentally subtracting...Ch. 3.3 - Prob. 30MCCh. 3.3 - Prob. 31MCCh. 3.3 - Prob. 32MCCh. 3.3 - Prob. 33MCCh. 3.3 - 8=21 What number should be put in the box to make...Ch. 3.3 - Prob. 2NAEPCh. 3.3 - Prob. 3NAEPCh. 3.3 - Prob. 4NAEPCh. 3.3 - Prob. 5NAEPCh. 3.3A - Illustrate 85=3 using each of the following...Ch. 3.3A - Write a word problem that corresponds to each of...Ch. 3.3A - a. One fact in a fact family is 6+5=11.What are...Ch. 3.3A - What conditions, if any, must be placed on a and b...Ch. 3.3A - Rewrite each of the following subtraction problems...Ch. 3.3A - a. Solve for x in each of the following equations....Ch. 3.3A - Kelsey has a marbles, Gena has b marbles, and Noah...Ch. 3.3A - Analyze the following computations. Explain what...Ch. 3.3A - a. At a volleyball game, the players stood in a...Ch. 3.3A - Toms diet allows only 1500 calories per day. For...Ch. 3.3A - Use the equal-additions approach to compute each...Ch. 3.3A - Compute each of the following using the counting...Ch. 3.3A - Compute 146-85 using the trades-first algorithm.Ch. 3.3A - Place the digits 7, 6, 8, 3, 5 and 2 in the boxes...Ch. 3.3A - Construct an addition table for base eight and...Ch. 3.3A - Find the number to put in the blank to make each...Ch. 3.3A - Perform the following operation...Ch. 3.3A - Prob. 20ACh. 3.3A - Compute each of the following mentally and...Ch. 3.3A - Use breaking and bridging to compute 99732...Ch. 3.3B - Illustrate 73=4 using each of the following...Ch. 3.3B - Write a word problem that corresponds to each of...Ch. 3.3B - a. One fact in a fact family is 127=5. what are...Ch. 3.3B - Prob. 4ACh. 3.3B - Prob. 5ACh. 3.3B - Find the solution in the set W for each of the...Ch. 3.3B - Ross has 11pencils. Kersten has 5pencils. Which...Ch. 3.3B - Analyze the following computations. Explain what...Ch. 3.3B - If, ab,cb,dc,andced, order the letters from the...Ch. 3.3B - Find the missing digits in each of the following...Ch. 3.3B - Use the equal-additions approach to compute each...Ch. 3.3B - Compute each of the following using the...Ch. 3.3B - Make a table similar to the one in Figure 23 to...Ch. 3.3B - Compute 12858 using trades-first algorithm.Ch. 3.3B - Construct an additional table for base six, and...Ch. 3.3B - Perform each of the following operations using the...Ch. 3.3B - Find the number to put in the blank to make each...Ch. 3.3B - Perform each of the following operations (2c=...Ch. 3.3B - The Hawks played the Elks in a basketball game....Ch. 3.3B - Compute each of the following mentally. a....Ch. 3.3B - Compute each of the following mentally and...Ch. 3.3B - Use trading-off to compute each of the following...Ch. 3.3B - In each of the following, answer the question...Ch. 3.4 - MATHEMATICAL CONNECTIONS Why is an odd number...Ch. 3.4 - MATHEMATICAL CONNECTIONS Can 0 be the identity for...Ch. 3.4 - MATHEMATICAL CONNECTIONS Suppose you forgot the...Ch. 3.4 - MATHEMATICAL CONNECTIONS Is xx ever equal to x?...Ch. 3.4 - MATHEMATICAL CONNECTIONS Describe all pairs of...Ch. 3.4 - MATHEMATICAL CONNECTIONS Explain how the...Ch. 3.4 - MATHEMATICAL CONNECTIONS Describe a real-life...Ch. 3.4 - MATHEMATICAL CONNECTIONS How would you explain to...Ch. 3.4 - MATHEMATICAL CONNECTIONS What happens when you...Ch. 3.4 - If a student presented a new algorithm for...Ch. 3.4 - MATHEMATICAL CONNECTIONS Dina calculated each of...Ch. 3.4 - Prob. 12MCCh. 3.4 - Amy claims that no finite set of whole numbers is...Ch. 3.4 - Prob. 14MCCh. 3.4 - Prob. 15MCCh. 3.4 - A student performs the following computation....Ch. 3.4 - Prob. 17MCCh. 3.4 - The School Book Page on Page 141 shows both the...Ch. 3.4 - MATHEMATICAL CONNECTIONS An example of using the...Ch. 3.4 - Prob. 20MCCh. 3.4 - Prob. 21MCCh. 3.4 - Prob. 22MCCh. 3.4 - Prob. 23MCCh. 3.4 - Prob. 1NAEPCh. 