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Bartleby Sitemap - Textbook Solutions

All Textbook Solutions for Finite Mathematics for Business, Economics, Life Sciences and Social Sciences

Replace each question mark with an appropriate expression that will illustrate the use of the indicated real number property: ACommutative():x(y+z)=?BAssociative(+):2+(x+y)=?CDistributive:(2+3)x=? :Problems 2-6 refer to the following polynomials: (A)3x4(B)x+2(C)23x2(D)x3+8 Add all four.Problems 2-6 refer to the following polynomials: (A)3x4(B)x+2(C)23x2(D)x3+8 Subtract the sum of (A) and (C) from the sum of (B) and (D).Problems 2-6 refer to the following polynomials: (A)3x4(B)x+2(C)23x2(D)x3+8 Multiply (C) and (D).Problems 2-6 refer to the following polynomials: (A)3x4(B)x+2(C)23x2(D)x3+8 What is the degree of each polynomial?Problems 2-6 refer to the following polynomials: (A)3x4(B)x+2(C)23x2(D)x3+8 What is the leading coefficient of each polynomial?In Problems 7 and 8, perform the indicated operations and simplify. 5x23x43x2 In Problems 7 and 8, perform the indicated operations and simplify. 2x+y3x4y In Problems 9 and 10, factor completely. x2+7x+10 In Problems 9 and 10, factor completely. x32x215x Write 0.35 as a fraction reduced to lowest terms.Write 78 in decimal form.Write in scientific notation: A4,065,000,000,000B0.0073 Write in standard decimal form: A2.55108B4.06104 Indicate true (T) or false (F): (A) A natural number is a rational number. (B) A number with a repeating decimal expansion is an irrational number.Give an example of an integer that is not a natural number.In Problems 17-24, simplify and write answers using positive exponents only. All variables represent positive real numbers. 6xy35 In Problems 17-24, simplify and write answers using positive exponents only. All variables represent positive real numbers. 9u8v63u4v8 In Problems 17-24, simplify and write answers using positive exponents only. All variables represent positive real numbers. 21053103 In Problems 17-24, simplify and write answers using positive exponents only. All variables represent positive real numbers. x3y22 In Problems 17-24, simplify and write answers using positive exponents only. All variables represent positive real numbers. u5/3u2/3 In Problems 17-24, simplify and write answers using positive exponents only. All variables represent positive real numbers. 9a4b21/2 In Problems 17-24, simplify and write answers using positive exponents only. All variables represent positive real numbers. 5032+3222 In Problems 17-24, simplify and write answers using positive exponents only. All variables represent positive real numbers. x1/2+y1/22 In Problems 25-30, perform the indicated operation and write the answer as a simple fraction reduced to lowest terms. All variables represent positive real numbers. ab+ba In Problems 25-30, perform the indicated operation and write the answer as a simple fraction reduced to lowest terms. All variables represent positive real numbers. abccab In Problems 25-30, perform the indicated operation and write the answer as a simple fraction reduced to lowest terms. All variables represent positive real numbers. x2yy6x3 In Problems 25-30, perform the indicated operation and write the answer as a simple fraction reduced to lowest terms. All variables represent positive real numbers. xy3x2y In Problems 25-30, perform the indicated operation and write the answer as a simple fraction reduced to lowest terms. All variables represent positive real numbers. 17+h17h In Problems 25-30, perform the indicated operation and write the answer as a simple fraction reduced to lowest terms. All variables represent positive real numbers. x1+y1x2y2 Each statement illustrates the use of one of the following real number properties or definitions. Indicate which one. A(7)(5)=(7)+[(5)] B5u+(3v+2)=(3v+2)+5u C(5m2)(2m+3)=(5m2)2m+(5m2)3 D9.(4y)=(9.4)y Eu(vw)=uwv F(xy)+0=(xy)32E Multiplying a number x by 4 gives the same result as subtracting 4 from x. Express as an equation, and solve for x.Find the slope of the line that contains the points (3,5) and (4,10).Find the x and y coordinates of the point at which the graph of y=7x4 intersects the x axis.Find the x and y coordinates of the point at which the graph of y=7x4 intersects the y axis.In Problems 37-40, solve for x. x2=5x In Problems 37-40, solve for x. 3x221=0 In Problems 37-40, solve for x. x2x20=0 In Problems 37-40, solve for x. 6x2+7x1=0 According to equality property 2, multiplying both sides of an equation by a nonzero number always produces an equivalent equation. What is the smallest positive number that you could use to multiply both sides of the following equation to produce an equivalent equation without fractions? x+13x4=12 Replace ? with < or > in each of the following: A1?3and2(1)?2(3)B1?3and2(1)?2(3)D12?8and124?84D12?8and124?84 Based on these examples, describe the effect of multiplying both sides of an inequality by a number.The solution to Example 5B shows the graph of the inequality x5.What is the graph of x5 ? What is the corresponding interval? Describe the relationship be-tween these sets.Solve and check: 3x2(2x5)=2(x+3)8 Solve and check: x+13x4=12 Matched Problem 3 If a cardboard box has length L, width W, and height H, then its surface area is given by the formula S=2LW+2LH+2WH. Solve the formula for (A) L in terms of S, W, and H (B) H in terms of S, L, and W Replace each question mark with either < or >. A2?8B20?0C3?30 (A) Write 7,4 as a double inequality and graph. (B) Write x3 in interval notation and graph.Solve and graph: 3(x1)5(x+2)5 Solve and graph: 83x57 Mary paid 8.5 sales tax and a 190 title and license fee when she bought a new car for a total of 28,400. What is the purchase price of the car?How many bike computers would a company have to make and sell to break even if the fixed costs are 36,000, variable costs are 10.40 per computer, and the computers are sold to retailers for 15.20 each?What net annual salary in 1973 would have had the same purchasing power as a net annual salary of 100,000 in 2016? Compute the answer to the nearest dollar.In Problems 1-6, solve for x. 5x+3=x+23 In Problems 1-6, solve for x. 7x6=5x24 In Problems 1-6, solve for x. 9(4x)=2(x+7)In Problems 1-6, solve for x. 3(x+6)=52(x+1)In Problems 1-6, solve for x. x+14=x2+5 In Problems 1-6, solve for x. 2x+135x2=4 In Problems 7-12, write the interval as an inequality or double inequality. 4,13 In Problems 7-12, write the interval as an inequality or double inequality. 3,5 In Problems 7-12, write the interval as an inequality or double inequality. (2,7)In Problems 7-12, write the interval as an inequality or double inequality [6,1]In Problems 7-12, write the interval as an inequality or double inequality. ,4 In Problems 7-12, write the interval as an inequality or double inequality. 9,In Problems 13-18, write the solution set using interval notation. 8x2 In Problems 13-18, write the solution set using interval notation. 1x5 In Problems 13-18, write the solution set using interval notation. 