a. Find an equation for the family of linear functions with slope 2 and sketch several members of the family. b. Find an equation for the family of linear functions such that f(2) = 1 and sketch several members of the family. c. Which function belongs to both families?
> At December 31, Gorden Corporation has total stockholders’ equity of $3,200,000. Included in this total are preferred stock $500,000 and paid-in capital in excess of par—preferred stock $50,000. There are 10,000 shares of $50 par value, 8% cumulative pre
> A recent stockholders’ equity section of Aluminum Company of America (Alcoa) showed the following (in alphabetical order): additional paid-in capital $6,101, common stock $925, preferred stock $56, retained earnings $7,428, and treasury stock $2,828. (Al
> At December 31, 2020, Millwood Corporation has 2,000 shares of $100 par value, 8%, preferred stock outstanding and 100,000 shares of $10 par value common stock issued. Millwood’s net income for the year is $241,000. Instructions Compute the earnings per
> This financial information is available for Klinger Corporation. The weighted-average number of shares of common stock outstanding was 180,000 for 2019 and 150,000 for 2020. Instructions Calculate earnings per share and return on common stockholders&a
> The following financial information is available for Plummer Corporation. The weighted-average number of shares of common stock outstanding was 80,000 for 2019 and 100,000 for 2020. Instructions Calculate earnings per share and return on common stockh
> Ringgold Corporation has outstanding at December 31, 2020, 50,000 shares of $20 par value, cumulative, 6% preferred stock and 200,000 shares of $5 par value common stock. All shares were outstanding the entire year. During 2020, Ringgold earned total rev
> In 2020, Pennington Corporation had net sales of $600,000 and cost of goods sold of $360,000. Operating expenses were $153,000, and interest expense was $7,500. The corporation’s tax rate is 30%. The corporation declared preferred dividends of $15,000 in
> The following information is available for Norman Corporation for the year ended December 31, 2020: sales revenue $700,000, other revenues and gains $92,000, operating expenses $110,000, cost of goods sold $465,000, other expenses and losses $32,000, and
> Suppose the following financial information is available for Walgreen Company. Instructions Calculate the payout ratio and return on common stockholders’ equity for 2020 and 2019. Comment on your findings. (in millions) 2020 2019
> The following financial information is available for Flintlock Corporation. Instructions Calculate the payout ratio and return on common stockholders’ equity for 2020 and 2019. Comment on your findings. (in millions) 2020 2019 Ave
> The financial statements of Louis Vuitton are presented in Appendix F. The complete annual report, including the notes to its financial statements, is available at the company’s website. Instructions Use the company’s annual report to answer the followi
> On January 1, Guillen Corporation had 95,000 shares of no-par common stock issued and outstanding. The stock has a stated value of $5 per share. During the year, the following occurred. Apr. 1 Issued 25,000 additional shares of common stock for $17 per s
> As an auditor for the CPA firm of Hinkson and Calvert, you encounter the following situations in auditing different clients. 1. LR Corporation is a closely held corporation whose stock is not publicly traded. On December 5, the corporation acquired land
> Quay Co. had the following transactions during the current period. Mar. 2 Issued 5,000 shares of $5 par value common stock to attorneys in payment of a bill for $30,000 for services performed in helping the company to incorporate. June 12 Issued 60,000 s
> Osage Corporation issued 2,000 shares of stock. Instructions Prepare the entry for the issuance under the following assumptions. a. The stock had a par value of $5 per share and was issued for a total of $52,000. b. The stock had a stated value of $5 pe
> During its first year of operations, Foyle Corporation had the following transactions pertaining to its common stock. Jan. 10 Issued 70,000 shares for cash at $5 per share. July 1 Issued 40,000 shares for cash at $7 per share. Instructions a. Journalize
> Andrea (see E13.1) has studied the information you gave her in that exercise and has come to you with more statements about corporations. 1. Corporation management is both an advantage and a disadvantage of a corporation compared to a proprietorship or a
> The following accounts appear in the ledger of Horner Inc. after the books are closed at December 31, 2020. Common Stock, no par, $1 stated value, 400,000 shares authorized; …………………………………. 300,000 shares issued …………………………………………………………………………….……….. $ 300
> The ledger of Rolling Hills Corporation contains the following accounts: Common Stock, Preferred Stock, Treasury Stock, Paid-in Capital in Excess of Par—Preferred Stock, Paid-in Capital in Excess of Stated Value—Common
> The stockholders’ equity section of Aluminum Company of America (Alcoa) showed the following (in alphabetical order): additional paid-in capital $6,101, common stock $925, preferred stock $56, retained earnings $7,428, and treasury stock 2,828. All dolla
> Why might a company choose to use a limited partnership?
