A Problem Solving Approach to Mathematics for Elementary School Teachers, Books a la Carte Edition plus NEW MyLab Math with Pearson eText - Access Card Package (12th Edition)
12th Edition
ISBN: 9780133865479
Author: Rick Billstein, Shlomo Libeskind, Johnny Lott
Publisher: PEARSON
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Chapter 7.4B, Problem 1A
To determine
To find:
The percent of the shaded region in the square.
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Chapter 7 Solutions
A Problem Solving Approach to Mathematics for Elementary School Teachers, Books a la Carte Edition plus NEW MyLab Math with Pearson eText - Access Card Package (12th Edition)
Ch. 7.1 - Using Simon Stevins notation see Historical Note,...Ch. 7.1 - MATHEMATICAL CONNECTIONS If 1 mL is 0.001 L, how...Ch. 7.1 - MATHEMATICAL CONNECTIONS
Explain whether day can...Ch. 7.1 - MATHEMATICAL CONNECTIONS
Using the number line...Ch. 7.1 - Explain why you think a sign on a copy machine...Ch. 7.1 - MATHEMATICAL CONNECTIONS Explain how you could use...Ch. 7.1 - MATHEMATICAL CONNECTIONS Explain why, in Theorem...Ch. 7.1 - MATHEMATICAL CONNECTIONS Explain why appending any...Ch. 7.1 - MATHEMATICAL CONNECTIONS
How can you tell each of...Ch. 7.1 - MATHEMATICAL CONNECTIONS Determine how decimal...
Ch. 7.1 - Using base-five blocks similar to base-ten blocks,...Ch. 7.1 - In small groups, research the history of decimals...Ch. 7.1 - MATHEMATICAL CONNECTIONS
A student claims that is...Ch. 7.1 - Prob. 16MCCh. 7.1 - MATHEMATICAL CONNECTIONS A student claims that...Ch. 7.1 - Connecting Mathematics to the Classroom A student...Ch. 7.1 - Joe rode his bicycle from his house to his friends...Ch. 7.1 - 50-YARD RACE Girl Time seconds Christa 8.28 Kelly...Ch. 7.1 - The diameter of a red blood cell, in inches, is...Ch. 7.1A - Assessment 71A Write each of the following as a...Ch. 7.1A - Assessment 71A Rewrite each of the following as a...Ch. 7.1A - Assessment 71A Write each of the following as a...Ch. 7.1A - Write each of the following numerals in words. a....Ch. 7.1A - Write each of the following terminating decimals...Ch. 7.1A - Mentally determine which of the following can be...Ch. 7.1A - When possible, write each of the numbers in...Ch. 7.1A - Seven minutes is part of an hour. If 7 min were to...Ch. 7.1A - Given the U.S. monetary system, what reason can...Ch. 7.1A - In each of the following order the decimals from...Ch. 7.1A - Write the numbers in each of the following...Ch. 7.1A - Use a decimal grid with 100 squares and represent...Ch. 7.1A - If the decimals 0.804,0.84, and 0.8399 are...Ch. 7.1A - Write a decimal that has a ten-thousandths place...Ch. 7.1A - a. Show that between any two terminating decimals,...Ch. 7.1A - If decimals in other number bases work the same as...Ch. 7.1A - The five top swimmers in an event had the...Ch. 7.1A - Suppose a carpenters ruler was marked in...Ch. 7.1B - ASSESSMENT Write each of the following as a sum in...Ch. 7.1B - Prob. 2ACh. 7.1B - ASSESSMENT Write each of the following as a...Ch. 7.1B - ASSESSMENT
Write each of the following numerals in...Ch. 7.1B - Write each of the following terminating decimals...Ch. 7.1B - ASSESSMENT Mentally determine which of the...Ch. 7.1B - ASSESSMENT