2x18 In Problems 13-18, write the solution set using interval notation. 3x12 In Problems 13-18, write the solution set using interval notation. 153x21 In Problems 13-18, write the solution set using interval notation. 84x12 In Problems 19-32, find the solution set. x4+12=18 In Problems 19-32, find the solution set. m34=23 In Problems 19-32, find the solution set. y532 In Problems 19-32, find the solution set. x456 In Problems 19-32, find the solution set. 2u+4=5u+17u In Problems 19-32, find the solution set. 3y+9+y=138y In Problems 19-32, find the solution set. 10x+25(x3)=275 In Problems 19-32, find the solution set. 34x=5x+1 In Problems 19-32, find the solution set. 3y4y3 In Problems 19-32, find the solution set. x22x5 In Problems 19-32, find the solution set. x5x6=65 In Problems 19-32, find the solution set. y4y3=12 In Problems 19-32, find the solution set. m5335m2 In Problems 19-32, find the solution set. u223u3+2 In Problems 33-36, solve and graph. 23x714 In Problems 33-36, solve and graph. 45x+621 In Problems 33-36, solve and graph. 495C+3268 In Problems 33-36, solve and graph. 123t+511 In Problems 37-42, solve for the indicated variable. 3x4y=12;fory In Problems 37-42, solve for the indicated variable. y=23x+8;forx In Problems 37-42, solve for the indicated variable. Ax+By=C;fory(B0)In Problems 37-42, solve for the indicated variable. y=mx+b;form In Problems 37-42, solve for the indicated variable. F=95C+32;forC In Problems 37-42, solve for the indicated variable. C=59(F32);forF In Problems 43 and 44, solve and graph. 347x18 In Problems 43 and 44, solve and graph. 1083u6 If both a and b are positive numbers and b/a. is greater than 1, then is ab positive or negative?If both a and b are negative numbers and b/a is greater than 1, then is ab positive or negative?Ticket sales. A rock concert brought in $432,500 on the sale of 9,500 tickets. If the tickets sold for $35 and $55 each, how many of each type of ticket were sold?Parking meter coins. An all-day parking meter takes only dimes and quarters. If it contains 100 coins with a total value of $14.50, how many of each type of coin are in the meter?IRA. You have $500,000 in an IRA (Individual Retirement Account) at the time you retire. You have the option of investing this money in two funds: Fund A pays 5.2 annually and Fund B pays 7.7 annually. How should you divide your money between Fund A and Fund B to produce an annual interest income of $34,000?IRA. Refer to Problem 49. How should you divide your money between Fund A and Fund B to produce an annual interest income of $30,000?Car prices. If the price change of cars parallels the change in the CPI (see Table2 in Example 10), what would a car sell for (to the nearest dollar) in 2016 if a comparable model sold for $10,000 in 1999?Home values. If the price change in houses parallels the CPI (see Table 2 in Example 10), what would a house valued at $200,000 in 2016 be valued at (to the nearest dollar) in 1960?Retail and wholesale prices. Retail prices in a department store are obtained by marking up the wholesale price by 40. That is, the retail price is obtained by adding 40 of the wholesale price to the wholesale price. (A) What is the retail price of a suit if the wholesale price is $300? (B) What is the wholesale price of a pair of jeans if the retail price is $77?Retail and sale prices. Sale prices in a department store are obtained by marking down the retail price by 15. That is, the sale price is obtained by subtracting 15 of the retail price from the retail price. (A) What is the sale price of a hat that has a retail price of $60? (B) What is the retail price of a dress that has a sale price of $136?Equipment rental. A golf course charges $52 for a round of golf using a set of their clubs, and $44 if you have your own clubs. If you buy a set of clubs for $270, how many rounds must you play to recover the cost of the clubs?Equipment rental. The local supermarket rents carpet cleaners for $20 a day. These cleaners use shampoo in a special cartridge that sells for $16 and is available only from the super- market. A home carpet cleaner can be purchased for $300. Shampoo for the home cleaner is readily available for $9 a bottle. Past experience has shown that it takes two shampoo cartridges to clean the 10-foot-by-12-foot carpet in your living room with the rented cleaner. Cleaning the same area with the home cleaner will consume three bottles of shampoo. If you buy the home cleaner, how many times must you clean the living-room carpet to make buying cheaper than renting?Sales commissions. One employee of a computer store is paid a base salary of $2,000 a month plus an 8 commission on all sales over $7,000 during the month. How much must the employee sell in one month to earn a total of $4,000 for the month?Sales commissions. A second employee of the computer store in Problem 57 is paid a base salary of $3,000 a month plus a 5 commission on all sales during the month. (A) How much must this employee sell in one month to earn a total of $4,000 for the month? (B) Determine the sales level at which both employees receive the same monthly income. (C) If employees can select either of these payment methods, how would you advise an employee to make this selection?Break-even analysis. A publisher for a promising new novel figures fixed costs (overhead, advances, promotion, copy editing, typesetting) at $55,000, and variable costs (printing, paper, binding, shipping) at $1.60 for each book produced. If the book is sold to distributors for $11 each, how many must be produced and sold for the publisher to break even?Break-even analysis. The publisher of a new book figures fixed costs at $92,000 and variable costs at $2.10 for each book produced. If the book is sold to distributors for $15 each, how many must be sold for the publisher to break even?Break-even analysis. The publisher in Problem 59 finds that rising prices for paper increase the variable costs to $2.10 per book. (A) Discuss possible strategies the company might use to deal with this increase in costs. (B) If the company continues to sell the books for $11, how many books must they sell now to make a profit? (C) If the company wants to start making a profit at the same production level as before the cost increase, how much should they sell the book for now?Break-even analysis. The publisher in Problem 60 finds that rising prices for paper increase the variable costs to $2.70 per book. (A) Discuss possible strategies the company might use to deal with this increase in costs. (B) If the company continues to sell the books for $15, how many books must they sell now to make a profit? (C) If the company wants to start making a profit at the same production level as before the cost increase, how much should they sell the book for now?Wildlife management. A naturalist estimated the total number of rainbow trout in a certain lake using the capture–mark–recapture technique. He netted, marked, and released 200 rainbow trout. A week later, allowing for thorough mixing, he again netted 200 trout, and found 8 marked ones among them. Assuming that the proportion of marked fish in the second sample was the same as the proportion of all marked fish in the total population, estimate the number of rainbow trout in the lake.Temperature conversion. If the temperature for a 24-hour period at an Antarctic station ranged between 49F and 14F (that is, 49F14) what was the range in degree Celsius? [Note:F=95C+32.]Psychology. The IQ (intelligence quotient) is found by dividing the mental age (MA), as indicated on standard tests, by the chronological age (CA) and multiplying by 100. For example, if a child has a mental age of 12 and a chronological age of 8, the calculated IQ is150. If a 9-year-old girl has an IQ of 140, compute her mental age.Psychology. Refer to Problem 65. If the IQ of a group of 12-year-old children varies between 80 and 140, what is the range of their mental ages?