3.4 - Prob. 2NAEPCh. 3.4 - Prob. 3NAEPCh. 3.4 - Prob. 4NAEPCh. 3.4 - Prob. 5NAEPCh. 3.4A - Show that 34=12 using each of the following...Ch. 3.4A - If A={a,b} and B={x,y,z}, find each of the...Ch. 3.4A - What multiplication is suggested by the following...Ch. 3.4A - For each of the following, find, if possible, a...Ch. 3.4A - A sporting goods store has designs for 6 shirts, 4...Ch. 3.4A - Prob. 6ACh. 3.4A - Prob. 7ACh. 3.4A - a. If 5 is removed from the set of whole numbers,...Ch. 3.4A - Rename each of the following using distributive...Ch. 3.4A - Using the distributive property of multiplication...Ch. 3.4A - Which property is illustrated in each of the...Ch. 3.4A - The product 614 can be found by thinking of the...Ch. 3.4A - Use the distributive property of multiplication...Ch. 3.4A - Show that (a+b)2=a2+2ab+b2 using a. the...Ch. 3.4A - If a and b are whole numbers with ab, use the...Ch. 3.4A - Use the property (a+b)2=a2+2ab+b2 to compute the...Ch. 3.4A - Factor each of the following expressions. a. xyy2...Ch. 3.4A - Simplify each of the following multiplications...Ch. 3.4A - a. Which is greater, 280+280 or 2100? Why? b....Ch. 3.4A - Illustrate how to use base-ten blocks to compute...Ch. 3.4A - Perform the following multiplications using the...Ch. 3.4A - Use lattice multiplication to compute...Ch. 3.4A - Find the least values of a and b such that...Ch. 3.4A - a. Use the distributive property of multiplication...Ch. 3.4A - Discuss possible error patterns in the following...Ch. 3.4A - Give reasons for each of the following steps....Ch. 3.4A - Place the digits 7, 6, 8, and 3 in the boxes to...Ch. 3.4A - Assessment Answer the following questions based on...Ch. 3.4A - Dan has 4520 pennies in three boxes. He says that...Ch. 3.4A - Assessment Fill in the missing numbers in each of...Ch. 3.4A - A car trip book 8 hrs of driving at an average of...Ch. 3.4A - A theater has 38 rows with 23 seats in each row....Ch. 3.4A - Without computing, tell which of the following...Ch. 3.4A - Use your calculator to calculate...Ch. 3.4A - A student uses front-end estimation to estimate...Ch. 3.4B - Prob. 1ACh. 3.4B - ASSESSMENT If A={a,b,c,d} and B={x,y,z}, find each...Ch. 3.4B - ASSESSMENT What multiplication is suggested by the...Ch. 3.4B - ASSESSMENT For each of the following, find, if...Ch. 3.4B - ASSESSMENT A new car comes in 5 exterior colors...Ch. 3.4B - ASSESSMENT A local coffee shop has 5 syrup...Ch. 3.4B - ASSESSMENT Determine if the following sets are...Ch. 3.4B - Prob. 8ACh. 3.4B - ASSESSMENT Rename each of the following using the...Ch. 3.4B - Prob. 10ACh. 3.4B - ASSESSMENT Which property of whole numbers is...Ch. 3.4B - The product 524 can be found by thinking of the...Ch. 3.4B - Prob. 13ACh. 3.4B - ASSESSMENT Show that if bc, then a(bc)=abac, using...Ch. 3.4B - ASSESSMENT Use the formula (a+b)(ab)=a2b2 to...Ch. 3.4B - ASSESSMENT Factor each of the following: a. xyyb....Ch. 3.4B - ASSESSMENT Simplify each of the following...Ch. 3.4B - ASSESSMENT a. Which is greater, l 220+220 or 221?...Ch. 3.4B - ASSESSMENT Illustrate how to use base-ten blocks...Ch. 3.4B - The following model illustrates 1312. a. Explain...Ch. 3.4B - Assessment Perform the following multiplications...Ch. 3.4B - Assessment Use lattice multiplication to compute...Ch. 3.4B - ASSESSMENT Find the least values of a and b such...Ch. 3.4B - ASSESSMENT a. Use a distributive property of...Ch. 3.4B - ASSESSMENT Discuss possible error patterns in each...Ch. 3.4B - ASSESSMENT Give reasons for each of the following...Ch. 3.4B - ASSESSMENT Answer the following