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If you work more than 40 hours during a week, then you are paid 1.5 times the normal hourly pay rate for those hours worked in excess of 40 hours. Write a formula that can be used to determine your gross pay earnings for work in excess of 40 hours. What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 3. On a certain golf course, the traditional play is to take two strokes to go around a small lake. Each stroke requires a drive of about 250 yards, as shown below. You wonder how strong a drive would be needed to make it across the lake in one stroke. Determine how far a single stroke would have to go to cross the lake. What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 5. Use the formula and insurance plan given below to find the total hospital bill if your share is $1500. E = [(T - D ) x (1.00 - P )] + D where E is the expense to you (how much you must pay), T is the total of the hospitalization bill, D is the deductible that you must first pay, and P is the decimal percentage that the insurance company pays after you meet the deductible. What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 7. When determining the usable log volume, deductions are made for slab, edgings, and saw kerf. To estimate the number of board feet that can be obtained from a log, the following formula may be used. V = 0.0655L (1-A) (D-S)2 where V is the usable volume of a log in board feet, L is the length of the log in feet, A is the decimal percent deduction for saw kerf, D is the log diameter in inches, and S is the slab and edging deduction in inches. Use the formula to estimate the usable volume of a 32-foot log having a diameter of 30 inches, allowing for 10% saw kerf and 3 inches of slab and edging deductions. What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 9. A commercial cherry grower estimates that when 30 trees are planted per acre, each tree can produce about 50 pounds of cherries per season. For each additional tree planted (per acre), the yield per tree is reduced by 1 pound. a. Make a table of the yield per tree for several different planting densities: 30 per acre, 31 per acre, 32 per acre, and so on, up to 35 per acre. b. Add a column to your table that shows how many pounds of cherries would be produced per acre for each of the densities. c. Someone proposes that this data can be described by the formula Y = 50 - (D-30) where Y is the yield per tree in pounds, and D is the density of the planting in trees per acre. Does this formula agree with the data in your table? d. How can the formula above be modified to describe the pounds of cherries produced per acre? Write out this modified formula, and compare it to the values in your table. 11. Suppose that you receive a 5% commission on the sale of a condominium for a customer. The customer would like to obtain at least $60,000 from the sale. Use the formula below to determine the lowest selling price for the condominium that will allow the customer to receive the amount asked for. (Round your answer to the nearest $100.) A = (100% - c) of s where A is the amount desired by the customer from the sale, c is the commission that you will get from the sale, and s is the selling price. What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 13. You are considering an investment in certificates of deposit. The formula shown below is used to determine the future value (FV ) of such a deposit earning compound interest. FV = PV (1+i )n where FV is the future value of the investment, PV is the present value of the investment, or the starting value, i is the decimal interest rate, for example 0.12 per year, and n is the number of periods over which the interest is compounded, for example 5 years. Note: The units of time for i and n must agree, for example a yearly percentage rate for i and years for n. a. A long-term certificate requires a deposit of $5000 for 5 years. Each year the deposit earns 8.5% interest. Use the formula to determine the future value of the deposit at the end of the five-year term. b. A short-term certificate requires a deposit of $1000 for 6 months. The deposit earns interest at an annual rate of 7%, or a monthly rate of 7%/12. Use the formula to determine the future value of the deposit at the end of the six- month term. 15. Series EE Savings Bonds can be purchased for one-half their face value. If they are held until maturity, they can then be redeemed for their full face value, plus a bonus. If you work as a securities teller you may have to explain to a customer how to compute the interest obtained on these bonds. The difference between the redemption value and the purchase price is the interest earned. a. Write a formula that shows how to compute the purchase price of a Series EE Savings Bond, knowing only its face value. b. Write a formula that shows how to compute the interest earned on a Series EE Savings Bond held until maturity, knowing only the purchase price and the redemption price. c. Determine the purchase price and interest for a $1000 Series EE bond that is redeemed for $1065.20 at maturity. 