(A) As noted earlier, (4,3) is a solution of the equation 3x2y=6 Find three more solutions of this equation. Plot these solutions in a Cartesian coordinate system. What familiar geometric shape could be used to describe the solution set of this equation? (B) Repeat part (A) for the equation x=2. (C) Repeat part (A) for the equation y=3.(A) Graph y=x+b for b=5,3,0,3 and 5 simultaneously in the same coordinate system. Verbally describe the geometric significance of b. (B) Graph y=mx1 for m=2,1,0,1, and 2 simultaneously in the same coordinate system. Verbally describe the geometric significance of m. (C) Using a graphing calculator, explore the graph of y=mx+b for different values of m and b.Graph:4x3y=12 Graph 4x-3y=12 on a graphing calculator and find the intercepts.(A) Graph x=5andy=3 simultaneously in the same rectangular coordinate system. (B) Write the equations of the vertical and horizontal lines that pass through the point 8,2.Find the slope of the line through each pair of points. (A) (2,4),(3,4) (B) (2,4),(0,4) (C) (1,5),(1,2) (D) (1,2),(2,1)Write the equation of the line with slope 12 and y intercept 1. Graph.(A) Find an equation for the line that has slope 23 and passes through 6,2. Write the resulting equation in the form Ax+By=C,A0. (B) Find an equation for the line that passes through (2,3) and (4,3). Write the resulting equation in the form y=mx+b.Answer parts (A) and (B) in Example 7 for fixed costs of $250 per day and total costs of $3,450 per day at an output of 80 skateboards per day.At a price of $12.59 per box of grapefruit, the supply is 595,000 boxes and the demand is 650,000 boxes. At a price of $13.19 per box, the supply is 695,000 boxes and the demand is 590,000 boxes. Assume that the relations -ship between price and supply is linear and that the relationship between price and demand is linear. (A) Find a price–supply equation of the form p=mx+b. (B) Find a price–demand equation of the form p=mx+b. (C) Find the equilibrium point.\ Problems 1-4 refer to graphs (A)-(D). Identify the graph(s) of lines with a negative slope.Problems 1-4 refer to graphs (A)-(D). Identify the graph(s) of lines with a positive slope.Problems 1-4 refer to graphs (A)-(D). Identify the graph(s) of any lines with slope zero.Problems 1-4 refer to graphs (A)-(D). Identify the graph(s) of any lines with undefined slope.In Problems 5-8, sketch a graph of each equation in a rectangular coordinate system. y=2x3 In Problems 5-8, sketch a graph of each equation in a rectangular coordinate system. y=x2+1 In Problems 5-8, sketch a graph of each equation in a rectangular coordinate system. 2x+3y=12 In Problems 5-8, sketch a graph of each equation in a rectangular coordinate system. 8x3y=24 In Problems 9-14, find the slope and y intercept of the graph of each equation y=5x7 In Problems 9-14, find the slope and y intercept of the graph of each equation. y=3x+2 In Problems 9-14, find the slope and y intercept of the graph of each equation. y=52x9 In Problems 9-14, find the slope and y intercept of the graph of each equation. y=103x+4 In Problems 9-14, find the slope and y intercept of the graph of each equation. y=x4+23 In Problems 9-14, find the slope and y intercept of the graph of each equation. y=x512 In Problems 15-20, find the slope and x intercept of the graph of each equation. y=2x+10 In Problems 15-20, find the slope and x intercept of the graph of each equation. y=4x+12 In Problems 15-20, find the slope and x intercept of the graph of each equation. 8xy=40 In Problems 15-20, find the slope and x intercept of the graph of each equation. 3x+y=6 In Problems 15-20, find the slope and x intercept of the graph of each equation. 6x+7y=42 In Problems 15-20, find the slope and x intercept of the graph of each equation. 9x+2y=4 In Problems 21-24, write an equation of the line with the indicated slope and y intercept. Slope= 2 y intercept= 1 In Problems 21-24, write an equation of the line with the indicated slope and y intercept. Slope = 1 y intercept=5 In Problems 21-24, write an equation of the line with the indicated slope and y intercept. Slope=13 yintercept=6 In Problems 21-24, write an equation of the line with the indicated slope and y intercept. Slope= 67 y intercept=92 In Problems 25-28, use the graph of each line to find the x intercept, y intercept, and slope. Write the slope-intercept form of the equation of the line.In Problems 25-28, use the graph of each line to find the x intercept, y intercept, and slope. Write the slope-intercept form of the equation of the line.In Problems 25-28, use the graph of each line to find the x intercept, y intercept, and slope. Write the slope-intercept form of the equation of the line.In Problems 25-28, use the graph of each line to find the x intercept, y intercept, and slope. Write the slope-intercept form of the equation of the line.In Problems 29-34, sketch a graph of each equation or pair of equations in a rectangular coordinate system. y=23x2 In Problems 29-34, sketch a graph of each equation or pair of equations in a rectangular coordinate system. y=32x+1 In Problems 29-34, sketch a graph of each equation or pair of equations in a rectangular coordinate system. 3x2y=10 In Problems 29-34, sketch a graph of each equation or pair of equations in a rectangular coordinate system. 5x6y=15 In Problems 29-34, sketch a graph of each equation or pair of equations in a rectangular coordinate system. x=3;y=2 In Problems 29-34, sketch a graph of each equation or pair of equations in a rectangular coordinate system. x=3;y=2 In Problems 35-40, find the slope of the graph of each equation. 4x+y=3 In Problems 35-40, find the slope of the graph of each equation. 5xy=2 In Problems 35-40, find the slope of the graph of each equation. 3x+5y=15 In Problems 35-40, find the slope of the graph of each equation. 2x3y=18 In Problems 35-40, find the slope of the graph of each equation. 