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linear algebra

Questions and Answers of Linear Algebra

The Gidget Widget Corporation produces widgets. The fixed expenses are $65,210, and the variable expenses are $4.22 per widget. Express the expense function algebraically.
A corporation produces mini-widgets. The variable expenses are $1.24 per mini-widget, and the fixed expenses are $142,900. a. How much does it cost to produce 1 mini-widget? b. How much does it cost
The expense function for the Wonder Widget is E = 4.14q + 55,789.a. What is the fixed cost in the expense function? b. What is the cost of producing 500 Wonder Widgets? c. What is the average cost
The fixed costs of producing a Wild Widget are $34,000. The variable costs are $5.00 per widget. What is the average cost per widget of producing 7,000 Wild Widgets? Round to the nearest cent.
Wanda's Widgets used market surveys and linear regression to develop a demand function based on the wholesale price. The demand function is q = -140p + 9,000. The expense function is E = 2.00q +
Wind Up Corporation manufactures widgets. The monthly expense equation is E = 3.20q + 56,000. They plan to sell the widgets to retailers at a wholesale price of $6.00 each. How many widgets must be
The Lerneg Corporation computed its monthly expense equation as E = 11.00q + 76,000. Its products will be sold to retailers at a whole-sale price of $20.00 each. How many items must be sold to reach
Rich and Betsy Cuik started a small business. They manufacture a microwavable coffee-to-go cup called Cuik Cuppa Coffee. It contains spring water and ground coffee beans in a tea-bag-like pouch. Each
Orange-U-Happy is an orange-scented cleaning product that is manufactured in disposable cloth pads. Each box of 100 pads costs $5 to manufacture. The fixed costs for Orange-U-Happy are $40,000. The
How might the quote apply to what you have learned?
An electronics store is selling car chargers for cell phones. The expense function is E = -300p + 13,000 and the revenue function is R = -32p2 + 1,200p. a. At what price would the maximum revenue be
At what price is the maximum profit reached?
A supplier of school kits has determined that the combined fixed and variable expenses to market and sell G kits is W. a. What expression models the price of a school kit at the breakeven point? b.
A jewelry manufacturer has determined the expense equation for necklaces to be E = 1,250q + 800,000, where q is the quantity demanded. At a particular price, the breakeven revenue is $2,600,000. a.
A manufacturer determines that a product will reach the breakeven point if sold at either $80 or $150. At $80, the expense and revenue values are both $300,000. At $150, the expense and revenue
iSports is considering producing a line of baseball caps with wire-less cellphone earpieces attached. The breakeven point occurs when the price of a cap is $170 or $350. At $170, the expense and
SeaShade produces beach umbrellas. The expense function is E = -19,000p + 6,300,000 and the revenue function is R = -1,000p2 + 155,000p. a. Graph the expense and revenue functions. Label the maximum
Where-R-U produces global positioning systems (GPS) that can be used in a car. The expense equation is E = -5,000p + $8,300,000, and the revenue equation is R = -100p2 + 55,500p. a. Graph the
The student government at State College is selling inexpensive bookcases for dorm rooms to raise money for school activities. The expense function is E = -200p + 10,000 and the revenue function is R
How might the quote apply to what has been outlined in this lesson?
The expense and revenue functions yield a profit function, but the equation can represent no profit made for any price. One of the profit functions in Exercises 6-9 models such a situation. a.
