Mathematics for Elementary Teachers with Activities (5th Edition)
5th Edition
ISBN: 9780134392790
Author: Beckmann, Sybilla
Publisher: PEARSON
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Textbook Question
Chapter 6.3, Problem 17P
a. Use the standard division algorithm to determine the decimal representation of
b. Interpret the steps to the hundredths place in part (a) in terms of dividing $1 equally among 9 people.
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An Arts group holds a raffle. Each raffle ticket costs $2 and the raffle consists of 2500 tickets. The prize is a vacation worth $3,000.
a. Determine your expected value if you buy one ticket.
b. Determine your expected value if you buy five tickets.
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Please show as much work as possible to clearly show the steps you used to find each solution. If you plan to use a calculator, please be sure to clearly indicate your strategy.
Consider the following game. It costs $3 each time you roll a six-sided number cube. If you roll a 6 you win $15. If you roll any other number, you receive nothing.
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(20 p) 1. Find a particular solution satisfying the given initial conditions for the third-order
homogeneous linear equation given below. (See Section 5.2 in your textbook if you need a
review of the subject.)
y(3)+2y"-y-2y = 0; y(0) = 1, y'(0) = 2, y"(0) = 0;
y₁ = e*, y2 = e¯x, y3 = e−2x
(20 p) 2. Find a particular solution satisfying the given initial conditions for the second-order
nonhomogeneous linear equation given below. (See Section 5.2 in your textbook if you need
a review of the subject.)
y"-2y-3y = 6; y(0) = 3, y'(0) = 11
yc = c₁ex + c2e³x; yp = −2
(60 p) 3. Find the general, and if possible, particular solutions of the linear systems of
differential equations given below using the eigenvalue-eigenvector method. (See Section
7.3 in your textbook if you need a review of the subject.)
=
a) x 4x1 + x2, x2 = 6x1-x2
b) x=6x17x2, x2 = x1-2x2
c) x = 9x1+5x2, x2 = −6x1-2x2; x1(0) = 1, x2(0)=0
Chapter 6 Solutions
Mathematics for Elementary Teachers with Activities (5th Edition)
Ch. 6.1 - For each of the following word problems, write the...Ch. 6.1 - Write two word problems for 637?, one for each of...Ch. 6.1 - a. Write an array problem for 213=? and make a...Ch. 6.1 - a. Write a multiplicative comparison problem for...Ch. 6.1 - a. Is 05 defined or not? Write a word problem for...Ch. 6.1 - a. Is 03 defined or not? Explain your reasoning....Ch. 6.1 - Write and solve one word problem for 3570=? and...Ch. 6.1 - a.Use the definition of powers of 10 to show how...Ch. 6.2 - Use the definition of fractions and...Ch. 6.2 - Using our definition of fractions, the idea of...
Ch. 6.2 - a. Explain why 115=.11using...Ch. 6.2 - Describe how to get the mixed number answer to 235...Ch. 6.2 - a. Write a simple how-many-units-in-1 -group word...Ch. 6.2 - Write and solve four different word problems for...Ch. 6.2 - For each of the problems that follow, write the...Ch. 6.2 - Explain how to solve the next problems with...Ch. 6.2 - In your own words, describe a procedure for...Ch. 6.2 - * Halloween (October 31) of 2014 was on a Friday,...Ch. 6.2 - Must there be at least one Friday the 13th in...Ch. 6.2 - Presidents' Day is the third Monday in February....Ch. 6.2 - I'm thinking of a number. When you divide it by 2,...Ch. 6.2 - I'm thinking of a number. When you divide it by...Ch. 6.2 - Three robbers have just acquired a large pile of...Ch. 6.2 - A year that is not a leap year has 365 days. (Leap...Ch. 6.3 - a. Calculate 42156 and 62,63532 in two ways: with...Ch. 6.3 - a. Use the scaffold method to calculate 7934. b....Ch. 6.3 - a. Use the common method for implementing the...Ch. 6.3 - a. Use the common method for implementing the...Ch. 6.3 - Tamarin calculates 83425 in the following way: I...Ch. 6.3 - Felicia is working on the following problem: There...Ch. 6.3 - Rodrigo