4x+2y=9 In Problems 35-40, find the slope of the graph of each equation. x+8y=4 Given Ax+By=12, graph each of the following three cases in the same coordinate system. (A) A=2andB=0 (B) A=0andB=3 (C) A=3andB=3 Given Ax+By=24, graph each of the following three cases in the same coordinate system. (A) A=6andB=0 (B) A=0andB=8 (C) A=2andB=3 Graph y=25x+200,x0.Graph y=40x+160,x0.(A) Graph y=1.2x4.2 in a rectangular coordinate system. (B) Find the x and y intercepts algebraically to one decimal place. (C) Graph y=1.2x4.2 in a graphing calculator. (D) Find the x and y intercepts to one decimal place using TRACE and the ZERO command.(A) Graph y=0.8x+5.2 in a rectangular coordinate system. (B) Find the x and y intercepts algebraically to one decimal place. (C) Graph y=0.8x+5.2 in a graphing calculator. (D) Find the x and y intercepts to one decimal place using trace and the zero command.In Problems 47-50, write the equations of the vertical and horizontal lines through each point. 4,3 In Problems 47-50, write the equations of the vertical and horizontal lines through each point. 5,6 In Problems 47-50, write the equations of the vertical and horizontal lines through each point. 1.5,3.5 In Problems 47-50, write the equations of the vertical and horizontal lines through each point. 2.6,3.8 In Problems 51-58, write the slope-intercept form of the equation of the line with the indicated slope that goes through the given point. m=5;3,0 In Problems 51-58, write the slope-intercept form of the equation of the line with the indicated slope that goes through the given point. m=4;0,6 In Problems 51-58, write the slope-intercept form of the equation of the line with the indicated slope that goes through the given point. m=2;1,9 In Problems 51-58, write the slope-intercept form of the equation of the line with the indicated slope that goes through the given point. m=10;2,5 In Problems 51-58, write the slope-intercept form of the equation of the line with the indicated slope that goes through the given point. m=13;4,8 In Problems 51-58, write the slope-intercept form of the equation of the line with the indicated slope that goes through the given point. m=27;7,1 In Problems 51-58, write the slope-intercept form of the equation of the line with the indicated slope that goes through the given point. m=3.2;(5.8,12.3)In Problems 51-58, write the slope-intercept form of the equation of the line with the indicated slope that goes through the given point. m=0.9;(2.3,6.7)In Problems 59-66, (A) Find the slope of the line that passes through the given points. (B) Find the standard form of the equation of the line. (C) Find the slope-intercept form of the equation of the line. 2,5and5,7 In Problems 59-66, (A) Find the slope of the line that passes through the given points. (B) Find the standard form of the equation of the line. (C) Find the slope-intercept form of the equation of the line. 1,2and3,5 In Problems 59-66, (A) Find the slope of the line that passes through the given points. (B) Find the standard form of the equation of the line. (C) Find the slope-intercept form of the equation of the line. 2,1and2,6 In Problems 59-66, (A) Find the slope of the line that passes through the given points. (B) Find the standard form of the equation of the line. (C) Find the slope-intercept form of the equation of the line. 2,3and3,7 In Problems 59-66, (A) Find the slope of the line that passes through the given points. (B) Find the standard form of the equation of the line. (C) Find the slope-intercept form of the equation of the line. 5,3and5,3 In Problems 59-66, (A) Find the slope of the line that passes through the given points. (B) Find the standard form of the equation of the line. (C) Find the slope-intercept form of the equation of the line. 1,4and0,4 In Problems 59-66, (A) Find the slope of the line that passes through the given points. (B) Find the standard form of the equation of the line. (C) Find the slope-intercept form of the equation of the line. 2,5and3,5 In Problems 59-66, (A) Find the slope of the line that passes through the given points. (B) Find the standard form of the equation of the line. (C) Find the slope-intercept form of the equation of the line. 2,0and2,3 Discuss the relationship among the graphs of the lines with equation y=mx+2, where m is any real number.Discuss the relationship among the graphs of the lines with equation y=0.5x+b, where b is any real number.Cost analysis. A donut shop has a fixed cost of $124 per day and a variable cost of $0.12 per donut. Find the total daily cost of producing x donuts. How many donuts can be produced for a total daily cost of $250?Cost analysis. A small company manufactures picnic tables. The weekly fixed cost is $1,200 and the variable cost is $45 per table. Find the total weekly cost of producing x picnic tables. How many picnic tables can be produced for a total weekly cost of $4,800?Cost analysis. A plant can manufacture 80 golf clubs per day for a total daily cost of 7,647 and 100 golf clubs per day for a total daily cost of 9,147. (A) Assuming that daily cost and production are linearly related, find the total daily cost of producing x golf clubs. (B) Graph the total daily cost for 0x200. (C) Interpret the slope and y intercept of this cost equation.Cost analysis. A plant can manufacture 50 tennis rackets per day for a total daily cost of $3,855 and 60 tennis rackets per day for a total daily cost of $4,245. (A) Assuming that daily cost and production are linearly related, find the total daily cost of producing x tennis rackets. (B) Graph the total daily cost for 0x100. (C) Interpret the slope and y intercept of this cost equation.Business-Markup policy. A drugstore sells a drug costing $85 for $112 and a drug costing $175 for $238. (A) If the markup policy of the drugstore is assumed to be linear, write an equation that expresses retail price R in terms of cost C (wholesale price). (B) What does a store pay (to the nearest dollar) for a drug that retails for $185?Business-Markup policy. A clothing store sells a shirt costing $20for$33 and a jacket costing $60 for $93. (A) If the markup policy of the store is assumed to be linear, write an equation that expresses retail price R in terms of cost C (wholesale price). (B) What does a store pay for a suit that retails for 240?Business-Depreciation. A farmer buys a new tractor for $157,000 and assumes that it will have a trade-in value of $82,000 after 10 years. The farmer uses a constant rate of depreciation (commonly called straight-line depreciation-one of several methods permitted by the IRS) to determine the annual value of the tractor. (A) Find a linear model for the depreciated value V of the tractor t years after it was purchased. (B) What is the depreciated value of the tractor after 6 years? (C) When will the depreciated value fall below $70,000? (D) Graph V for 0t20 and illustrate the answers from parts (B) and (C) on the graph.Business-Depreciation. A charter fishing company buys a new boat for $224,000 and assumes that it will have a trade-in value of $115,200 after 16 years. (A) Find a linear model for the depreciated value V of the boat t years after it was purchased. (B) What is the