questions based on...Ch. 3.4B - ASSESSMENT Debbie has 340 dimes in three boxes....Ch. 3.4B - ASSESSMENT Fill in the missing numbers in the...Ch. 3.4B - ASSESSMENT A car trip took 6hours at an average of...Ch. 3.4B - ASSESSMENT About 3540 calories must be burned to...Ch. 3.4B - Without computing, tell which of the following...Ch. 3.4B - Use your calculator to multiply several two-digit...Ch. 3.4B - A student users front-end estimation to estimation...Ch. 3.5 - Is xx always equal to 1? Explain your answer.Ch. 3.5 - Is the answer to 203(2+4) equal to 38,18,2, or 10?...Ch. 3.5 - Prob. 3MCCh. 3.5 - Pick a number Double it. Multiply the result by 3....Ch. 3.5 - Prob. 5MCCh. 3.5 - Prob. 6MCCh. 3.5 - For the given computation, answer the following...Ch. 3.5 - Prob. 8MCCh. 3.5 - Suppose a student argued that 00=1 because every...Ch. 3.5 - A student claims that for all whole numbers...Ch. 3.5 - Prob. 11MCCh. 3.5 - Prob. 12MCCh. 3.5 - A student divides as follows. How do you help?Ch. 3.5 - A student asks how you can find the quotient and...Ch. 3.5 - A student claim that to divide a number with the...Ch. 3.5 - a. A student notices that 39+41=40+40 and wonders...Ch. 3.5 - What errors do you think the student is making in...Ch. 3.5 - Complete the Convince Me on the School Book Page...Ch. 3.5 - Prob. 19MCCh. 3.5 - The School Book Page on page 171 shows the partial...Ch. 3.5 - Prob. 21MCCh. 3.5 - Prob. 22MCCh. 3.5 - At the beginning of a trip, the mileage odometer...Ch. 3.5 - Prob. 1NAEPCh. 3.5 - Prob. 2NAEPCh. 3.5 - Ms. Kim has 45 stickers that she wants to give out...Ch. 3.5 - Which expression has the least value? a. 2+7+0+4...Ch. 3.5 - Prob. 5NAEPCh. 3.5A - Rewrite each of the following division problems as...Ch. 3.5A - For each of the following equation, find whole...Ch. 3.5A - If /108/a=b then find 108/b.Ch. 3.5A - Write the complete fact family for 72/8=9.Ch. 3.5A - Perform each of the following divisions using both...Ch. 3.5A - Show that, in general, each of the following is...Ch. 3.5A - Suppose all of the operations result in whole...Ch. 3.5A - Is it possible to find a whole number less than...Ch. 3.5A - Place the digits 4,5,7, and 3 in the boxes ____ to...Ch. 3.5A - Using a calculator, Ralph multiplied by 10 when he...Ch. 3.5A - Use base ten block to illustrate 1325.Ch. 3.5A - Use the partial quotients algorithm to computer...Ch. 3.5A - Students were divided into 10 teams with 12 on...Ch. 3.5A - Prob. 16ACh. 3.5A - Assessment Deborah Lynn purchases a 50,000 life...Ch. 3.5A - a. Find all whole numbers that leave have 3 upon...Ch. 3.5A - Place parentheses, if needed, to make each of the...Ch. 3.5A - In each of the following, tell what computation...Ch. 3.5A - Think of a number. Multiply it by 5.Add 5. Divide...Ch. 3.5A - In each of the following, determine if the...Ch. 3.5B - Rewrite each of the following division problems as...Ch. 3.5B - For each of the following equations, find whole...Ch. 3.5B - If 64a=b, then find 64b.Ch. 3.5B - Show that, in general, each of the following is...Ch. 3.5B - Suppose all operations result in whole numbers....Ch. 3.5B - Jonah has a large collection of marbles. He...Ch. 3.5B - Place the digits 7, 6, 8, and 3 in the boxes to...Ch. 3.5B - Using a calculator, Jody multiplied by 5 when she...Ch. 3.5B - Use base-ten blocks to illustrate 2568.Ch. 3.5B - Use the partial-quotients algorithm to compute...Ch. 3.5B - Prob. 14ACh. 3.5B - Students were divided into eight teams with nine...Ch. 3.5B - Find all whole numbers that leave remainder 3 upon...Ch. 3.5B - Marry Kaye purchased a 30000 life insurance policy...Ch. 3.5B - a. Find all the whole numbers that have remainder...Ch. 3.5B - Place