calculates 65015 in the following way: 150...Ch. 6.3 - Meili calculates 120045 in the following way:...Ch. 6.3 - Calculate 6238 without using a calculator or any...Ch. 6.3 - Calculate 200075 without using a calculator or any...Ch. 6.3 - Use some or all of the multiplication facts...Ch. 6.3 - Use the two multiplication facts, 3012=360 and...Ch. 6.3 - how the whole-number-with-remainder and the...Ch. 6.3 - Show how to use division to determine the decimal...Ch. 6.3 - Describe how to use either dimes and pennies or a...Ch. 6.3 - Describe how to use either dimes and pennies or a...Ch. 6.3 - a. Use the standard division algorithm to...Ch. 6.3 - Describe how to use either dimes and pennies or a...Ch. 6.3 - a. Use division to determine the decimal...Ch. 6.3 - Jessica calculates that 73=2, remainder 1. When...Ch. 6.3 - a. Write and solve a simple word problem for...Ch. 6.3 - a. Suppose you want to estimate 45938 By rounding...Ch. 6.3 - Bob wants to estimate 1893275. He decides to round...Ch. 6.3 - * A student calculates 69987 as follows, and...Ch. 6.3 - When you divide whole numbers using an ordinary...Ch. 6.4 - Explain how to use the math drawings of Figures...Ch. 6.4 - A Bread Problem: If 1 loaf of bread requires 114...Ch. 6.4 - A Measuring Problem: You are making a recipe that...Ch. 6.4 - wWrite a how-many-groups word problem for 423=?...Ch. 6.4 - Write a how-many-groups word problem for 514134=?...Ch. 6.4 - Jose and Mark are making cookies for a bake sale....Ch. 6.4 - Marvin has 11 yards of cloth to make costumes for...Ch. 6.4 - A Laundry Problem: You need 34 cup of laundry...Ch. 6.4 - Write a how-many-groups word problem for 234=? and...Ch. 6.4 - Write a how-many-groups word problem for 1314=?...Ch. 6.4 - Write a how-many-groups word problem for 1223=?...Ch. 6.4 - Write a simple how-many-groups word problem for...Ch. 6.4 - a. By rewriting the division problem 1833911=? as...Ch. 6.4 - Use the fact that we can rewrite the division...Ch. 6.4 - a. Tyrone says that 125 doesn't make sense because...Ch. 6.4 - * Fraction division word problems involve the...Ch. 6.5 - Explain how to use the math drawings of Figures...Ch. 6.5 - Write a how-many-units-in-1-group word problem for...Ch. 6.5 - Write a how-many-units-in-1-group word problem for...Ch. 6.5 - Write a how-many-units-in-1-group word problem for...Ch. 6.5 - Write a how-many-units-in-I-group word problem for...Ch. 6.5 - If 112 cups of a cereal weigh 2 pounds, how much...Ch. 6.5 - It took a mule 23 of an hour to go 45 of a mile....Ch. 6.5 - It took 113 cans of paint to paint 25 of a room....Ch. 6.5 - Write a word problem for 3412=? and another word...Ch. 6.5 - For each of the following problems, determine if...Ch. 6.5 - Sam picked 12 gallon of blueberries. He poured the...Ch. 6.5 - A road crew is building a road. So far, 23 of the...Ch. 6.5 - Will has mowed 23 of his lawn, and so far it has...Ch. 6.5 - Grandma's favorite muffin recipe uses 134 cups of...Ch. 6.5 - Tran write following word problem for 13412?:...Ch. 6.6 - Sue needs to cut a piece of wood 0.4 of an inch...Ch. 6.6 - a. Write a how-many-groups word problem for...Ch. 6.6 - a. Calculate 28.30.07to the hundredths place...Ch. 6.6 - a. Calculate 16.80.35to the hundredths place...Ch. 6.6 - Ramin must calculate 8.423.6 longhand, but he...Ch. 6.6 - a. Make a math drawing like Figure 6.30, and use...Ch. 6.6 - A federal debt problem: If the federal debt is $11...Ch. 6.6 - A tax cut problem: If a 1.3 trillion dollar tax...Ch. 6.6 - Light travels at about 300,000 kilometers per...Ch. 6.6 - A newly discovered star is about 75 trillion...Ch. 6.6 - Light travels at a speed of about 300,000...Ch. 6.6 - Susan has a 5-pound bag of flour and an old recipe...Ch. 6.6 - In ordinary language, the term divide means...Ch. 6.6 - When Mary converted a recipe from metric...Ch. 6.6 - * Suppose you need to know how many...Ch. 6.6 - Sarah is building a carefully crafted cabinet and...
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