depreciated value of the boat after 10 years? (C) When will the depreciated value fall below $100,000? (D) Graph V for 0t30 and illustrate the answers from (B) and (C) on the graph.Boiling point. The temperature at which water starts to boil is called its boiling point and is linearly related to the altitude. Water boils at 212F at sea level and at 193.6F at an altitude of 10,000 feet. (A) Find a relationship of the form T=mx+b where T is degrees Fahrenheit and x is altitude in thousands of feet. (B) Find the boiling point at an altitude of 3,500 feet. (C) Find the altitude if the boiling point is 200F. (D) Graph T and illustrate the answers to (B) and (C) on the graph.Boiling point. The temperature at which water starts to boil is also linearly related to barometric pressure. Water boils at 212F at a pressure of 29.9 inHg (inches of mercury) and at 191F at a pressure of 28.4 inHg. (A) Find a relationship of the form T=mx+b, where T is degrees Fahrenheit and x is pressure in inches of mercury. (B) Find the boiling point at a pressure of 31 inHg. (C) Find the pressure if the boiling point is 199F. (D) Graph T and illustrate the answers to (B) and (C) on the graph.Flight conditions. In stable air, the air temperature drops about 3.6F for each 1,000-foot rise in altitude. (A) If the temperature at sea level is 70F, write a linear equation that expresses temperature T in terms of altitude A in thousands of feet. (B) At what altitude is the temperature 34F?Flight navigation. The airspeed indicator on some aircraft is affected by the changes in atmospheric pressure at different altitudes. A pilot can estimate the true airspeed by observing the indicated airspeed and adding to it about 1.6 for every 1,000feet of altitude. (A) A pilot maintains a constant reading of 200 miles per hour on the airspeed indicator as the aircraft climbs from sea level to an altitude of 10,000feet. Write a linear equation that expresses true airspeed T (in miles per hour) in terms of altitude A (in thousands of feet). (B) What would be the true airspeed of the aircraft at 6,500feet?Demographics. The average number of persons per house-hold in the United States has been shrinking steadily for as long as statistics have been kept and is approximately linear with respect to time. In 1980 there were about 2.76 persons per household, and in 2015 about2.54. (A) If N represents the average number of persons per house-hold and t represents the number of years since 1980, write a linear equation that expresses N in terms of t. (B) Use this equation to estimate household size in the year 2030.Demographics. The median household income divides the households into two groups: the half whose income is less than or equal to the median, and the half whose income is greater than the median. The median household income in the United States grew from about $30,000 in 1990 to about $55,775 in 2015. (A) If I represents the median household income and t represents the number of years since 1990, write a linear equation that expresses I in terms of t. (B) Use this equation to estimate median household income in the year 2030 Cigarette smoking. The percentage of female cigarette smokers in the United States declined from 21.0 in 2000 to 13.6 in 2015. (A) Find a linear equation relating percentage of female smokers f to years since 2000 t. (B) Use this equation to predict the year in which the percentage of female smokers falls below 7.Cigarette smoking. The percentage of male cigarette smokers in the United States declined from 25.7 in 2000 to 16.7 in 2015. (A) Find a linear equation relating percentage of male smokers m to years since 2000 t. (B) Use this equation to predict the year in which the per-centage of male smokers falls below 7.Supply and demand. At a price of $9.00 per bushel, the supply of soybeans is 3,600 million bushels and the demand is 4,000 million bushels. At a price of 9.50 per bushel, the supply is 4,100 million bushels and the demand is 3,500 million bushels. (A) Find a price-supply equation of the form p=mx+b. (B) Find a price-demand equation of the form p=mx+b. (C) Find the equilibrium point. (D) Graph the price-supply equation, price-demand equation, and equilibrium point in the same coordinate system.Supply and demand. At a price of $3.20 per bushel, the supply of corn is 9,800 million bushels and the demand is 9,200 million bushels. At a price of $2.95 per bushel, the supply is 9,300 million bushels and the demand is 9,700 million bushels. (A) Find a price-supply equation of the form p=mx+b. (B) Find a price-demand equation of the form p=mx+b. (C) Find the equilibrium point. (D) Graph the price-supply equation, price-demand equation, and equilibrium point in the same coordinate system.Physics. Hooke’s law states that the relationship between the stretch s of a spring and the weight w causing the stretch is linear. For a particular spring, a 5-pound weight causes a stretch of 2 inches, while with no weight, the stretch of the spring is 0. (A) Find a linear equation that expresses s in terms of w. (B) What is the stretch for a weight of 20 pounds? (C) What weight will cause a stretch of 3.6 inches?Physics. The distance d between a fixed spring and the floor is a linear function of the weight w attached to the bottom of the spring. The bottom of the spring is 18 inches from the floor when the weight is 3 pounds, and 10 inches from the floor when the weight is 5 pounds. (A) Find a linear equation that expresses d in terms of w. (B) Find the distance from the bottom of the spring to the floor if no weight is attached. (C) Find the smallest weight that will make the bottom of the spring touch the floor. (Ignore the height of the weight.)As illustrated in Example 1A, the slope m of a line with equation y=mx+b has two interpretations: 1. m is the rate of change of y with respect to x. 2. Increasing x by one unit will change y by m units. How are these two interpretations related?As stated previously, we used linear regression to produce the model in Example 3. If you have a graphing calculator that supports linear regression, then you can find this model. The linear regression process varies greatly from one calculator to another. Consult the user’s manual for the details of linear regression. The screens in Figure 3 are related to the construction of the model in Example 3 on a Texas Instruments TI-84 Plus CE. (A) Produce similar screens on your graphing calculator. (B) Do the same for Matched Problem 3.The equation a=28.55w+118.7 expresses BSA for felines in terms of weight, where a is BSA in square inches and w is weight in pounds. (A) Interpret the slope of the BSA equation. (B) What is the effect of a one-pound increase in weight?A 400-pound load of grain is dropped from an altitude of 2,880 feet and lands 80 seconds later. Find a linear model relating altitude a (in feet) and time in the air t (in seconds). (B) How fast is the cargo moving when it lands?Prices for emerald-shaped diamonds from an online trader are given in Table 2. Repeat