Math

CalculusFinite Mathematics and Applied Calculus (MindTap Course List)The Normal Curve Exercises 49–52 require the use of a graphing calculator or computer programmed to do numerical integration. The normal distribution curve, which models the distributions of data in a wide range of applications, is given by the function p ( x ) = 1 2 π σ e − ( x − μ ) 2 ( 2 σ 2 ) , Where π = 3.14149265…. and σ and μ are constants called the standard deviation and the mean, respectively. Its graph (for σ = 1 and μ = 2 ) is shown in the figure. With σ = 1 and μ = 0 , approximate ∫ − ∞ + ∞ p ( x ) d x .BuyFind*launch*

7th Edition

Stefan Waner + 1 other

Publisher: Cengage Learning

ISBN: 9781337274203

Chapter 14.5, Problem 50E

Textbook Problem

**The Normal Curve** Exercises 49–52 require the use of a graphing calculator or computer programmed to do numerical integration. The normal distribution curve, which models the distributions of data in a wide range of applications, is given by the function

*Where*
*and*
*are constants called the standard deviation and the mean, respectively. Its graph (for*

*) is shown in the figure.*

With

Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 14.1 - In Exercises 140, evaluate the integral using...Ch. 14.1 - In Exercises 140, evaluate the integral using...Ch. 14.1 - In Exercises 140, evaluate the integral using...Ch. 14.1 - In Exercises 140, evaluate the integral using...Ch. 14.1 - In Exercises 140, evaluate the integral using...Ch. 14.1 - In Exercises 140, evaluate the integral using...Ch. 14.1 - In Exercises 140, evaluate the integral using...Ch. 14.1 - In Exercises 140, evaluate the integral using...Ch. 14.1 - In Exercises 140, evaluate the integral using...Ch. 14.1 - In Exercises 140, evaluate the integral using...