> The stockholders’ equity section of Haley Corporation at December 31 is as follows. Instructions From a review of the stockholders’ equity section, as chief accountant, write a memo to the president of the company an
> The following stockholders’ equity accounts, arranged alphabetically, are in the ledger of Eudaley Corporation at December 31, 2020. Common Stock ($5 stated value) …………………………………………..…………… $1,500,000 Paid-in Capital in Excess of Par—Preferred Stock ……………
> Gilliam Corporation recently hired a new accountant with extensive experience in accounting for partnerships. Because of the pressure of the new job, the accountant was unable to review his textbooks on the topic of corporation accounting. During the fir
> Andrea has prepared the following list of statements about corporations. 1. A corporation is an entity separate and distinct from its owners. 2. As a legal entity, a corporation has most of the rights and privileges of a person. 3. Most of the largest U.
> Foss, Albertson, and Espinosa are partners who share profits and losses 50%, 30%, and 20%, respectively. Their capital balances are $100,000, $60,000, and $40,000, respectively. Instructions a. Assume Garrett joins the partnership by investing $88,000 f
> N. Essex, C. Gilmore, and C. Heganbart have capital balances of $50,000, $40,000, and $30,000, respectively. Their income ratios are 4:4:2. Heganbart withdraws from the partnership under each of the following independent conditions. 1. Essex and Gilmore
> S. Pagan and T. Tabor share income on a 6:4 basis. They have capital balances of $100,000 and $60,000, respectively, when W. Wolford is admitted to the partnership. Instructions Prepare the journal entry to record the admission of W. Wolford under each
> K. Kolmer, C. Eidman, and C. Ryno share income on a 5:3:2 basis. They have capital balances of $34,000, $26,000, and $21,000, respectively, when Don Jernigan is admitted to the partnership. Instructions Prepare the journal entry to record the admission
> Prior to the distribution of cash to the partners, the accounts in the VUP Company are Cash $24,000; Vogel, Capital (Cr.) $17,000; Utech, Capital (Cr.) $15,000; and Pena, Capital (Dr.) $8,000. The income ratios are 5:3:2, respectively. VUP Company decide
> Parsons Company wishes to liquidate the firm by distributing the company’s cash to the three partners. Prior to the distribution of cash, the company’s balances are Cash $73,000; Oakley, Capital (Cr.) $47,000; Quaney, Capital (Dr.) $14,000; and Ellis, Ca
> The characteristics of a partnership include the following: (a) association of individuals, (b) limited life, and (c) co-ownership of property. Explain each of these terms.