Example 3 for this data with the linear model p=5,600c1,100 where p is the price of an emerald-shaped diamond weighing c carats.Using the model of Example 4, estimate the concentration of carbon dioxide in the atmosphere in the year 1990.Figure 5 shows the scatter plot for white spruce trees in the Jack Haggerty Forest at Lakehead University in Canada. A regression model produced by a spreadsheet (Fig. 5), after rounding, is h=1.8d+34 where d is Dbh in inches and h is the height in feet. (A) Interpret the slope of this model. (B) What is the effect of a 1-inch increase in Dbh? (C) Estimate the height of a white spruce with a Dbh of 10 inches. Round your answer to the nearest foot. (D) Estimate the Dbh of a white spruce that is 65 feet tall. Round your answer to the nearest inch.Ideal weight. Dr. J. D. Robinson published the following estimate of the ideal body weight of a woman: 49kg+1.7kg for each inch over 5 ft (A) Find a linear model for Robinson’s estimate of the ideal weight of a woman using w for ideal body weight (in kilograms) and h for height over 5 ft (in inches). (B) Interpret the slope of the model. (C) If a woman is 54 tall, what does the model predict her weight to be? (D) If a woman weighs 60 kg, what does the model predict her height to be?Ideal weight. Dr. J. D. Robinson also published the following estimate of the ideal body weight of a man: 52kg+1.9kg for each inch over 5 ft (A) Find a linear model for Robinson’s estimate of the ideal weight of a man using w for ideal body weight (in kilo-grams) and h for height over 5 ft (in inches). (B) Interpret the slope of the model. (C) If a man is 58 tall, what does the model predict his weight to be? (D) If a man weighs 70 kg, what does the model predict his height to be?Underwater pressure. At sea level, the weight of the atmosphere exerts a pressure of 14.7 pounds per square inch, commonly referred to as 1 atmosphere of pressure. As an object descends in water, pressure P and depth d are linearly related. In salt water, the pressure at a depth of 33 ft is 2 atms, or 29.4 pounds per square inch. (A) Find a linear model that relates pressure P (in pounds per square inch) to depth d (in feet). (B) Interpret the slope of the model. (C) Find the pressure at a depth of 50 ft. (D) Find the depth at which the pressure is 4 atms.Underwater pressure. Refer to Problem 3. In fresh water, the pressure at a depth of 34 ft is 2 atms, or 29.4 pounds per square inch. (A) Find a linear model that relates pressure P (in pounds per square inch) to depth d (in feet). (B) Interpret the slope of the model. (C) Find the pressure at a depth of 50 ft. (D) Find the depth at which the pressure is 4 atms.Rate of descent Parachutes. At low altitudes, the altitude of a parachutist and time in the air are linearly related. A jump at 2,880 ft using the U.S. Army’s T-10 parachute system lasts 120 secs. Find a linear model relating altitude a (in feet) and time in the air t (in seconds). Find the rate of descent for a T-10 system. (C) Find the speed of the parachutist at landing.Rate of descent Parachutes. The U.S Army is considering a new parachute, the Advanced Tactical Parachute System (ATPS). A jump at 2,880 ft using the ATPS system lasts 180 secs. (A) Find a linear model relating altitude a (in feet) and time in the air t (in seconds). (B) Find the rate of descent for an ATPS system parachute. (C) Find the speed of the parachutist at landing.Speed of sound. The speed of sound through air is linearly related to the temperature of the air. If sound travels at 331m/secat0Candat343m/secat20C, construct a linear model relating the speed of sound s and the air temperature t. Interpret the slope of this model.Speed of sound. The speed of sound through sea water is linearly related to the temperature of the water. If sound travels at 1,403m/secat0Candat1,481m/secat20C, construct a linear model relating the speed of sound s and the air temperature t. Interpret the slope of this model.Energy production. Table 5 lists U.S. fossil fuel production as a percentage of total energy production for selected years. A linear regression model for this data is y=0.19x+83.75 where x represents years since 1985 and y represents the corresponding percentage of total energy production. (A) Draw a scatter plot of the data and a graph of the model on the same axes. (B) Interpret the slope of the model. (C) Use the model to predict fossil fuel production in 2025. (D) Use the model to estimate the first year for which fossil fuel production is less than 70 of total energy Energy consumption. Table 6 lists U.S. fossil fuel consumption as a percentage of total energy consumption for selected years. A linear regression model for this data is y=0.14x+86.18 Where x represents years since 1985 and y represents the corresponding percentage of fossil fuel consumption. (A) Draw a scatter plot of the data and a graph of the model on the same axes. (B) Interpret the slope of the model. (C) Use the model to predict fossil fuel consumption in 2025. (D) Use the model to estimate the first year for which fossil fuel consumption is less than 80#37; of total energy consumption.Cigarette smoking. The data in Table 7 shows that the percentage of female cigarette smokers in the United States declined from 22.1 in 1997 to 13.6 in 2015. Applying linear regression to the data for females in Table 7 produces the model f=0.45t+22.20 where f is percentage of female smokers and t is time in years since 1997. Draw a scatter plot of the female smoker data and a graph of the regression model on the same axes. (B) Estimate the first year in which the percentage of female smokers is less than 10.Cigarette smoking. The data in Table 7 shows that the percentage of male cigarette smokers in the United States declined from 27.6 in 1997 to 16.7 in 2015. Applying linear regression to the data for males in Table 7 produces the model m=0.56t+27.82 where m is percentage of male smokers and t is time in years since 1997. Draw a scatter plot of the male smoker data and a graph of the regression model. (B) Estimate the first year in which the percentage of male smokers is less than 10.Licensed drivers. Table 8 contains the state population and the number of licensed drivers in the state (both in millions) for the states with population under 1 million in 2014. The regression model for this data is y=0.75x where x is the state population (in millions) and y is the number of licensed drivers (in millions) in the state. (A) Draw a scatter plot of the data and a graph of the model on the same axes. (B) If the population of Hawaii in 2014 was about 1.4 million, use the model to estimate the number of licensed drivers in Hawaii in 2014 to the nearest thousand. (C) If the number of licensed drivers in Maine in 2014 was about 1,019,000, use the model to estimate the population of Maine in 2014 to the nearest thousand.Licensed drivers. Table 9 contains the state population and the number of licensed drivers in the state (both in millions) for the most