Determine the maximum profit and the price that would yield the maximum profit for each. a. P = -400p2 + 12,400p - 50,000 b. P = -370p2 + 8,800p - 25,000 c. P = -170p2 + 88,800p - 55,000
Greenyard's manufactures and sells yard furniture made out of recycled materials. It is considering making a lawn chair from recycled aluminum and fabric products. The expense and revenue functions
Mountaineer Products Incorporated manufactures mountain-bike accessories. It is considering making a new type of reflector for night biking. The expense and revenue functions are E = -450p + 90,000
Business Bargains manufactures office supplies. It is considering selling sticky-notes in the shape of the state in which they will be sold. The expense and revenue functions are E = -250p + 50,000
FlipFlops manufactures beach sandals. Their expense and revenue functions are E = -300p + 32,000 and R = -275p2 + 6,500p. a. Determine the profit function. b. Determine the price, to the nearest
Examine each of the graphs in Exercises 1-4. In each case, the blue graph represents the expense function and the black graph represents the revenue function. Describe the profit situation in terms
In Exercises 1-4, write the profit function for the given expense and revenue functions. 1. E = -20,000p + 90,000 R = -2,170p2 + 87,000p 2. E = -6,500p + 300,000 R = -720p2 + 19,000p 3. E = -2,500p +
How might those words apply to what has been outlined in this lesson?
Use the transitive property of dependence to express expense, E, in terms of p. Round to the nearest hundredth. A company produces a security device known as Toejack. Toejack is a computer chip that
Graph the expense and revenue functions. a. Determine an appropriate maximum horizontal-axis value. b. Determine an appropriate maximum vertical-axis value. c. Sketch the graphs of the expense and
Determine the coordinates of the maximum point on the revenue graph. Round the coordinates to the nearest hundredth.A company produces a security device known as Toejack. Toejack is a computer chip
Express the profit, P, in terms of p. A company produces a security device known as Toejack. Toejack is a computer chip that parents attach between the toes of a child, so parents can track the
Graph the profit function. Determine the coordinates of the maxi- mum point of the profit graph. At what price, p, is profit maximized? Round to the nearest cent. This will be the price at which
Write the business summary statement by filling in the blanks.In summary, to start this business, __a.__ Toejacks should be manufactured. Each should be sold at $__b.__. The breakeven point is
Use the following graph to answer the questions below. Let Y1 = cost function and Y2 = revenue function.a. Explain the significance of point (D, B). b. Explain the significance of point (E, A). c.
If shares of stock are sold with an initial value of $5 each, how many shares must be sold to get enough money to start the business? A company produces a security device known as Toejack. Toejack is
Draw a graph of cost function Y1 and revenue function Y2 that meet the following criteria. Maximum revenue: $125,000 Breakeven points: $40 and $160 Price at which no revenue is made: $200 Maximum
The company decides to conduct a market research survey to deter- mine the best price for the device. The variable p represents price, and q represents quantity demanded. The points are listed as (p,
Find the regression equation. Remember the quantity demanded, q, is the dependent variable. Round the slope and y-intercept to the nearest hundredth. A company produces a security device known as
Examine each scatterplot. Identify each as showing a positive correlation, a negative correlation, or no correlation.a.b. c.
The market research department conducted consumer surveys at college campuses and reported its results. In these ordered pairs, the first number represents price, p, and the second number represents
What is the correlation coefficient? Round it to the nearest hundredth. Is this line a good predictor? Explain. A company is interested in producing and selling a new device called an eyePOD (eyewear
Write the regression equation. Remember that the demanded quantity, q, is the dependent variable. Round the slope and y-intercept to the nearest hundredth.
