Write an equation relating the variables in each of the following situations.a. The pay P for t hours at $17 an hour.b. The total pay P for a day of t working hours on which you charge a base rate of$26 and $19 for each hour worked.c. The total pay P for t hours at $20 for the first hour and $14 for each additional hour.

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Answered: Write an equation relating the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Set up and solve an equation for the following business situation. Suppose one-ninth of a certain company's sales are made in New England. If New England sales amount to $800,000, what are the total sales (in dollars) of the company?
In a certain city, the cost of a taxi ride is.computed as follows. There is a fixed charge of $2.75 as soon as you get in the taxi, to which a charge of $2.30 per mile is added. Find an equation that can be used to determine the cost, C, of an x-mile taxi ride. OA. C=5.05x OB. C 2.75 +2.30x OC. C=2.30 +2.75x OD. C=3.55x
In Phoenix, rental of a U-Haul 24-foot moving truck for 6 hours costs $39.95 plus $0.56 per mile. The same truck from Budget costs $69.95 plus $0.54 per mile.(a) State the equation found by setting the costs equal. (Let x represent the number of miles driven. Do not simplify the equation.)
if the profit from the sale of x units of a product is p=900x-200-x2 what level of production yeilds a profit of $1200
A company manufactures notebook computers. Its marketing research department, using statistical techniques, collected the data shown in the table, where p is the wholesale price per computer at which x thousand computers can be sold. Using special analytical techniques (regression analysis), an analyst produced the price-demand function p(x) = 2,400 - 40x, 1 ≤ x ≤ 25 to model the data. Complete parts (A) and (B) below. x(thousands) 1 3 19 24 25 p($) 2360 2280 1640 1440 1400
2. The local community hall is hired out at a rate of $20 per hour plus a fee of $60 for cleaning. (a) Write a formula relating total cost of hiring the hall to the number of hours required. Be sure to carefully define all variables that you use. (b) Complete the following table of values for the costs to hire the hall for the hours given Hours Required 1 2 3 4 Cost of Hall ($) (c) Plot the values from the table on a graph and draw a trend line. (d) Use your graph to determine the cost of hiring the hall for 4.5 hours. (e) If your group has only budgeted for a total of $130 for how long could they hire the hall?
There is a 20% discounted price of $48 and calculate the original price by setting up an algebraic equation as the original value "V".
A firm produces headphones in two qualities, Basic (B) and Premium (P). For the coming year, the estimated quantity produced of B is 60% higher than that of P. The firm makes a markup of 170% on both products. The ratio between the profits per unit between P and B is 2. The cost price for P is $260. If the profit target is $115 362 over the next year, how much of each of the two qualities must be produced and what are the two selling prices? (Round the quantities to the nearest unit and the prices to 2 digits after the decimal point if needed) Quantity of B = Answer units Quantity of P = Answer units Selling price of B = Answer $ Selling price of P = Answer $
In a given year, the U.S. federal income tax owed by a married couple filing jointly can be found from the following table. Married Filing Jointly Taxable Income $0-$18,550 T(x) = $18,551-$75,300 $75,301-$151,900 amount over $75,300 $413,351-$466,950 Tax Rate 10% $1,855 plus 15% of the amount over $18,550 $10,367.50 plus 25% of the $151,901-$231,450 amount over $151,900 $466,951 or more if $29,517.50 plus 28% of the $231,451-$413,350 amount over $231,450 $51,791.50 plus 33% of the $130,578.50 plus 39.6% of the amount over $466,950 (a) For incomes up to $151,900, write the piecewise defined function T with input x that models the federal tax dollars due as a function of x, the taxable income dollars earned. $111,818.50 plus 35% of the amount over $413,350 0 < x≤ 18,550 if 18,550 < x≤ 75,300 if 75,300 < x≤ 151,900 (b) Use the function to find T(40,000). $ (c) Find the tax due on a taxable inco of $90,000. $ (d) A friend tells Jack Waddell not to earn any money over $75,300 because it…
5. Assume food prices have risen about 4% per year for the last five years. a. If a gallon of milk cost $2 five years ago, what does it cost today? b. If a gallon of milk cost Sx five years ago, write an expression for its cost today. c. If a gallon of milk costs $3.50 now, what did it cost five years ago? Write and solve an equation to answer the question. Let x cost of a gallon of milk five years ago d. Ifmilk prices increase 4% per year for five years, what is the overall percent ncrease
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