17. It costs a record company $9000 to prepare a record album for production. This represents the one-time fixed cost. Manufacturing, marketing, royalty payments, and so on, are variable costs. Suppose the variable costs total to $4.50 per album. The records are sold to the record shops for $6.75 each. You need to determine how many records must be sold for the income from record sales to equal the total costs. (This is the break-even point for the record company.) a. Write an equation for the income (I ), based on the number of records sold (N ). b. Write an equation for the total costs (C ), based on the number of records produced (N ). c. Set the expression for I equal to the expression for C , and isolate the variable N to find out what value of N is needed to make I equal to C . What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 19. As a financial counselor, you help people develop a balanced budget. You mainly concern yourself with variable expense money, that is, the amount left over from a clients income after fixed expenses are paid. You use the formula shown below to allocate the variable expense to various areas. T x A = R xV where T is the total percent budgeted for variable expenses, A is the amount budgeted for a certain area, R is the percent budgeted for a certain area, and V is the total amount of variable expense money available. a. Write a formula for computing a clients variable expense money, knowing the total income and the amount of fixed expenses. b. Suppose the Boxer family income each month is $1450. They have fixed expenses of $890. You advise them to budget 12% for savings, 10% for clothing, and 7% for miscellaneous expenses. Determine the total percent (T ) youve recommended in your budget for variable expenses. Use your formula from Part a and the formula given above to determine the amount of the Boxer income that should be set aside each month for savings (rounded to the nearest $10). What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 21. You are performing some laboratory tests on blood samples. You need to find the amount of oxygen in the hemoglobin of the red blood cells. A blood test tells you that a 100-milliliter sample contains 12 grams of hemoglobin, and the hemoglobin is 91% oxygen. Use the formula shown below to determine how much oxygen is in the hemoglobin of this sample. (Round your answer to 2 decimal places.) H = 1.36 g s where H is the milliliters of oxygen in the hemoglobin from 100 ml of whole blood, g is the number of grams of hemoglobin in 100 ml of whole blood, and s is the decimal value of oxygen in the hemoglobin. What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 23. In a hospital, the doctor frequently orders a volume V (in ccs), of IV (intravenous) fluid to be given over a specified period of hours, T. The nurse must convert the rate from cc per hour to drops per min using a conversion ratio of 15 drops per cc of fluid. A formula that can be used to tell a nurse how many drops per minute to set the IV is shown below. D = V 4T where D is the number of drops per minute, V is the volume of fluid ordered by the doctor, and T is the total time over which the fluid is to be given. Suppose the doctor orders 1000 cc of D5W to be given to a patient over an 8- hour time span. How many drops per minute should the IV supply to the patient? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 25. A persons vital capacity is the amount of air that can be exhaled after one deep breath. An estimate of the vital capacity for women can be obtained by the formula below. V = 0.041h - 0.018A - 2.69 where V is the vital capacity in liters, h is the persons height in centimeters, and A is the persons age in years. a. Determine an estimated vital capacity for yourself using your height and age. Does this formula apply to you? b. Suppose that by using a spirometer, the lung capacity of a healthy elderly woman is measured at 3.4 liters. The woman is 56 tall. Isolate the variable A in the formula above, and use the given data to find a value for A and complete the sentence that follows: This elderly woman exhibited the breathing capacity of a -year old woman. What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 27. You are designing some rod-pocket curtains with a heading above the pocket. When determining the fabric requirements you must allow for the top and lower hems. A magazine article offers the following formula as a guideline for the top hem, where the pocket for the curtain rod and the heading are created, as shown. Top hem = Circumference of rod + 1 1/2 inches + 2 times the desired width of the heading. a. Rewrite the formula for the top hem, using variables of your choice. Include a description of your variables and the required units. b. Determine the amount of fabric needed for the top hem of such a curtain to be hung with a 1/2-inch-diameter curtain rod and with a 4-inch-width heading. 