> The table shows (lifetime) peptic ulcer rates (per 100 population) for various family incomes as reported by the National Health Interview Survey. a. Make a scatter plot of these data and decide whether a linear model is appropriate. b. Find and graph
> For each scatter plot, decide what type of function you might choose as a model for the data. Explain your choices. (а) у4 (b) у
> For each scatter plot, decide what type of function you might choose as a model for the data. Explain your choices. (а) yA (b) y4
> The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $380 to drive 480 mi and in June it cost her $460 to drive 800 mi. a. Express the monthly cost C as a function of the distance driven d, assuming
> At the surface of the ocean, the water pressure is the same as the air pressure above the water, 15 lb/in2. Below the surface, the water pressure increases by 4.34 lb/in2 for every 10 ft of descent. a. Express the water pressure as a function of the dep
> The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day. a. Express the cost as a function of the number of chairs produced, assuming that it is linear. Then sketch the
> Biologists have noticed that the chirping rate of crickets of a certain species is related to temperature, and the relationship appears to be very nearly linear. A cricket produces 113 chirps per minute at 70°F and 173 chirps per minute at 80°F. a. Find
> Jason leaves Detroit at 2:00 pm and drives at a constant speed west along I-94. He passes Ann Arbor, 40 mi from Detroit, at 2:50 pm. a. Express the distance traveled in terms of the time elapsed. b. Draw the graph of the equation in part (a). c. What
> The relationship between the Fahrenheit (F) and Celsius (C) temperature scales is given by the linear function F = 9/5 C + 32. a. Sketch a graph of this function. b. What is the slope of the graph and what does it represent? What is the F-intercept and
> The manager of a weekend flea market knows from past experience that if he charges x dollars for a rental space at the market, then the number y of spaces he can rent is given by the equation y = 200 - 4x. a. Sketch a graph of this linear function. (Rem
> Determine whether the curve is the graph of a function of x. If it is, state the domain and range of the function. i
> If the recommended adult dosage for a drug is D (in mg), then to determine the appropriate dosage c for a child of age a, pharmacists use the equation c = 0.0417D(a + 1). Suppose the dosage for an adult is 200 mg. a. Find the slope of the graph of c. Wh
> Recent studies indicate that the average surface temperature of the earth has been rising steadily. Some scientists have modeled the temperature by the linear function T = 0.02t + 8.50, where T is temperature in °C and t represents years since 1900. a.
> Find an expression for a cubic function f if f(1) = 6 and f(-1) = f(0) = f(2) = 0.
> Find expressions for the quadratic functions whose graphs are shown. yA (-2, 2), f (0, 1) (4, 2) (1, –2.5) 3.
> What do all members of the family of linear functions f(x) = c - x have in common? Sketch several members of the family
> What do all members of the family of linear functions f(x) = 1 + m(x + 3) have in common? Sketch several members of the family.
> Find the domain of the function. g(x) = 1 / 1 - tan x
> Find the domain of the function. f(x) = cos x / 1 - sin x
> If f and g are both even functions, is the product fg even? If f and g are both odd functions, is fg odd? What if f is even and g is odd? Justify your answers.
> Determine whether the curve is the graph of a function of x. If it is, state the domain and range of the function.
> If f and g are both even functions, is f + g even? If f and g are both odd functions, is f + g odd? What if f is even and g is odd? Justify your answers.
> Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually. f(x) = 1 + 3x3 - x5
> Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually. f(x) = 1 + 3x2 - x4
> Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually. f(x) = x|x|
> Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually. f(x) x + 1
> Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually. .2 f(x) x* + 1
> Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually. f(x) = .2 + 1
> A function f has domain f[5,5] and a portion of its graph is shown. a. Complete the graph of f if it is known that f is even. b. Complete the graph of f if it is known that f is odd. y4 -5 5
> a. If the point (5,3) is on the graph of an even function, what other point must also be on the graph? b. If the point (5,3) is on the graph of an odd function, what other point must also be on the graph?
> Graphs of f and g are shown. Decide whether each function is even, odd, or neither. Explain your reasoning.
> Determine whether the curve is the graph of a function of x. If it is, state the domain and range of the function. y4 1
> Graphs of f and g are shown. Decide whether each function is even, odd, or neither. Explain your reasoning. y4
> The functions in Example 10 and Exercise 67 are called step functions because their graphs look like stairs. Give two other examples of step functions that arise in everyday life.