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Integrals of Functions Involving Absolute Values...Ch. 14.1 - Integrals of Functions Involving Absolute Values...Ch. 14.1 - Integrals of Functions Involving Absolute Values...Ch. 14.1 - Integrals of Functions Involving Absolute Values...Ch. 14.1 - Integrals of Functions Involving Absolute Values...Ch. 14.1 - Integrals of Functions Involving Absolute Values...Ch. 14.1 - Integrals of Functions Involving Absolute Values...Ch. 14.1 - Integrals of Functions Involving Absolute Values...Ch. 14.1 - Displacement A rocket rising from the ground has a...Ch. 14.1 - Sales Weekly sales of graphing calculators can be...Ch. 14.1 - Total Cost The marginal cost of the x thbox of...Ch. 14.1 - Total Revenue The marginal revenue for selling the...Ch. 14.1 - Spending on Gasoline From the beginning of 2000 to...Ch. 14.1 - Spending on Gasoline From the beginning of 2007 to...Ch. 14.1 - Housing The following graph shows the annual...Ch. 14.1 - Housing for Sale The following graph shows the...Ch. 14.1 - Bottled Water Sales The rate of U.S. sales of...Ch. 14.1 - Bottled Water Sales The rate of U.S. sales of...Ch. 14.1 - Oil Production in Mexico The rate of crude oil...Ch. 14.1 - Oil Imports from Mexico The rate of crude oil...Ch. 14.1 - Revenue You have been raising the price of your...Ch. 14.1 - Revenue Luckily, sales of your Star Wars and Peace...Ch. 14.1 - Integrals of Piecewise-Linear Functions Exercises...Ch. 14.1 - Integrals of Piecewise-Linear Functions Exercises...Ch. 14.1 - Your friend Janice claims that integration by...Ch. 14.1 - Complete the following sentence in words: The...Ch. 14.1 - Give an example of an integral that can be...Ch. 14.1 - Give an example of an integral that can be...Ch. 14.1 - In Exercises 7380, indicate whether the given...Ch. 14.1 - In Exercises 7380, indicate whether the given...Ch. 14.1 - In Exercises 7380, indicate whether the given...Ch. 14.1 - In Exercises 7380, indicate whether the given...Ch. 14.1 - In Exercises 7380, indicate whether the given...Ch. 14.1 - In Exercises 7380, indicate whether the given...Ch. 14.1 - In Exercises 7380, indicate whether the given...Ch. 14.1 - In Exercises 7380, indicate whether the given...Ch. 14.1 - If P(x) isa polynomial of degree n and f(x) issome...Ch. 14.1 - Use integration by parts to show that...Ch. 14.1 - Hermites Identity If f(x) isa polynomial of degree...Ch. 14.1 - Write down a formula similar to Hermites identity...Ch. 14.2 - In Exercises 18, find the area of the shaded...Ch. 14.2 - In Exercises 18, find the area of the shaded...Ch. 14.2 - In Exercises 18, find the area of the shaded...Ch. 14.2 - In Exercises 18, find the area of the shaded...Ch. 14.2 - In Exercises 18, find the area of the shaded...Ch. 14.2 - In Exercises 18, find the area of the shaded...Ch. 14.2 - In Exercises 18, find the area of the shaded...Ch. 14.2 - In Exercises 18, find the area of the shaded...Ch. 14.2 - In Exercises 942, find the area of the indicated...Ch. 14.2 - In Exercises 942, find the area of the indicated...Ch. 14.2 - In Exercises 942, find the area of the indicated...Ch. 14.2 - 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Oil Production in Mexico: Pemex The rate of crude...Ch. 14.2 - MySpace and Facebook Exercises 47 and 48 are based...Ch. 14.2 - MySpace and Facebook Exercises 47 and 48 are based...Ch. 14.2 - Big Brother Exercises 49 and 50 are based on the...Ch. 14.2 - Big Brother Exercises 49 and 50 are based on the...Ch. 14.2 - If f and g are continuous function with...Ch. 14.2 - Your know that f and g are continuous and their...Ch. 14.2 - The following graph shows annual U.S. exports and...Ch. 14.2 - The following graph shown a fictitious countrys...Ch. 14.2 - The following graph shown the daily revenue and...Ch. 14.2 - The following graph shown daily orders and...Ch. 14.2 - What is wrong with the following claim? I...Ch. 14.2 - Your pharmaceutical company monitors the amount of...Ch. 14.3 - In Exercises 1-8, find the average of the function...Ch. 14.3 - In Exercises 1-8, find the average of the function...Ch. 14.3 - In Exercises 