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The altitude of Owens Telescope Peak in southern California is 11,045 feet above sea level. Just a few miles away, the floor of Death Valley is 282 feet below sea level. a. Express the altitude of each of these locations as a signed number with regard to sea level. b. How many feet of altitude would a helicopter pilot have to climb to rise from the floor of Death Valley to the top of Owens Telescope Peak? What are you looking for? What do you need to answer the question? Estimate what your answer(s) might be (think of both numbers and terms to be used): 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. An experimental process is being tested and compared to the results predicted by many months of computer research. Below is a table of the predicted values and actual values for several trials of this process. Test results for secret process XYZ Predicted Actual Trial A 1.103 1.007 Trial B 4.198 4.225 Trial C 14.611 14.803 Trial D 8.014 7.891 a. To evaluate the results of the test, you must compare the actual values to the predicted. Using the above table, add a column to show the difference Actual - Predicted. Show the proper sign for each difference. b. You need to report the average difference for the test. Add the differences and divide by the number of trials. Whats happening here? c. As another approach, determine the absolute values of the differences, and compute the average of these values. How does this result differ from the approach taken in Part b? 5. A small airplane flies cross-country under various wind conditions. During all the conditions, the plane maintains an air speed of 115 miles per hour and a compass heading due east. For each of the conditions below, draw a sketch of the vectors representing the planes air velocity (speed and direction), the wind velocity (speed and direction), and the actual ground velocity (speed and direction). a. Wind from the east with a speed of 25 mph. b. Wind from the west with a speed of 20 mph. c. Wind from the south with a speed of 30 mph. 7. A business firm acquires ownership of a second building across the street. Most of the prime office space is located on the second floor of each building. A raised walkway is proposed to reduce the walking time needed to travel from one office area to the other. An overhead view of the proposed raised walkway and current route is shown below. Place overhead view, page 38, here. a. The current route involves many detours through hallways and doorways. List the vectors that describe the paths taken along the current route. Assume that the distance from one dash to the next represents 10 feet. (Dont forget the elevator rides between the second and first floors!) b. Does the sum of these vectors equal the vector representing the travel that will be required along the proposed walkway? If not, why? c. Can you draw all the vectors on your paper? Explain your answer. d. If the current route requires 10 minutes (assume the two elevator trips last 2 minutes combined), about how long would you estimate the trip across the walkway might take? 9. When an airplane crew parachutes a load of supplies to the ground, it must account for wind velocity for an accurate drop. Suppose the parachuting package falls (vertically) at a speed of 25 feet per second. But on a certain day, the wind is blowing out of the north at 15 feet per second (approximately 10 mph). a. Identify the two vectors described above. b. On your paper, make a scale drawing of the addition of the two vectors. Determine the sum of the two vectors, that is, the actual velocity of the parachuting package. What is the magnitude and direction of this velocity? (Hint: Use your protractor to find the direction.) 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): 11. When you apply insecticide with a granular applicator, it is a good idea to calibrate your applicator. If the application rate is higher or lower than the recommended amount, an adjustment is in order. A common method of testing is to hang small bags to collect the output with a set distance and speed. On one particular day, you collect, adjust, and recollect samples, as shown below. According to your calculations, each sample should have 9 oz. Calibration samples Trial Sample amount 1 7oz 2 12 oz 3 10 oz 4 9 oz Make a table similar to that shown above. For each sample, compute the difference between the actual amount and target amount of 9 ounces. Record your values as signed numbers. Which trial was farthest away from the target application rate? 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). Yours answer(s) are (make sure the units used are correct): 13. A newspaper reported how various investments performed since the beginning of the year in a table, as shown below. Place table, page 41, here. Which investments values have increased? Which haveL decreased? How can you use the Percent change data to quickly answer this question? 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). Yours answer(s) are (make sure the units used are correct): 15. The total cost of merchandise sold in a clothing store can be computed by adding together the following amounts, with the appropriate sign: Total cost of merchandise = Cost of beginning inventory + billed cost of net purch\ases + inbound transportation + cost of net transfers in - cost of ending inventory - cash discounts + Workroom and alteration costs A certain sportswear store showed the following figures for a six-month period: beginning inventory, $13,651; billed cost of net purchases, $87,055; transportation charges $4,879; cash discounts earned on purchases, $7,510; ending inventory at cost, $12,402; workroom costs, $748. Compute the total cost of the merchandise sold. 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): 17. During the week, the warehouse for Comfy Footwear posted several adjustments to the inventory, as shown below. Place chart, page 43, here. a. What is the total of the adjustments made for this week? b. If the inventory at the beginning of the week was 18,384 units, and a total of 720 units were shipped out, what should be the inventory at the end of this week, allowing for the adjustments? 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. The EZ-Duzzit Company budgeted a total of $5580 for Project Number 2468, to be completed over a span of six months. The management projected that the money would be equally spent during each of the six months. During the first four months, the following total amounts for each month were reported spent: March $570, April $1071, May $1247, and June $928. a. What is the budgeted monthly amount for each of the six months of Project Number 2468? b. Make a table of monthly spending. For each month, compare the actual spending to the budgeted amount, and compute the amount over/under budget. c. What is the total amount over/under budget for the first four months of the project? 21. A market research study for River City reported on the median income for various age groups. You decide to compare this report with a similar report done five years ago. You know that during this past five years, wages should have increased about 35% to keep up with inflation. The table that follows shows the results of the two studies. Place table, page 45, here. a. Construct a table with the age groups shown above. For each age group calculate the income necessary to keep pace with the inflation figure of 35% over the five years. Record this projected income in your table. b. Copy the current studys results to your table. Compare the projected incomes with the results of the current study. Add a column to your table showing the difference between the current and the projected incomes. Record each difference as a signed number. c. In your table, does a negative number mean that the income has not kept pace with inflation, or that it has exceeded the value projected by the inflation rate? d. Which age group(s) in River City is within $500 of its projected income? 