Recall the transitive property of dependence. Express expenses, E, in terms of p. Round to the nearest hundredth. A company is interested in producing and selling a new device called an eyePOD
Graph the expense and revenue functions. a. Determine an appropriate maximum horizontal-axis value. b. Determine an appropriate maximum vertical-axis value. c. Sketch the graphs of the expense and
If each set of bivariate data has a causal relationship, determine the explanatory and response variables for each set of data. a. Number of hours spent reading and page number on which you are
Determine the coordinates of the maximum point on the revenue graph. Round to the nearest hundredth.A company is interested in producing and selling a new device called an eyePOD (eyewear personal
Express the profit, P, in terms of p. A company is interested in producing and selling a new device called an eyePOD (eyewear personal optical device). The eyePOD is an MP3 and video player built
Graph the profit function. Determine the coordinates of the maxi- mum point of the profit graph. At what price, p, is profit maximized? Round to the nearest cent. This will be the price at which one
Write the business summary statement by filling in the blanks.In summary, to start this business, __a.__ eyePODS should be manufactured. Each should be sold at $__b.__. The breakeven point is reached
If shares of stock are sold with an initial value of $10 each, how many shares must be sold to get enough money to start the business? A company is interested in producing and selling a new device
Describe each of the following correlation coefficients using the terms strong, moderate, or weak and positive or negative. a. r = 0.17 b. r = - 0.62c. r = - 0.88 d. r = 0.33 e. r = 0.49 f. r = -
The graph shows supply and demand curves for the newest game controller for the VVV video game system.a. What is the equilibrium price?b. What will happen if the price is set at $7.99?c. How many
The demand function for a certain product is q = -300p + 10,000. The fixed expenses are $500,000 and the variable expenses are $2 per item produced. a. Express the expense function in terms of q.b.
Let the expense function for a particular item be defined as y = -1,950x + 53,000. Let the revenue function be defined as y = -450x2 + 10,000x, where x represents price in each equation. Use this
Express the revenue equation in terms of price given the demand function. a. q = - 900p + 120,000 b. q = - 88,000p + 234,000,000
The expense function for a widget is E = -3,000p + 250,000. The revenue function is R = -600p2 +25,000p. a. Write the profit equation in simplified form. b. Use the axis of symmetry formula to
Olivia cashed a check for $113. The teller gave her four twenty-dollar bills, x ten-dollar bills, and three one-dollar bills. Find the value of x.
Hector had y dollars in his savings account. He made a deposit of twenty-dollar bills and dollar coins. He had four times as many dollar coins as he had twenty-dollar bills and the total of his
On September 1, Chris Eugene made the following band equipment purchases at Leslie's Music Store. Calculate her total bill. Complete a check for the correct amount. Print a copy of the check from
Create a check register for the transactions listed. There is a $2.25 fee for each ATM use. a. Your balance on 10/29 is $237.47 b. You write check 115 on 10/29 for $18.00 to Fox High School.c. You
Ridgewood Savings Bank charges a $27 per check overdraft protection fee. On July 8, Nancy had $1,400 in her account. Over the next four days, the following checks arrived for payment at her bank:
Create a check register for the transactions listed. Download a blank check register from www.cengage.com/school/math/financialalgebra.a. Your balance on 12/15 is $2,546.50. b. On 12/16, you write
Download a copy of the check register shown below from www.cengage.com/school/math/financialalgebra.Complete items a through y.
John cashed a check for $630. The teller gave him three fifty-dollar bills, eighteen twenty-dollar bills, and t ten-dollar bills. Determine the value of t.
Anna has a checking account at Garden City Bank. Her balance at the beginning of February was $5,195.65. During the month, she made deposits totaling $6,873.22, wrote checks totaling c dollars, was
Neka cashed a check for $245. The teller gave him two fifty-dollar bills, six twenty-dollar bills and f five-dollar bills. Determine the value of f.
How might the quote apply to this lesson?
Use Allison Shannon's bank statement and check register to reconcile her account.
Fill in the missing balances in Raymond Marshall's check register. Use the spreadsheet from www.cengage.com/school/math/financial algebra to determine if Raymond's checking account reconciles with
Alisha has a February starting balance of $678.98 in her checking account. During the month, she made deposits that totaled d dollars and wrote checks that totaled c dollars. Let E = her ending
Hannah wants to write a general formula and a comparison statement that she can use each month when she reconciles her checking account. Use the Checking Account Summary at the right to write a
Jill has not been able to maintain the $1,000 minimum balance required to avoid fees on her checking account. She wants to switch to a different account with a fee of $0.20 per check and a $12.50
Use Tina Weaver's monthly statement and check register to reconcile her account.a. What is the ending balance on the statement?b. What is the total of the outstanding deposits?c. What is the total of
When Payne removed his bank statement from the envelope, it got caught on a staple and a corner was ripped from the page. Now he cannot read his ending balance. Explain the computations he can do to
How might those words apply to what has been outlined in this lesson? What "play on words" do you notice in Greenspan's quote?