1-8, find the average of the function...Ch. 14.3 - In Exercises 1-8, find the average of the function...Ch. 14.3 - In Exercises 1-8, find the average of the function...Ch. 14.3 - In Exercises 1-8, find the average of the function...Ch. 14.3 - In Exercises 1-8, find the average of the function...Ch. 14.3 - In Exercises 1-8, find the average of the function...Ch. 14.3 - In Exercises 9 and 10, complete the given table...Ch. 14.3 - In Exercises 9 and 10, complete the given table...Ch. 14.3 - In Exercises 11 and 12, some values of a function...Ch. 14.3 - In Exercises 11 and 12, some values of a function...Ch. 14.3 - In Exercises 1324, calculate the 5-unit moving...Ch. 14.3 - In Exercises 1324, calculate the 5-unit moving...Ch. 14.3 - In Exercises 1324, calculate the 5-unit moving...Ch. 14.3 - In Exercises 1324, calculate the 5-unit moving...Ch. 14.3 - In Exercises 1324, calculate the 5-unit moving...Ch. 14.3 - In Exercises 1324, calculate the 5-unit moving...Ch. 14.3 - In Exercises 1324, calculate the 5-unit moving...Ch. 14.3 - In Exercises 1324, calculate the 5-unit moving...Ch. 14.3 - In Exercises 1324, calculate the 5-unit moving...Ch. 14.3 - In Exercises 1324, calculate the 5-unit moving...Ch. 14.3 - In Exercises 1324, calculate the 5-unit moving...Ch. 14.3 - In Exercises 1324, calculate the 5-unit moving...Ch. 14.3 - In Exercises 2534, use graphing technology to plot...Ch. 14.3 - In Exercises 2534, use graphing technology to plot...Ch. 14.3 - In Exercises 2534, use graphing technology to plot...Ch. 14.3 - In Exercises 2534, use graphing technology to plot...Ch. 14.3 - In Exercises 2534, use graphing technology to plot...Ch. 14.3 - In Exercises 2534, use graphing technology to plot...Ch. 14.3 - In Exercises 2534, use graphing technology to plot...Ch. 14.3 - In Exercises 2534, use graphing technology to plot...Ch. 14.3 - In Exercises 2534, use graphing technology to plot...Ch. 14.3 - In Exercises 2534, use graphing technology to plot...Ch. 14.3 - Television Advertising The cost, in millions of...Ch. 14.3 - Television Advertising The cost, in millions of...Ch. 14.3 - Membership: Facebook The number of new members...Ch. 14.3 - Membership: MySpace The number of new members...Ch. 14.3 - Freon Production Annual production of ozone-layer-...Ch. 14.3 - Health Expenditures Annual expenditures on health...Ch. 14.3 - Investments If you invest $10,000 at 8% interest...Ch. 14.3 - Investments If you invest $10,000 at 12% interest...Ch. 14.3 - Average Balance Suppose you have an account...Ch. 14.3 - Average Balance Suppose you have an account...Ch. 14.3 - Online Payments The value of payments made through...Ch. 14.3 - Online Auctions The net number of new active eBay...Ch. 14.3 - Stock Prices: Exxon Mobil The following table...Ch. 14.3 - Stock Prices: Nokia The following table shows the...Ch. 14.3 - Cancun The Playa Loca Hotel in Cancun has an...Ch. 14.3 - Reykjavik Repeat Exercise 49, using the following...Ch. 14.3 - Sales: Apple The following table shows approximate...Ch. 14.3 - Housing Starts The following table shows the...Ch. 14.3 - Bottled Water Sales The rate of U.S. sales of...Ch. 14.3 - Bottled Water Sales The rate of U.S. per capita...Ch. 14.3 - Medicare Spending Annual spending on Medicare was...Ch. 14.3 - Pasta Imports in the 1990s In 1990 the United...Ch. 14.3 - Moving Average of a Linear Function Find a formula...Ch. 14.3 - Moving Average of an Exponential Function Find a...Ch. 14.3 - Explain why it is sometimes more useful to...Ch. 14.3 - Sales this month were sharply lower than they were...Ch. 14.3 - Your companys 6-month moving average of sales is...Ch. 14.3 - Your monthly salary has been increasing steadily...Ch. 14.3 - What property does the graph of a (nonconstant)...Ch. 14.3 - Can the average value of a function f on an...Ch. 14.3 - Criticize the following claim: The average value...Ch. 14.3 - Your manager tells you that 12-month moving...Ch. 14.3 - Which of the following most closely approximates...Ch. 14.3 - Is an increasing function larger or smaller than...Ch. 14.4 - In Exercises 112, calculate the consumers surplus...Ch. 14.4 - In