populous states in 2014. The regression model for this data is y=0.62x+0.29 where x is the state population (in millions) and y is the number of licensed drivers (in millions) in the state. (A) Draw a scatter plot of the data and a graph of the model on the same axes. (B) If the population of Michigan in 2014 was about 9.9 million, use the model to estimate the number of licensed drivers in Michigan in 2014 to the nearest thousand. (C) If the number of licensed drivers in Georgia in 2014 was about 6.7 million, use the model to estimate the population of Georgia in 2014 to the nearest thousand.Net sales. A linear regression model for the net sales data in Table 10 is S=15.85t+250.1 Where S is net sales and t is time since 2000 in years. (A) Draw a scatter plot of the data and a graph of the model on the same axes. (B) Predict Walmart’s net sales for 2026.Operating income. A linear regression model for the operating income data in Table 10 is I=0.82t+15.84 where I is operating income and t is time since 2000 in years. (A) Draw a scatter plot of the data and a graph of the model on the same axes. (B) Predict Walmart’s annual operating income for 2026.Freezing temperature. Ethylene glycol and propylene glycol are liquids used in antifreeze and deicing solutions. Ethylene glycol is listed as a hazardous chemical by the Environmental Protection Agency, while propylene glycol is generally regarded as safe. Table 11 lists the freezing temperature for various concentrations (as a percentage of total weight) of each chemical in a solution used to deice airplanes. A linear regression model for the ethylene glycol data in Table 11 is E=0.55T+31 where E is the percentage of ethylene glycol in the deicing solution and T is the temperature at which the solution freezes. (A) Draw a scatter plot of the data and a graph of the model on the same axes. (B) Use the model to estimate the freezing temperature to the nearest degree of a solution that is 30#37; ethylene glycol. (C) Use the model to estimate the percentage of ethylene glycol in a solution that freezes at 15F.Freezing temperature. A linear regression model for the propylene glycol data in Table 11 is P=0.54T+34 where P is the percentage of propylene glycol in the deicing solution and T is the temperature at which the solution freezes. (A) Draw a scatter plot of the data and a graph of the model on the same axes. (B) Use the model to estimate the freezing temperature to the nearest degree of a solution that is 30#37; propylene glycol. (C) Use the model to estimate the percentage of propylene glycol in a solution that freezes at 15F.Forestry. The figure contains a scatter plot of 100 data points for black spruce trees and the linear regression model for this data. (A) Interpret the slope of the model. (B) What is the effect of a 1-in. increase in Dbh? (C) Estimate the height of a black spruce with a Dbh of 15 in. Round your answer to the nearest foot. (D) Estimate the Dbh of a black spruce that is 25 ft tall. Round your answer to the nearest inch.Forestry. The figure contains a scatter plot of 100 data points for black walnut trees and the linear regression model for this data. (A) Interpret the slope of the model. (B) What is the effect of a 1-in. increase in Dbh? (C) Estimate the height of a black walnut with a Dbh of 12 in. Round your answer to the nearest foot. (D) Estimate the Dbh of a black walnut that is 25 ft tall. Round your answer to the nearest inch.Undergraduate enrollment. Table 12 lists fall undergraduate enrollment by gender in U.S. degree-granting institutions. The figure contains a scatter plot and regression line for each data set, where x represents years since 1980 and y represents enrollment (in millions). (A) Interpret the slope of each model. (B) Use the regression models to predict the male and female undergraduate enrollments in 2025. (C) Use the regression models to estimate the first year in which female undergraduate enrollment will exceed male undergraduate enrollment by at least 3 million.Graduate enrollment. Table 13 lists fall graduate enrollment by gender in U.S. degree-granting institutions. The figure contains a scatter plot and regression line for each data set, where x represents years since 1980 and y represents enrollment (in millions). (A) Interpret the slope of each model. (B) Use the regression models to predict the male and female graduate enrollments in 2025. (C) Use the regression models to estimate the first year in which female graduate enrollment will exceed male graduate enrollment by at least 1 million.Climate. Find a linear regression model for the data on aver-age annual temperature in Table 14, where x is years since 1960 and y is temperature inF. (Round regression coefficients to three decimal places). Use the model to estimate the average annual temperature in the contiguous United States in 2025.Climate. Find a linear regression model for the data on average annual precipitation in Table 14, where x is years since 1960 and y is precipitation (in inches). (Round regression coefficients to three decimal places). Use the model to estimate the average annual precipitation in the contiguous United States in 2025.Olympic Games. Find a linear regression model for the men’s 100-meter freestyle data given in Table 15, where x is years since 1990 and y is winning time (in seconds). Do the same for the women’s 100-meter freestyle data. (Round regression coefficients to three decimal places.) Do these models indicate that the women will eventually catch up with the men?Olympic Games. Find a linear regression model for the men’s 200-meter backstroke data given in Table 15, where x is years since 1990 and y is winning time (in seconds). Do the same for the women’s 200-meter backstroke data. (Round regression coefficients to three decimal places.) Do these models indicate that the women will eventually catch up with the men?Supply and demand. Table 16 contains price supply data and price demand data for corn. Find a linear regression model for the price supply data where x is supply (in billions of bushels) and y is price (in dollars). Do the same for the price demand data. (Round regression coefficients to two decimal places.) Find the equilibrium price for corn.Supply and demand. Table 17 contains price supply data and price demand data for soybeans. Find a linear regression model for the price–supply data where x is supply (in billions of bushels) and y is price (in dollars). Do the same for the price demand data. (Round regression coefficients to two decimal places.) Find the equilibrium price for soybeans.Solve2x+3=7x11.Solvex12x33=12.Solve2x+5y=9fory.Solve3x4y=7forx.Solve Problems 5-7 and graph on a real number line. 4y310 Solve Problems 5-7 and graph on a real number line. 12x+53 Solve Problems 5-7 and graph on a real number line. 1x3312 Sketch a graph of 3x+2y=9.Write an equation of a line with x intercept 6 and y intercept 4. Write the final answer in the form Ax+By=C.Sketch a graph of 2x3y=18. What are the intercepts and slope of the line?Write an equation in the form y=mx+b for a line with slope 23 and y intercept6.Write the equations of the vertical line and the horizontal line that pass through (6,5).Write the equation of a line through each indicated point with the indicated slope. Write the final answer in the form y=mx+b. (A)m=23;3,2 (B)m=0;3,3 Write the equation of the line through the two indicated points. Write the final answer in the form Ax+By=C. (A)3,5,1,1 (B)1,5,4,5 (C)2,7,2,2 Solve Problems 15-19. 