23. When a patient is recovering from an illness, it is important to monitor the patients fluid intake-output. A fluid imbalance should be remedied as soon as possible. Below is a record of a patients fluids for several 8-hour periods during a hospital stay. Place record, page 47, here. a. A fluid balance is indicated by a difference between the intake and output of nearly zero. On your paper make a table of the differences between the intake and output for each shift shown above. b. What sign on your differences (plus or minus) indicates an imbalance of insufficient output of fluids? c. What is the absolute value of your differences? Would these numbers be useful in spotting a condition of fluid imbalances? H"ave you lost any information if you show only the absolute values of the differences on your chart? If so, what information? 25. Eyeglass prescriptions define the amount of curvature required in a lens to correct a patients poor vision. The amount of curvature is expressed in units of diopters (D). To correct a near-sighted condition requires a negative value of sphere power, while to correct a far-sighted condition requires a positive value. A value close to zero indicates very little correction. Examine the values of sphere power listed below. Place the table, page 49, here. a. Draw a number line on your paper. For each patient above, label the position on your number line representing the amount of correction prescribed. Label the range of corrections applicable to near-sighted persons, and the range for far-sighted persons. b. Which patient requires the most correction for near-sightedness? for far- sightedness? 27. In completing federal tax forms, you encounter instructions for filling out the forms. At one point, for example, you may find the instructions for line 43 read: Subtract line 42 from line 39. Enter the result (but not less than zero). For each set of values for line 42 and line 39 shown below, determine the proper value for line 43. a. Line 39: 12,600 Line 42: 4267 b. Line 39: 2328 Line 42: 2230 c. Line 39: 3125  Line 42: 3419 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): 29. You are a flight attendant who travels worldwide with an international airline. As you fly you experience many changes in local time zones. You have discovered that the local time increases when you travel east (+), and decreases when you travel west (-). The table below shows some of the cities your airline travels to, and the relative local time, compared to the time in London. Place table, page 51, here. a. Suppose you leave London, England, and travel to Helsinki, Finland. Identify the relative hour values for these cities. What is the difference in these values from London to Helsinki (final value minus starting value, indicating how many hours you should adjust your watch)? Should you adjust your watch forward or backward when you arrive in Helsinki? b. The next day you fly from Helsinki to Moscow, and then on to Rome. Again, identify the relative hour values for these cities. What is the total difference in these values, from Helsinki to Rome? Should you adjust your watch forward or backward when you arrive in Rome? c. Soon after this, you leave Rome, flying westward to New York and then on to Denver. Identify the relative hour values for these cities. What is the difference in these values, from Rome to Denver? Should you adjust your watch forward or backward when you arrive in Denver? 31. One of the angles used for front-end alignment of an automobile is the included angle. It is the sum of the steering axis and the camber angle. What is the included angle for a car having a steering axis inclination of 6 1/2o and a camber angle of -1/4o? 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. An automobile manufacturer recommends a caster angle within +1/2o and -1/2o, without exceeding a spread (a difference) of 1/2o between the wheel readings. You measure the caster angles on a customers front wheels and find they are +1/4o on the left wheel and -1/2o on the right wheel. a. Are the caster angles within the range of values recommended by the manufacturer? If not, which one(s) is outside the limits? b. What is the spread of the caster angles between the two readings? Is this within the manufacturers recommended limit? 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. Suppose a tank is filled at the rate of 10 gallons of a fluid per minute. Meanwhile, a valve is opened to drain off 8 gallons per minute into a pipeline. a. Express each of the movement rates of the fluid as a signed number. b. Use these signed numbers to compute how many gallons of fluid are moved into the tank in 10 minutes, and how many gallons are moved out of the tank in 10 minutes. Keep the signs with your answers. c. If the tank starts out empty, what is the total amount of material in the tank after 10 minutes? 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. You are installing a cruise control on a customers car. A small adjustment screw is provided to adjust the sensitivity of the device. Your first test drive shows that when you set the speed on 50 mph, the device keeps the cars speed between 45 mph and 57 mph. On the second test drive, after you turn the adjustment screw one notch, the device is able to maintain the cars speed between 47 mph and 55 mph. One final adjustment narrows the range to 48 mph and 54 mph, but the ride becomes jerky, so you return the adjustment to the previous setting and sign off the cruise control sensitivity adjustment. a. What are the deviations from the set speed in your first test drive? your second test drive? your final test drive? (Express your answers as signed numbers.) b. What is the difference between the high and low deviation for the second test drivev results? c. The manufacturer advertises that the device can control the speed to within +/- 4 mph of the set speed. What does this mean in terms of deviation from set speed? Should you obtain another unit, or accept the performance of this unit as within the manufacturers advertised limits? 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. A manufacturing plant instituted statistical process control charts, where measurements are taken at regular intervals of a process, and compared to the specification (spec). One of the processes being charted is length of a piece of bar stock. The spec calls for a length of 48.7 inches, with 4a tolerance of +/- 0.2 inches. Every 15 minutes the operator measures a sample of 4 bars and records the average length, as shown below. Place table, page 56, here. a. Compute the deviation from spec for each of the lengths reported in the table above. Represent each as a signed number. b. Compare each of the deviations you computed in Part a to the tolerance. Indicate which (if any) of the deviations are outside the tolerance, that is, greater than the tolerance.  . DSET|(H-X>"9 *6*>"9DSET(H8-T9>96*=9DSETR -H-P-L-   -DUnit 11 Odd Questions