29. Cosmetologists are frequently paid by the salary and commission method. One way this can work is that the cosmetologist is paid a base salary agreed upon with the employer. Then the employee receives a percentage of any money received from services performed that exceeds an amount equal to twice this base salary. This can be stated more plainly by the formula shown below. G = S + C (I - 2S) where G is the gross pay (in dollars) for the period if I is greater than twice the salary amount, S is the salary amount for the period, C is the commission percentage rate (a decimal percent), and I is the gross income for services performed. a. Suppose your weekly salary is $260, with a 15% commission on all sales over twice your salary. Use the formula to determine your gross pay, if the gross income for your services totaled $685 during this week. b. Using the above salary and commission arrangements, you would like to know how much income for services would be needed to be able to have a gross pay of $300. Isolate the variable I in the formula above and use it to determine what value of I is needed if G = 300. 31. Greenshields formula can be used to determine the amount of time that a traffic light at an intersection should remain green. This formula is shown below. G = 2.1n + 3.7 where G is the green time in seconds, and n is the average number of vehicles traveling in each lane per light cycle. Find the green time for a traffic signal on a street that averages 19 vehicles in each lane per cycle.  What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 33. A simplified method to estimate the size of air conditioning needed for a room is to use theWHILE formula, along with certain rules. The formula is BTU = WHILE 60 where BTU is the number of Btu (British thermal units) per hour of cooling power needed for the room, W is the width of the room in feet, H is the height of the room in feet, I is the insulation factor, defined by the rule shown below, L is the length of the room in feet, and E is the exposure factor, defined by the rule shown below. The insulation rule determines I = 10 for well-insulated rooms, and I = 18 for uninsulated or poorly insulated rooms. The exposure rule is determined by the direction that the longest wall faces: if it faces north, E = 16; if east, E = 17; if south, E = 18; if west, E = 20. If two or more walls are equally the longest, use the largest possible value for E. Suppose a newly constructed room is to be air conditioned. It is 18 feet wide, 24 feet long, and 9 feet high. The room is well-insulated, and one 24-foot wall faces south and one faces north. What size air conditioner does the formula predict is needed to cool this room? (Round your answer to the nearest 1000 Btu.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 35. You are constructing a small shed and want to consider different roof slopes. Your desired floor plan is for a 24-foot span, and you would like to use 16-foot rafters that have a 1-foot overhang, as shown below. What is the maximum rise that can be obtained under these circumstances? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 37. In close-up photography, the distance of the object from the lens controls how far the lens must be from the film. This requires special lenses and focusing mechanisms. These distances (all measured in the same units) are controlled by the formula 1 = 1 + 1 f p q where f is the focal length of the lens, p is the distance of the object being viewed from the center of the lens, and q is the distance of the image formed on the film from the center of the lens. You have a 50-mm close-up lens. With this lens, the maximum distance that you can position the lens from the film plate is 4.2 cm. You need to find the closest that you can position an object to the lens to get a sharp photograph. a. Rewrite the formula, isolating the variable representing the object distance. b. Determine the object distance predicted by the equation for a lens with a focal length of 50 mm and a maximum image distance of 6.2 cm. What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 39. You need to custom-make a wire-wound resistor with a resistance of 15 ohms using 22-gauge copper wire. From a table you find that 22-gauge copper wire has a resistance of 0.0135 ohm per centimeter. Thus you can determine the resistance of a wire by multipl ying the length of the wire by the number of ohms per centimeter. a. Write a formula that you can use to determine the resistance of any length of 22-gauge wire. Be sure to define your variables and their units. b. Use your formula to determine the resistance of 75 feet of 22-gauge copper wire. c. Rewrite your formula, isolating the length of wire variable. Use this formula to determine what length of 22-gauge copper wire you need to create the 15- ohm wire-wound resistor. What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). 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