Where possible, write each of the...Ch. 7.1B - ASSESSMENT What whole numbers of minutes less than...Ch. 7.1B - Prob. 9ACh. 7.1B - Prob. 10ACh. 7.1B - Write the numbers in each of the following...Ch. 7.1B - Use a grid with 100 squares and represent 0.23.Ch. 7.1B - Prob. 13ACh. 7.1B - Write a decimal that is between 8.345 and 8.3456.Ch. 7.1B - Prob. 15ACh. 7.1B - Prob. 16ACh. 7.1B - Assessment The five top swimmers in an event had...Ch. 7.1B - Prob. 18ACh. 7.2 - How much greater is 0.763 than 0.753? How can you...Ch. 7.2 - How is multiplication of decimals like...Ch. 7.2 - Prob. 3MCCh. 7.2 - Is a product of two positive decimals each less...Ch. 7.2 - What is the significance of the 1 above the 6 in...Ch. 7.2 - Prob. 8MCCh. 7.2 - Prob. 9MCCh. 7.2 - Prob. 10MCCh. 7.2 - Prob. 11MCCh. 7.2 - In multiplying 0.1250.08, Roger knew the rule that...Ch. 7.2 - Jamal wants to know why 0.3 and 0.30 are equal....Ch. 7.2 - Fred says that to multiply 32.72.6, he just...Ch. 7.2 - Prob. 16MCCh. 7.2 - Prob. 17MCCh. 7.2 - How would you respond to the following situations?...Ch. 7.2 - Write 14.0479 in expanded form.Ch. 7.2 - With out dividing, determine which of the...Ch. 7.2 - If the denominator of a fraction is 26, is it...Ch. 7.2 - 3556 can be written as a terminating decimal....Ch. 7.2 - How much greater is 0.763 than 0.753? How can you...Ch. 7.2 - Prob. 2NAEPCh. 7.2 - Prob. 3NAEPCh. 7.2 - Explain why subtraction of terminating decimals...Ch. 7.2A - Use base-ten blocks to model 3.2+2.32.Ch. 7.2A - Write the decimals as fractions and then add....Ch. 7.2A - ASSESSMENT Write the decimals as fractions and...Ch. 7.2A - Prob. 4ACh. 7.2A - Johns calculator calculates correctly but does not...Ch. 7.2A - ASSESSMENT Multiply each number below by 0.01...Ch. 7.2A - ASSESSMENT
When you multiply a natural number by a...Ch. 7.2A - If Maura went to the store and bought a chair for...Ch. 7.2A - ASSESSMENT a. Complete the following magic square;...Ch. 7.2A - ASSESSMENT
Karin bought lb of peaches at lb and lb...Ch. 7.2A - Automobile engines were once measured in cubic...Ch. 7.2A - ASSESSMENT A stock rose 0.24 in the market on...Ch. 7.2A - Prob. 13ACh. 7.2A - A kilowatt hour means 1000 watts of electricity...Ch. 7.2A - Prob. 15ACh. 7.2A - ASSESSMENT
If each of the following sequences is...Ch. 7.2A - Prob. 17ACh. 7.2A - Prob. 18ACh. 7.2A - Estimate the placement of each of the following...Ch. 7.2A - Prob. 20ACh. 7.2A - Mikes class is building a model of the new World...Ch. 7.2A - Prob. 22ACh. 7.2A - Prob. 23ACh. 7.2A - Prob. 24ACh. 7.2A - Prob. 25ACh. 7.2A - ASSESSMENT Convert each of the following to...Ch. 7.2A - ASSESSMENT
Write the numerals in each of the...Ch. 7.2A - Prob. 28ACh. 7.2A - ASSESSMENT
Write the numerals in each of the...Ch. 7.2A - ASSESSMENT
Write the results of each of the...Ch. 7.2A - Round each of the following numbers as specified....Ch. 7.2A - Prob. 32ACh. 7.2A - Audrey wants to buy some camera equipment to take...Ch. 7.2A - ASSESSMENT Estimate the sum or difference in each...Ch. 7.2A - ASSESSMENT
Find the least and the greatest...Ch. 7.2A - Some digits in the following number are covered by...Ch. 7.2A - Iris worked a 40-hour week at 8.25/hr. Mentally...Ch. 7.2A - ASSESSMENT Mentally compute the number to fill in...Ch. 7.2A - ASSESSMENT