Exercises 112, calculate the consumers surplus...Ch. 14.4 - In Exercises 112, calculate the consumers surplus...Ch. 14.4 - In Exercises 112, calculate the consumers surplus...Ch. 14.4 - In Exercises 112, calculate the consumers surplus...Ch. 14.4 - In Exercises 112, calculate the consumers surplus...Ch. 14.4 - In Exercises 112, calculate the consumers surplus...Ch. 14.4 - In Exercises 112, calculate the consumers surplus...Ch. 14.4 - In Exercises 112, calculate the consumers surplus...Ch. 14.4 - In Exercises 112, calculate the consumers surplus...Ch. 14.4 - In Exercises 112, calculate the consumers surplus...Ch. 14.4 - In Exercises 112, calculate the consumers surplus...Ch. 14.4 - In Exercises 1324, calculate the producers surplus...Ch. 14.4 - In Exercises 1324, calculate the producers surplus...Ch. 14.4 - In Exercises 1324, calculate the producers surplus...Ch. 14.4 - In Exercises 1324, calculate the producers surplus...Ch. 14.4 - In Exercises 1324, calculate the producers surplus...Ch. 14.4 - In Exercises 1324, calculate the producers surplus...Ch. 14.4 - In Exercises 1324, calculate the producers surplus...Ch. 14.4 - In Exercises 1324, calculate the producers surplus...Ch. 14.4 - In Exercises 1324, calculate the producers surplus...Ch. 14.4 - In Exercises 1324, calculate the producers surplus...Ch. 14.4 - In Exercises 1324, calculate the producers surplus...Ch. 14.4 - In Exercises 1324, calculate the producers surplus...Ch. 14.4 - In Exercises 2530, find the total value of the...Ch. 14.4 - In Exercises 2530, find the total value of the...Ch. 14.4 - In Exercises 2530, find the total value of the...Ch. 14.4 - In Exercises 2530, find the total value of the...Ch. 14.4 - In Exercises 2530, find the total value of the...Ch. 14.4 - In Exercises 2530, find the total value of the...Ch. 14.4 - In Exercises 3136, find the total value of the...Ch. 14.4 - In Exercises 3136, find the total value of the...Ch. 14.4 - In Exercises 3136, find the total value of the...Ch. 14.4 - In Exercises 3136, find the total value of the...Ch. 14.4 - In Exercises 3136, find the total value of the...Ch. 14.4 - In Exercises 3136, find the total value of the...Ch. 14.4 - College Tuition A study of U.S. colleges and...Ch. 14.4 - Fast Food A fast-food outlet finds that the demand...Ch. 14.4 - Revenue: Nokia The annual net sales (revenue)...Ch. 14.4 - Revenue: Nintendo The annual net sales (revenue)...Ch. 14.4 - Revenue: Walmart The annual revenue earned by...Ch. 14.4 - Revenue: Target The annual revenue earned by...Ch. 14.4 - Revenue Refer back to Exercise 39. Suppose that,...Ch. 14.4 - Revenue Refer back to Exercise 40. Suppose that,...Ch. 14.4 - Revenue Refer back to Exercise 41. Suppose that,...Ch. 14.4 - Revenue Refer back to Exercise 42. Suppose that,...Ch. 14.4 - Saving for Retirement You are saving for your...Ch. 14.4 - Saving for College When your first child is born,...Ch. 14.4 - Saving for Retirement You begin saving for your...Ch. 14.4 - Saving for College When your first child is born,...Ch. 14.4 - Bonds The U.S. Treasury issued a 30-year bond on...Ch. 14.4 - Bonds The Megabucks Corporation is issuing a...Ch. 14.4 - Valuing Future Income Inga was injured and can no...Ch. 14.4 - Valuing Future Income Max was injured and can no...Ch. 14.4 - Complete the following: The future value of a...Ch. 14.4 - Complete the following: The present value of a...Ch. 14.4 - Linear Demand Given a linear demand equation...Ch. 14.4 - Linear Supply Given a linear supply equation of...Ch. 14.4 - Your study group friend says that the future value...Ch. 14.4 - Your other study group friend says that the...Ch. 14.4 - Arrange from smallest to largest: total value,...Ch. 14.4 - a. Arrange the following function from smallest to...Ch. 14.5 - In Exercises 126, decide whether or not the given...Ch. 14.5 - In Exercises 126, decide whether or not the given...Ch. 14.5 - In Exercises 126, decide whether or not the given...Ch. 14.5 - In Exercises 126, decide whether or not the given...Ch. 14.5 - In Exercises 126, decide whether or not the given...Ch. 14.5 - In Exercises 126, decide whether or not the