parentheses, if needed, to make each of the...Ch. 3.5B - In each of the following, tell what computation...Ch. 3.5B - Think of a number. Multiply it by 2. Add 2. Divide...Ch. 3.5B - In each of the following, determine if the...Ch. 3.CR - Prob. 1CRCh. 3.CR - Prob. 2CRCh. 3.CR - Simplify each of the following products, if...Ch. 3.CR - Write the base-three numeral for the base-three...Ch. 3.CR - What is the fewest number of base-three blocks...Ch. 3.CR - Draw multi base blocks to represent. a. 123four b....Ch. 3.CR - Prob. 7CRCh. 3.CR - Prob. 8CRCh. 3.CR - Write 128 in each of the following bases. a. Five...Ch. 3.CR - Prob. 10CRCh. 3.CR - Prob. 11CRCh. 3.CR - Prob. 12CRCh. 3.CR - Prob. 13CRCh. 3.CR - Prob. 14CRCh. 3.CR - Prob. 15CRCh. 3.CR - Prob. 16CRCh. 3.CR - Prob. 17CRCh. 3.CR - Prob. 18CRCh. 3.CR - Prob. 19CRCh. 3.CR - Prob. 20CRCh. 3.CR - Prob. 21CRCh. 3.CR - Prob. 22CRCh. 3.CR - Prob. 23CRCh. 3.CR - Prob. 24CRCh. 3.CR - Prob. 25CRCh. 3.CR - Prob. 26CRCh. 3.CR - Prob. 27CRCh. 3.CR - Prob. 28CRCh. 3.CR - Prob. 29CRCh. 3.CR - Prob. 30CRCh. 3.CR - Prob. 31CRCh. 3.CR - Prob. 32CRCh. 3.CR - Prob. 33CRCh. 3.CR - Prob. 34CRCh. 3.CR - Prob. 35CRCh. 3.CR - Prob. 36CRCh. 3.CR - Prob. 37CRCh. 3.CR - Prob. 38CRCh. 3.CR - Prob. 39CRCh. 3.CR - Recall that addition problems like 3478+521 can be...Ch. 3.CR - Prob. 41CRCh. 3.CR - Prob. 42CRCh. 3.CR - Prob. 43CRCh. 3.CR - Prob. 44CRCh. 3.CR - Prob. 45CRCh. 3.CR - Prob. 46CRCh. 3 - Now Try this 1 a. Trade base-ten blocks to write 3...Ch. 3 - Now Try this 2 A different method of converting...Ch. 3 - Now Try this 3 If the sets in the preceding...Ch. 3 - Now Try this 4 A common error is that students...Ch. 3 - Prob. 5NTCh. 3 - Prob. 6NTCh. 3 - Prob. 7NTCh. 3 - Prob. 8NTCh. 3 - Prob. 9NTCh. 3 - Prob. 10NTCh. 3 - Prob. 11NTCh. 3 - Now Try this 12 Find a solution for each of the...Ch. 3 - Prob. 13NTCh. 3 - NOW TRY THIS a. Build an addition table for base...Ch. 3 - Now Try this 15 Perform each of the following...Ch. 3 - Now Try this 16 Estimate the following mentally,...Ch. 3 - Prob. 17NTCh. 3 - Prob. 18NTCh. 3 - Prob. 19NTCh. 3 - Prob. 20NT
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- Refer to page 9 for a problem requiring finding the tangent plane to a given surface at a point. Instructions: Use partial derivatives to calculate the equation of the tangent plane. Show all calculations step-by-step. Link [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]arrow_forwardRefer to page 8 for a problem involving solving a second-order linear homogeneous differential equation. Instructions: Solve using characteristic equations. Show all intermediate steps leading to the general solution. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]arrow_forwardRefer to page 17 for a problem requiring solving a nonlinear algebraic equation using the bisection method. Instructions: Show iterative calculations for each step, ensuring convergence criteria are satisfied. Clearly outline all steps. Link [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440AZF/view?usp=sharing]arrow_forward
- Problem: The probability density function of a random variable is given by the exponential distribution Find the probability that f(x) = {0.55e−0.55x 0 < x, O elsewhere} a. the time to observe a particle is more than 200 microseconds. b. the time to observe a particle is less than 10 microseconds.arrow_forwardThe OU process studied in the previous problem is a common model for interest rates. Another common model is the CIR model, which solves the SDE: dX₁ = (a = X₁) dt + σ √X+dWt, - under the condition Xoxo. We cannot solve this SDE explicitly. = (a) Use the Brownian trajectory simulated in part (a) of Problem 1, and the Euler scheme to simulate a trajectory of the CIR process. On a graph, represent both the trajectory of the OU process and the trajectory of the CIR process for the same Brownian path. (b) Repeat the simulation of the CIR process above M times (M large), for a large value of T, and use the result to estimate the long-term expectation and variance of the CIR process. How do they compare to the ones of the OU process? Numerical application: T = 10, N = 500, a = 0.04, x0 = 0.05, σ = 0.01, M = 1000. 