Which of the following result in equal...Ch. 7.2A - Prob. 40ACh. 7.2B - Prob. 1ACh. 7.2B - Prob. 2ACh. 7.2B - Prob. 3ACh. 7.2B - Assume the multiplication shown below is correct...Ch. 7.2B - Prob. 5ACh. 7.2B - Prob. 6ACh. 7.2B - When you multiply a positive decimal less than 1...Ch. 7.2B - Prob. 8ACh. 7.2B - Prob. 9ACh. 7.2B - Prob. 10ACh. 7.2B - Prob. 11ACh. 7.2B - Prob. 12ACh. 7.2B - Prob. 13ACh. 7.2B - Prob. 14ACh. 7.2B - Prob. 15ACh. 7.2B - If the first term of a finite geometric sequence...Ch. 7.2B - Prob. 17ACh. 7.2B - Prob. 18ACh. 7.2B - Prob. 19ACh. 7.2B - Prob. 20ACh. 7.2B - Prob. 21ACh. 7.2B - Prob. 22ACh. 7.2B - Prob. 23ACh. 7.2B - Prob. 24ACh. 7.2B - Prob. 25ACh. 7.2B - Prob. 26ACh. 7.2B - Prob. 27ACh. 7.2B - Prob. 28ACh. 7.2B - Prob. 29ACh. 7.2B - Round each of the following numbers as specified...Ch. 7.2B - Prob. 31ACh. 7.2B - Prob. 32ACh. 7.2B - Find the least and the greatest possible products...Ch. 7.2B - Prob. 35ACh. 7.2B - Prob. 36ACh. 7.2B - Prob. 37ACh. 7.2B - Prob. 39ACh. 7.3 - a. If a grocery store advertised three lemons for...Ch. 7.3 - A friend claims that every finite decimal is equal...Ch. 7.3 - Some addition problems are easier to compute with...Ch. 7.3 - Prob. 4MCCh. 7.3 - Notice that...Ch. 7.3 - Prob. 6MCCh. 7.3 - a. Does your calculator allow you to enter...Ch. 7.3 - Prob. 8MCCh. 7.3 - A student argues that repeating decimals are of...Ch. 7.3 - A student asks if a sum of two repeating decimals...Ch. 7.3 - A student needs to find 0.333348 without using a...Ch. 7.3 - Joe says terminating decimals are those with...Ch. 7.3 - Prob. 14MCCh. 7.3 - Prob. 15MCCh. 7.3 - Prob. 16MCCh. 7.3 - Prob. 17MCCh. 7.3 - Prob. 18MCCh. 7.3 - Prob. 19MCCh. 7.3A - Prob. 1ACh. 7.3A - a. Do 0.45777,0.4577 and 0.457 represent different...Ch. 7.3A - Write the first 10 decimal places for each of the...Ch. 7.3A - Which of the following is greater: 0.3625or0.3625?Ch. 7.3A - Write the following using a bar to indicate the...Ch. 7.3A - Prob. 6ACh. 7.3A - ASSESSMENT Convert each of the following repeating...Ch. 7.3A - Express 1 min as a repeating decimal part of an...Ch. 7.3A - ASSESSMENT Order the following decimals from...Ch. 7.3A - Prob. 10ACh. 7.3A - Prob. 11ACh. 7.3A - Give an argument why 317 must be a repeating...Ch. 7.3A - Prob. 13ACh. 7.3A - Explain whether a terminating decimal could ever...Ch. 7.3A - Find three decimals between each of the following...Ch. 7.3A - Find the decimal halfway between the decimals 0.4...Ch. 7.3A - a. Find three rational numbers between 34 and...Ch. 7.3A - Prob. 18ACh. 7.3A - a. 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- 29% of all college students major in STEM (Science, Technology, Engineering, and Math). If 46 college students are randomly selected, find the probability thata. Exactly 11 of them major in STEM. b. At most 12 of them major in STEM. c. At least 11 of them major in STEM. d. Between 11 and 15 (including 11 and 15) of them major in STEM.arrow_forward4. Assume that a risk-free money market account is added to the market described in Q3. The continuously compounded rate of return on the money market account is log (1.1). (i) For each given μ, use Lagrange multipliers to determine the proportions (as a function of μ) of wealth invested in the three assets available for the minimum variance portfolio with expected return μ. (ii) Determine the market portfolio in this market and calculate its Sharp ratio.arrow_forward3. A market consists of two risky assets with rates of return R₁ and R2 and no risk-free asset. From market data the following have been estimated: ER₁ = 0.25, ER2 = 0.05, Var R₁ = 0.01, Var R2 = 0.04 and the correlation between R1 and R2 is p = -0.75. (i) Given that an investor is targeting