3x+25=5x Solve Problems 15-19. u5=u6+65 Solve Problems 15-19. 5x34+x2=x24+1 Solve Problems 15-19. 0.05x+0.2530x=3.3 Solve Problems 15-19. 0.2x3+0.05x=0.4 Solve Problems 20-24 and graph on a real number line. 2x+45x4 Solve Problems 20-24 and graph on a real number line. 32x22x1 Solve Problems 20-24 and graph on a real number line. x+384+x252x3 Solve Problems 20-24 and graph on a real number line. 532x1 Solve Problems 20-24 and graph on a real number line. 1.524x0.5 Given Ax+By=30, graph each of the following cases on the same coordinate axes. (A)A=5andB=0 (B)A=0andB=6 (C)A=6andB=5 Describe the graphs of x=3 and y=2 Graph both simultaneously in the same coordinate system.Describe the lines defined by the following equations: A3x+4y=0B3x+4=0C4y=0D3x+4y36=0 Solve Problems 28 and 29 for the indicated variable. A=12a+bh;forah0 Solve Problems 28 and 29 for the indicated variable. S=P1dt;forddt1 For what values of a and b is the inequality a+bba true?If a and b are negative numbers and ab, then is a/b greater than 1 or less than 1?Graph y=mx+bandy=1mx+b simultaneously in the same coordinate system for b fixed and several different values of m,m0. Describe the apparent relationship between the graphs of the two equations.Investing. An investor has $300,000 to invest. If part is invested at 5 and the rest at 9, how much should be invested at 5 to yield 8 on the total amount?Break-even analysis. A producer of educational DVDs is producing an instructional DVD. She estimates that it will cost 90,000 to record the DVD and 5.10 per unit to copy and distribute the DVD. If the wholesale price of the DVD is 14.70, how many DVDs must be sold for the producer to break even?Sports medicine. A simple rule of thumb for determining your maximum safe heart rate (in beats per minute) is to subtract your age from 220. While exercising, you should maintain a heart rate between 60 and 85 of your maxi-mum safe rate. (A) Find a linear model for the minimum heart rate m that a person of age x years should maintain while exercising. (B) Find a linear model for the maximum heart rate M that a person of age x years should maintain while exercising. (C) What range of heartbeats should you maintain while exercising if you are 20 years old? (D) What range of heartbeats should you maintain while exercising if you are 50 years old?Linear depreciation. A bulldozer was purchased by a construction company for $224,000 and has a depreciated value of 100,000 after 8 years. If the value is depreciated linearly from 224,000 to $100,000, (A) Find the linear equation that relates value V (in dollars) to time t (in years). (B) What would be the depreciated value after 12 years?Business Pricing. A sporting goods store sells tennis rackets that cost $130 for 208 and court shoes that cost 50 for $80. (A) If the markup policy of the store for items that cost over $10 is linear and is reflected in the pricing of these two items, write an equation that expresses retail price R in terms of cost C. (B) What would be the retail price of a pair of in-line skates that cost $120? (C) What would be the cost of a pair of cross-country skis that had a retail price of $176? (D) What is the slope of the graph of the equation found in part (A)? Interpret the slope relative to the problem.Income. A salesperson receives a base salary of $400 per week and a commission of 10 on all sales over $6,000 during the week. Find the weekly earnings for weekly sales of $4,000 and for weekly sales of $10,000.Price demand. The weekly demand for mouthwash in a chain of drug stores is 1,160 bottles at a price of $3.79 each. If the price is lowered to $3.59, the weekly demand increases to 1,320 bottles. Assuming that the relationship between the weekly demand x and price per bottle p is linear, express p in terms of x. How many bottles would the stores sell each week if the price were lowered to $3.29?Freezing temperature. Methanol, also known as wood alcohol, can be used as a fuel for suitably equipped vehicles. Table 1 lists the freezing temperature for various concentrations (as a percentage of total weight) of methanol in water. A linear regression model for the data in Table 1 is T=402M where M is the percentage of methanol in the solution and T is the temperature at which the solution freezes. (A) Draw a scatter plot of the data and a graph of the model on the same axes. (B) Use the model to estimate the freezing temperature to the nearest degree of a solution that is 35 methanol. (C) Use the model to estimate the percentage of methanol in a solution that freezes at -50F.High school dropout rates. Table 2 gives U.S. high school dropout rates as percentages for selected years since 1990. A linear regression model for the data is r=0.308t+13.9 where t represents years since 1990 and r is the dropout rate. (A) Interpret the slope of the model. (B) Draw a scatter plot of the data and the model in the same coordinate system. (C) Use the model to predict the first year for which the dropout rate is less than 3.Consumer Price Index. The U.S. Consumer Price Index (CPI) in recent years is given in Table 3. A scatter plot of the data and linear regression line are shown in the figure, where x represents years since 1990. (A) Interpret the slope of the model. (B) Predict the CPI in 2024.Forestry. The figure contains a scatter plot of 20 data points for white pine trees and the linear regression model for this data. (A) Interpret the slope of the model. (B) What is the effect of a 1-in. increase in Dbh? (C) Estimate the height of a white pine tree with a Dbh of 25 in. Round your answer to the nearest foot. (D) Estimate the Dbh of a white pine tree that is 15 ft tall. Round your answer to the nearest inch.To graph the equation y=x3+3x, we use point-by-point plotting to obtain the graph in Figure. (A) Do you think this is the correct graph of the equation? Why or why not? (B) Add points on the graph for x=2,1.5,0.5,0.5,1.5,and2 (C) Now, what do you think the graph looks like? Sketch your version of the graph, adding more points as necessary. (D) Graph this equation on a graphing calculator and compare it with your graph from part (C).2ED Sketch the graph of each equation. (A) y=x24 (B) y2=100x2+1 Determine which of the following equations specify functions with independent variable x. Ay2x4=9, x is a real number. B3y2x=3, x is a real number.Find the domain of the function specified by the equation y=x2, assuming x is the independent variable.

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