> In a certain country, income tax is assessed as follows. There is no tax on income up to $10,000. Any income over $10,000 is taxed at a rate of 10%, up to an income of $20,000. Any income over $20,000 is taxed at 15%. a. Sketch the graph of the tax rate
> An electricity company charges its customers a base rate of $10 a month, plus 6 cents per kilowatthour (kWh) for the first 1200 kWh and 7 cents per kWh for all usage over 1200 kWh. Express the monthly cost E as a function of the amount x of electricity
> In a certain state the maximum speed permitted on freeways is 65 mi/h and the minimum speed is 40 mi/h. The fine for violating these limits is $15 for every mile per hour above the maximum speed or below the minimum speed. Express the amount of the fine
> A cell phone plan has a basic charge of $35 a month. The plan includes 400 free minutes and charges 10 cents for each additional minute of usage. Write the monthly cost C as a function of the number x of minutes used and graph C as a function of x for 0
> A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a
> A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 30 ft, express the area A of the window as a function of the width x of the window.
> Find a formula for the described function and state its domain. An open rectangular box with volume 2m3 has a square base. Express the surface area of the box as a function of the length of a side of the base.
> Find a formula for the described function and state its domain. A closed rectangular box with volume 8 ft3 has length twice the width. Express the height of the box as a function of the width.
> In this section we discussed examples of ordinary, everyday functions: Population is a function of time, postage cost is a function of weight, water temperature is a function of time. Give three other examples of functions from everyday life that are des
> Find a formula for the described function and state its domain. Express the area of an equilateral triangle as a function of the length of a side.
> Find a formula for the described function and state its domain. A rectangle has area 16 m2. Express the perimeter of the rectangle as a function of the length of one of its sides.
> Find a formula for the described function and state its domain. A rectangle has perimeter 20 m. Express the area of the rectangle as a function of the length of one of its sides.
> Find an expression for the function whose graph is the given curve. y 1
> Find an expression for the function whose graph is the given curve. 1
> Find an expression for the function whose graph is the given curve. The top half of the circle x2 + (y – 2)2 = 4
> Find an expression for the function whose graph is the given curve. The bottom half of the parabola x + (y – 1)2 = 0
> Find an expression for the function whose graph is the given curve. The line segment joining the points (-5, 10) and (7, -10)
> Find an expression for the function whose graph is the given curve. The line segment joining the points (1, -3) and (5, 7)
> Sketch the graph of the function. g(x) =||x|- 1|
> Figure 1 was recorded by an instrument operated by the California Department of Mines and Geology at the University Hospital of the University of Southern California in Los Angeles. Use it to estimate the range of the vertical ground acceleration functio
> Sketch the graph of the function. S(x)- |지 if |x| < 1 if |x|>1
> Sketch the graph of the function. h(t) =|t|+ |t + 1|
> Sketch the graph of the function. g(t) = |1 - 3t|
> Sketch the graph of the function. f(x) = |x + 2|
> Sketch the graph of the function. f(x) = x +|x|
> Evaluate f(-3), f(0), and f(2) for the piecewise defined function. Then sketch the graph of the function. |-1 if x<1 f(x) 7- 2x if x>1
> Evaluate f(-3), f(0), and f(2) for the piecewise defined function. Then sketch the graph of the function. x + 1 if x< -1 |x² f(x) = if x> -1
> Evaluate f(-3), f(0), and f(2) for the piecewise defined function. Then sketch the graph of the function. [3 – }x if x<2 f(x)* | 2x – 5 if x> 2
> Evaluate f(-3), f(0), and f(2) for the piecewise defined function. Then sketch the graph of the function. x + 2 if x<0 (x) = - x if x> 0
> Find the domain and sketch the graph of the function. t2 – 1 g(t)- t + 1
> The graphs of f and g are given. a. State the values of f(-4) and g(3). b. For what values of x is f(x) – g(x)? c. Estimate the solution of the equation f(x) = -1. d. On what interval is f decreasing? e. State the domain and range
> Find the domain and sketch the graph of the function. f(x) = 1.6x – 2.4
> Find the domain and range and sketch the graph of the function h(x) = 4 − x2 .
> Find the domain of the function. F(p) — /2 — ур