a total expected return of μ = 0.2. What portfolio weights should they choose to meet this goal with minimum portfolio variance? Correct all your calculations up to 4 decimal points. (ii) Determine the global minimum-variance portfolio and the expected return and variance of return of this portfolio (4 d.p.). (iii) Sketch the minimum-variance frontier in the μ-σ² plane and indicate the efficient frontier. (iv) Without further calculation, explain how the minimum variance of the investor's portfolio return will change if the two risky assets were independent.arrow_forward
- 2. A landlord is about to write a rental contract for a tenant which lasts T months. The landlord first decides the length T > 0 (need not be an integer) of the contract, the tenant then signs it and pays an initial handling fee of £100 before moving in. The landlord collects the total amount of rent erT at the end of the contract at a continuously compounded rate r> 0, but the contract stipulates that the tenant may leave before T, in which case the landlord only collects the total rent up until the tenant's departure time 7. Assume that 7 is exponentially distributed with rate > 0, λ‡r. (i) Calculate the expected total payment EW the landlord will receive in terms of T. (ii) Assume that the landlord has logarithmic utility U(w) = log(w - 100) and decides that the rental rate r should depend on the contract length T by r(T) = λ √T 1 For each given λ, what T (as a function of X) should the landlord choose so as to maximise their expected utility? Justify your answer. Hint. It might be…arrow_forwardPlease solving problem2 Problem1 We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. (This model is the same as in Prob. 1 of HW#2).We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.arrow_forwardPlease ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.arrow_forward
- This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. A B A B at some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 2 cos(3πt) and y= 2 sin(3t) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot(3πt) sin(3лt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411- 4 -2 sin (3лt) (d)…arrow_forward5. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.AE.003. y y= ex² 0 Video Example x EXAMPLE 3 (a) Use the Midpoint Rule with n = 10 to approximate the integral कर L'ex² dx. (b) Give an upper bound for the error involved in this approximation. SOLUTION 8+2 1 L'ex² d (a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.) dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)] 0.1 [0.0025 +0.0225 + + e0.0625 + 0.1225 e0.3025 + e0.4225 + e0.2025 + + e0.5625 €0.7225 +0.9025] The figure illustrates this approximation. (b) Since f(x) = ex², we have f'(x) = 0 ≤ f'(x) = < 6e. ASK YOUR TEACHER and f'(x) = Also, since 0 ≤ x ≤ 1 we have x² ≤ and so Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final answer to five decimal places.) 6e(1)3 e 24( = ≈arrow_forward1. Consider the following preference ballots: Number of voters Rankings 6 5 4 2 1st choice A DCB DC 2nd choice B B D 3rd choice DCBD 4th choice CA AAA For each of the four voting systems we have studied, determine who would win the election in each case. (Remember: For plurality with runoff, all but the top two vote-getters are simultaneously eliminated at the end of round 1.)arrow_forward
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