given...Ch. 14.5 - In Exercises 126, decide whether or not the given...Ch. 14.5 - In Exercises 126, decide whether or not the given...Ch. 14.5 - In Exercises 126, decide whether or not the given...Ch. 14.5 - In Exercises 126, decide whether or not the given...Ch. 14.5 - In Exercises 126, decide whether or not the given...Ch. 14.5 - In Exercises 126, decide whether or not the given...Ch. 14.5 - In Exercises 126, decide whether or not the given...Ch. 14.5 - In Exercises 126, decide whether or not the given...Ch. 14.5 - In Exercises 126, decide whether or not the given...Ch. 14.5 - 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In Exercises 2734, use technology to approximate...Ch. 14.5 - In Exercises 2734, use technology to approximate...Ch. 14.5 - In Exercises 2734, use technology to approximate...Ch. 14.5 - New Home Sales Sales of new homes in the United...Ch. 14.5 - Revenue from New Home Sales Revenue from the sale...Ch. 14.5 - Cigarette Sales According to data published by the...Ch. 14.5 - Sales Sales of the text Calculus and You have been...Ch. 14.5 - Sales My financial adviser has predicted that...Ch. 14.5 - Revenue Alarmed about the sales prospects for my...Ch. 14.5 - Education Let N(t) be the number of high school...Ch. 14.5 - Education: Martian Let M(t) be the number of high...Ch. 14.5 - Cellphone Revenues The number of cellphone...Ch. 14.5 - Vidphone Revenues The number of vidphone...Ch. 14.5 - Development Assistance According to data published...Ch. 14.5 - Humanitarian Aid Repeat Exercise 45, using the...Ch. 14.5 - Hair Mousse Sales The amount of extremely popular...Ch. 14.5 - Chocolate Mousse Sales The weekly demand for your...Ch. 14.5 - The Normal Curve Exercises 4952 require the use of...Ch. 14.5 - The Normal Curve Exercises 4952 require the use of...Ch. 14.5 - The Normal Curve Exercises 4952 require the use of...Ch. 14.5 - The Normal Curve Exercises 4952 require the use of...Ch. 14.5 - Variable Sales The value of your Chateau Petit...Ch. 14.5 - Panic Sales Unfortunately, your large supply of...Ch. 14.5 - Meteor Impacts The frequency of meteor impacts on...Ch. 14.5 - Meteor Impacts (continuing Exercise 55.) a....Ch. 14.5 - The Gamma Function The gamma function is defined...Ch. 14.5 - Laplace Transforms The Laplace transform F(x) ofa...Ch. 14.5 - Why cant the Fundamental Theorem of Calculus be...Ch. 14.5 - Why cant the Fundamental Theorem of Calculus be...Ch. 14.5 - It sometimes happens that the Fundamental Theorem...Ch. 14.5 - Does the FTC give the correct answer for improper...Ch. 14.5 - Which of the following integrals are improper, and...Ch. 14.5 - Which of the following integrals are improper, and...Ch. 14.5 - How could you use technology to approximate...Ch. 14.6 - In Exercises 1-10, find the general solution of...Ch. 14.6 - In Exercises 1-10, find the general solution of...Ch. 14.6 - In Exercises 1-10, find the general solution of...Ch. 14.6 - In Exercises 1-10, find the general solution of...Ch. 14.6 - In Exercises 1-10, find the general solution of...Ch. 14.6 - In Exercises 1-10, find the general solution of...Ch. 14.6 - In Exercises 1-10, find the general solution of...Ch. 14.6 - In Exercises 1-10, find the general solution of...Ch. 14.6 - In Exercises 1-10, find the general solution of...Ch. 14.6 - In Exercises 1-10, find the general solution of...Ch. 14.6 - In Execises11-20, find the indicated particular...Ch. 14.6 - In Execises11-20, find the indicated particular...Ch. 14.6 - In Execises11-20, find the indicated particular...Ch. 14.6 - In Execises11-20, find the indicated particular...Ch. 14.6 - In Execises11-20, find the indicated particular...Ch. 14.6 - In Execises11-20, find the indicated particular...Ch. 14.6 - In Execises11-20, find the indicated particular...Ch. 14.6 - In Execises11-20, find the indicated particular...Ch. 14.6 - In Execises11-20, find the indicated particular...Ch. 14.6 - In Execises11-20, find the indicated particular...Ch. 14.6 - Sales Your monthly sales of green tea ice cream...Ch. 14.6 - Profit Your monthly profit on sales of avocado ice...Ch. 14.6 - Newtons Law of Cooling For coffee