1 (c) If you use larger values than above for the parameters, such as the ones in Problem 1, you may encounter errors when implementing the Euler scheme for CIR. Explain why.arrow_forwardRefer to page 1 for a problem involving proving the distributive property of matrix multiplication. Instructions: Provide a detailed proof using matrix definitions and element-wise operations. Show all calculations clearly. Link [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]arrow_forward
- Refer to page 30 for a problem requiring solving a nonhomogeneous differential equation using the method of undetermined coefficients. Instructions: Solve step-by-step, including the complementary and particular solutions. Clearly justify each step. Link [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]arrow_forwardRefer to page 5 for a problem requiring finding the critical points of a multivariable function. Instructions: Use partial derivatives and the second partial derivative test to classify the critical points. Provide detailed calculations. Link [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440AZF/view?usp=sharing]arrow_forwardRefer to page 3 for a problem on evaluating limits involving indeterminate forms using L'Hôpital's rule. Instructions: Apply L'Hôpital's rule rigorously. Show all derivatives and justify the steps leading to the solution. Link [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440AZF/view?usp=sharing]arrow_forward
- 3. Let {X} be an autoregressive process of order one, usually written as AR(1). (a) Write down an equation defining X₁ in terms of an autoregression coefficient a and a white noise process {} with variance σ². Explain what the phrase "{} is a white noise process with variance o?" means. (b) Derive expressions for the variance 70 and the autocorrelation function Pk, k 0,1,. of the {X} in terms of o2 and a. Use these expressions to suggest an estimate of a in terms of the sample autocor- relations {k}. (c) Suppose that only every second value of X is observed, resulting in a time series Y X2, t = 1, 2,.... Show that {Y} forms an AR(1) process. Find its autoregression coefficient, say d', and the variance of the underlying white noise process, in terms of a and o². (d) Given a time series data set X1, ..., X256 with sample mean = 9.23 and sample autocorrelations ₁ = -0.6, 2 = 0.36, 3 = -0.22, p = 0.13, 5 = -0.08, estimate the autoregression coefficients a and a' of {X} and {Y}.arrow_forward#8 (a) Find the equation of the tangent line to y = √x+3 at x=6 (b) Find the differential dy at y = √x +3 and evaluate it for x=6 and dx = 0.3arrow_forwardRefer to page 96 for a problem involving the heat equation. Solve the PDE using the method of separation of variables. Derive the solution step-by-step, including the boundary conditions. Instructions: Stick to solving the heat equation. Show all intermediate steps, including separation of variables, solving for eigenvalues, and constructing the solution. Irrelevant explanations are not allowed. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]arrow_forward
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