Assume $20,000 is deposited into a savings account. Bedford Bank offers an annual rate of 4% simple interest for five years. Slick Bank offers a rate of 20% simple interest for one year. Which earns
Zoe creates a spreadsheet to make simple interest calculations. The user inputs values for the principal, rate, and time in years in row 2. Write each formula.a. For A2 to compute the interest.b. For
Arrange the following interest rates in ascending order: 3.4%, 3.039%, 3 3/16%, 3.499%, 3 1/2%
Josh has a savings account at a bank that charges a $10 fee for every month his balance falls below $1,000. His account has a balance of $1,203.44 and he withdraws $300. What will his balance be in
Linda's savings account has fallen below the $1,000 minimum balance required to receive interest. It is currently $871.43. The monthly fee charged by the bank for falling below the minimum is x
John, Paul, and George are having a disagreement over interest rates. John says that 6 3/4% can be expressed as 6.75%. George thinks that 6 3/4% can be expressed as 0.0675. Paul remembers converting
Ryan deposits $775 in an account that pays 4.24% simple interest for four years. Brian deposits $775 in an account that pays 4.24% simple interest for one year. a. What is Ryan's interest after the
Use the simple interest formula to find the missing entries in the table. Round monetary amounts to the nearest cent.
How might those words apply to what you learned in this lesson?
Jacob opens a savings account in a non-leap year on August 10 with a $4,550 deposit. The account pays 4% interest, compounded daily. On August 11 he deposits $300, and on August 12 he withdraws $900.
On December 18 of a leap year, Stacy opened a savings account by depositing $6,000. The account pays 3.45% interest, compounded daily. On December 19 she deposited $500, and on December 20 she
On May 29, Rocky had an opening balance of x dollars in an account that pays 3% interest, compounded daily. He deposits y dollars.Express his ending balance on May 30 algebraically.
The table represents the compound interest calculations for an account that pays 2% interest compounded daily. Represent a-g algebraically.
One day before the end of the month, George had an opening balance of m dollars in an account that pays 2.25% interest com- pounded monthly. On the last day of the month, he made a deposit equal to
Regina deposits $3,500 in a savings account that pays 7 1/2% interest compounded semiannually.a. How much interest does the account earn in the first six months?b. What is the balance at the end of
Liam deposits $3,500 in a saving account that pays 7 1/2% interest, compounded quarterly.a. Find the first quarter's interest. b. Find the first quarter's ending balance. c. Find the second quarter's
Mike and Julie receive $20,000 in gifts from friends and relatives for their wedding. They deposit the money into an account that pays 4.75% interest, compounded daily. a. Will their money double in
Lindsay invests $80 in an account that pays 5% annual interest, compounded monthly. Michele invests $60 in an account that pays 8% annual interest, compounded weekly. a. Whose balance is greater
Investigate the difference between compounding annually and simple interest for parts a-j. a. Find the simple interest for a one-year CD for $5,000 at a 6% interest rate. b. Find the interest for a
Rodney invests a sum of money, P, into an account that earns interest at a rate of r, compounded yearly. Gerald invests half that amount into an account that pays twice Rodney's interest rate. Which
Businesses deposit large sums of money into bank accounts. Imagine an account with 10 million dollars in it. a. How much would the account earn in one year of simple interest at a rate of 5.12%? b.
An elite private college receives large donations from successful alumni. The account that holds these donations has $955,000,000 currently. a. How much would the account earn in one year of simple
Joanne deposits $4,300 into a one-year CD at a rate of 4.3%, compounded daily. a. What is her ending balance after the year? b. How much interest does she earn?c. What is her annual percentage yield

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