in a ceramic...Ch. 14.6 - Newtons Law of Cooling For coffee in a paper cup,...Ch. 14.6 - Cooling A bowl of clam chowder at 190F is placed...Ch. 14.6 - Heating Suppose that a pie at 20F is put in an...Ch. 14.6 - Market Saturation You have just introduced a new...Ch. 14.6 - Market Saturation Repeat Exercise 27, assuming...Ch. 14.6 - Determining Demand Nancys Chocolates estimates...Ch. 14.6 - Determining Demand Nancys Chocolates estimates...Ch. 14.6 - Linear Differential Equations Exercises 3136 are...Ch. 14.6 - Linear Differential Equations Exercises 3136 are...Ch. 14.6 - Linear Differential Equations Exercises 3136 are...Ch. 14.6 - Linear Differential Equations Exercises 3136 are...Ch. 14.6 - Linear Differential Equations Exercises 3136 are...Ch. 14.6 - Linear Differential Equations Exercises 3136 are...Ch. 14.6 - Approach to Equilibrium The Extrasoft Toy Co. has...Ch. 14.6 - Approach to Equilibrium Spacely Sprockets has just...Ch. 14.6 - Logistic Equation There are many examples of...Ch. 14.6 - Logistic Equation Using separation of variables...Ch. 14.6 - Exercises 4144 require the use of technology....Ch. 14.6 - Exercises 4144 require the use of technology....Ch. 14.6 - Exercises 4144 require the use of technology....Ch. 14.6 - Exercises 4144 require the use of technology....Ch. 14.6 - What is the difference between a particular...Ch. 14.6 - Why is there always an arbitrary constant in the...Ch. 14.6 - Show by example that a second-order differential...Ch. 14.6 - Find a differential equation that is not...Ch. 14.6 - Find a differential equation whose general...Ch. 14.6 - Explain how, knowing the elasticity of demand as a...Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 1-10, evaluate the given integral....Ch. 14 - In Exercises 11-14, find the area of the given...Ch. 14 - In Exercises 11-14, find the area of the given...Ch. 14 - In Exercises 11-14, find the area of the given...Ch. 14 - In Exercises 11-14, find the area of the given...Ch. 14 - In Exercises15-18, find the average value of the...Ch. 14 - In Exercises15-18, find the average value of the...Ch. 14 - In Exercises15-18, find the average value of the...Ch. 14 - In Exercises15-18, find the average value of the...Ch. 14 - In Exercises 19-22, find the 2-unit moving...Ch. 14 - In Exercises 19-22, find the 2-unit moving...Ch. 14 - In Exercises 19-22, find the 2-unit moving...Ch. 14 - In Exercises 19-22, find the 2-unit moving...Ch. 14 - In Exercises 23 and 24, calculate the consumers...Ch. 14 - In Exercises 23 and 24, calculate the consumers...Ch. 14 - In Exercises 25 and 26, calculate the consumers...Ch. 14 - In Exercises 25 and 26, calculate the consumers...Ch. 14 - In Exercises 27-32, decide whether the given...Ch. 14 - In Exercises 27-32, decide whether the given...Ch. 14 - In Exercises 27-32, decide whether the given...Ch. 14 - In Exercises 27-32, decide whether the given...Ch. 14 - In Exercises 27-32, decide whether the given...Ch. 14 - In Exercises 27-32, decide whether the given...Ch. 14 - In Exercises 33-36, solve the given differential...Ch. 14 - In Exercises 33-36, solve the given differential...Ch. 14 - In Exercises 33-36, solve the given differential...Ch. 14 - In Exercises 33-36, solve the given differential...Ch. 14 - Spending on Stationery Alarmed by the volume of...Ch. 14 - Spending on Shipping During the past 10 months,...Ch. 14 - Education Costs Billy-Sean OHagan, having...Ch. 14 - Investments OHaganBooks.com keeps its cash...Ch. 14 - Consumerss and Producerss Surplus Currently, the...Ch. 14 - Consumers and Producers Surplus OHaganBooks.com is...Ch. 14 - Revenue Sales of the best seller A River Burns...Ch. 14 - Foreign Investments Panicked by the performance of...Ch. 14 - Investments OHaganBooks.com CEO John OHagan has...Ch. 14 - Savings John OHagan had been saving money for...Ch. 14 - Acquisitions The Megabucks Corporation is...Ch. 14 - More Acquisitions OHaganBooks.com is thinking of...Ch. 14 - Incompetence OHaganBooks.com is shopping around...Ch. 14 - Shrewd Bankers The new junior officer at the bank...

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