Mathematics for the Trades: A Guided Approach, Books a la Carte edition (11th Edition)
11th Edition
ISBN: 9780134765785
Author: Hal Saunders
Publisher: PEARSON
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Chapter 12, Problem 34APS
Graph V Business and Finance
During which month were projected sales highest?
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1. Abel's Theorem. The goal in this problem is to prove Abel's theorem by following a series of steps
(each step must be justified).
Theorem 0.1 (Abel's Theorem).
If y1 and y2 are solutions of the differential equation
y" + p(t) y′ + q(t) y = 0,
where p and q are continuous on an open interval, then the Wronskian is given by
W (¥1, v2)(t) = c exp(− [p(t) dt),
where C is a constant that does not depend on t. Moreover, either W (y1, y2)(t) = 0 for every t in I or
W (y1, y2)(t) = 0 for every t in I.
1. (a) From the two equations (which follow from the hypotheses),
show that
y" + p(t) y₁ + q(t) y₁ = 0 and y½ + p(t) y2 + q(t) y2 = 0,
2. (b) Observe that
Hence, conclude that
(YY2 - Y1 y2) + P(t) (y₁ Y2 - Y1 Y2) = 0.
W'(y1, y2)(t) = yY2 - Y1 y2-
W' + p(t) W = 0.
3. (c) Use the result from the previous step to complete the proof of the theorem.
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Support Department Cost Allocation—Reciprocal Services Method
Blue Africa Inc. produces laptops and desktop computers. The company’s production activities mainly occur in what the company calls its Laser and Forming departments. The Cafeteria and Security departments support the company’s production activities and allocate costs based on the number of employees and square feet, respectively. The total cost of the Security Department is $261,000. The total cost of the Cafeteria Department is $300,000. The number of employees and the square footage in each department are as follows:
Department
Employees
Square Feet
Security
10
570
Cafeteria
28
2,400
Laser
40
4,800
Forming
50
800
Using the reciprocal services method of support department cost allocation, determine the total costs from the Security Department that should be allocated to…
Chapter 12 Solutions
Mathematics for the Trades: A Guided Approach, Books a la Carte edition (11th Edition)
Ch. 12.1 - Solve: 0.82=x100Ch. 12.1 - Prob. 2LCCh. 12.1 - Automotive Trades The following bar graph shows...Ch. 12.1 - Trades Management The following graph shows the...Ch. 12.1 - General Interest The following double bar graph...Ch. 12.1 - General Interest The following stacked bar graph...Ch. 12.1 - Allied Health When Dr. Friedrich began working at...Ch. 12.1 - Automotive Trades The following line graph shows...Ch. 12.1 - Construction The following double-line graph...Ch. 12.1 - General Interest Study the circle graph at the top...
Ch. 12.1 - Prob. 9AECh. 12.1 - Allied Health An assistant at a pharmaceutical...Ch. 12.1 - Fire Protection Plot the following data as a bar...Ch. 12.1 - Transportation The following table lists the total...Ch. 12.1 - Metalworking Draw a bar graph from the following...Ch. 12.1 - Trades Management Plot the following data as a bar...Ch. 12.1 - Construction Plot the following data as a double...Ch. 12.1 - General Interest The following table shows the...Ch. 12.1 - Automotive Trades The following table shows the...Ch. 12.1 - Trades Management The following table shows the...Ch. 12.1 - General Interest The following table shows, by...Ch. 12.1 - Agriculture The following table shows the price...Ch. 12.1 - Allied Health The following table shows the...Ch. 12.1 - General Interest The following data show the U.S....Ch. 12.1 - Fire Protection The following data show the number...Ch. 12.1 - General Interest The following table shows the...Ch. 12.1 - Hydrology The following table shows the daily...Ch. 12.1 - Business and Finance Plot a double broken-line...Ch. 12.1 - Electrical Engineering Plot the following data as...Ch. 12.1 - Water/Wastewater Treatment The following table...Ch. 12.1 - Aviation An aircraft mechanic spends 12.5% of a...Ch. 12.1 - General Interest Recent surveys have shown that...Ch. 12.2 - Find the average of these numbers: 6, 8, 12, 14Ch. 12.2 - What number is halfway between 12 and 15?Ch. 12.2 - Find the mean, median, and mode for each set of...Ch. 12.2 - A. Find the mean, median, and mode for each set of...Ch. 12.2 - A. Find the mean, median, and mode for each set of...Ch. 12.2 - A. Find the mean, median, and mode for each set of...Ch. 12.2 - A. Find the mean, median, and mode for each set of...Ch. 12.2 - A. Find the mean, median, and mode for each set of...Ch. 12.2 - A. Find the mean, median, and mode for each set of...Ch. 12.2 - A. Find the mean, median, and mode for each set of...Ch. 12.2 - Construct an extended frequency distribution for...Ch. 12.2 - Construct an extended frequency distribution for...Ch. 12.2 - Aviation BF Goodrich produces brake pads for...Ch. 12.2 - General Trades The U.S. Department of Labor...Ch. 12.2 - Forestry The following table shows both the total...Ch. 12.2 - Water/Wastewater Treatment The seven-day mean of...Ch. 12.2 - Automotive Trades A mechanic has logged the...Ch. 12.2 - Forestry A forest ranger wishes to determine the...Ch. 12.2 - Hydrology The following table shows the monthly...Ch. 12.2 - Meteorology The National Weather Service provides...Ch. 12.2 - Automotive Trades The following table shows both...Ch. 12.2 - Hydrology The following table shows the daily...Ch. 12.2 - Allied Health The Apgar score is widely used to...Ch. 12.2 - Allied Health A pharmacist keeps careful track of...Ch. 12.2 - Prob. 13CECh. 12.2 - Prob. 14CECh. 12.3 - Calculate: 65 72.5Ch. 12.3 - Calculate: (2.5)2Ch. 12.3 - Prob. 1AECh. 12.3 - Prob. 2AECh. 12.3 - Prob. 3AECh. 12.3 - Calculate the range and the standard deviation for...Ch. 12.3 - Prob. 5AECh. 12.3 - Calculate the range and the standard deviation for...Ch. 12.3 - Prob. 7AECh. 12.3 - Prob. 8AECh. 12.3 - Prob. 1BECh. 12.3 - Prob. 2BECh. 12.3 - Prob. 3BECh. 12.3 - Calculate the standard deviation of the grouped...Ch. 12.3 - Prob. 1CECh. 12.3 - For each set of data, (a) calculate the standard...Ch. 12.3 - Prob. 1DECh. 12.3 - For each set of data, (a) calculate the standard...Ch. 12.3 - Prob. 1EECh. 12.3 - Prob. 2EECh. 12.3 - Prob. 3EECh. 12.3 - Prob. 4EECh. 12.3 - Prob. 5EECh. 12.3 - Prob. 6EECh. 12.3 - Prob. 7EECh. 12.3 - Prob. 8EECh. 12.3 - Prob. 9EECh. 12.3 - Prob. 10EECh. 12.3 - Prob. 11EECh. 12.3 - Prob. 12EECh. 12.3 - Prob. 13EECh. 12.3 - Automotive Trades In testing the acceleration from...Ch. 12 - Read bar graphs, line graphs, and circle graphs....Ch. 12 - Prob. 2PCh. 12 - Prob. 3PCh. 12 - Prob. 4PCh. 12 - Prob. 5PCh. 12 - Prob. 6PCh. 12 - Graph I Electrical Trades In general, as amps...Ch. 12 - Graph I Electrical Trades What is the minimum size...Ch. 12 - Graph I Electrical Trades What is the minimum wire...Ch. 12 - Prob. 4APSCh. 12 - Prob. 5APSCh. 12 - How many grams of fat are contained in a Peanut...Ch. 12 - How many grams of sugar are contained in a...Ch. 12 - How many grams of fat would you consume if you ate...Ch. 12 - How many grams of sugar would you consume if you...Ch. 12 - How many more grams of fat are in two Caramel...Ch. 12 - How many more grams of sugar are in three Peanut...Ch. 12 - Which cookie appears to be the healthiest (as...Ch. 12 - Which cookie appears to be the least healthy (as...Ch. 12 - By what percent does the amount of fat in a...Ch. 12 - By what percent does the amount of sugar in a...Ch. 12 - Retail Merchandising A small computer store is...Ch. 12 - Retail Merchandising A small computer store is...Ch. 12 - Retail Merchandising A small computer store is...Ch. 12 - Retail Merchandising A small computer store is...Ch. 12 - In September, what was the ratio of computer...Ch. 12 - Retail Merchandising A small computer store is...Ch. 12 - Retail Merchandising A small computer store is...Ch. 12 - Retail Merchandising A small computer store is...Ch. 12 - Graph IV Automotive Trades What was the cost per...Ch. 12 - Graph IV Automotive Trades When was the next time...Ch. 12 - Graph IV Automotive Trades During which time...Ch. 12 - Graph IV Automotive Trades During which time...Ch. 12 - Graph IV Automotive Trades What was the difference...Ch. 12 - Graph IV Automotive Trades By what percent did the...Ch. 12 - Graph IV Automotive Trades How much more did it...Ch. 12 - Graph V Business and Finance What was the actual...Ch. 12 - Graph V Business and Finance What was the...Ch. 12 - Graph V Business and Finance During which month...Ch. 12 - Graph V Business and Finance During which month...Ch. 12 - Graph V Business and Finance During which month...Ch. 12 - Graph V Business and Finance During which month...Ch. 12 - Graph V Business and Finance During which months...Ch. 12 - Graph V Business and Finance During which month...Ch. 12 - Graph VI Metalworking What percent of marine...Ch. 12 - Graph VI Metalworking What percent of this alloy...Ch. 12 - Graph VI Metalworking Without measuring, calculate...Ch. 12 - Graph VI Metalworking How many ounces of zinc are...Ch. 12 - Graph VI Metalworking How many grams of bismuth...Ch. 12 - Prob. 1BPSCh. 12 - General Interest The following table shows the...Ch. 12 - Prob. 3BPSCh. 12 - Prob. 4BPSCh. 12 - Prob. 5BPSCh. 12 - Prob. 6BPSCh. 12 - Metalworking Construct a circle graph based on the...Ch. 12 - Fire Protection Construct a circle graph based on...Ch. 12 - General Interest Students in a community college...Ch. 12 - C. Find the mean, median, and mode for each set of...Ch. 12 - C. Find the mean, median, and mode for each set of...Ch. 12 - C. Find the mean, median, and mode for each set of...Ch. 12 - C. Find the mean, median, and mode for each set of...Ch. 12 - Prob. 5CPSCh. 12 - C. Find the mean, median, and mode for each set of...Ch. 12 - D. Calculate (a) the range and (b) the standard...Ch. 12 - D. Calculate (a) the range and (b) the standard...Ch. 12 - Prob. 3DPSCh. 12 - Prob. 4DPSCh. 12 - E. Calculate the mean and the standard deviation...Ch. 12 - Prob. 2EPSCh. 12 - Prob. 1FPSCh. 12 - Meteorology The following table shows the average...Ch. 12 - Agriculture The following data from the United...Ch. 12 - Industrial Technology The Energy Information...Ch. 12 - Police Science To determine the speed that a...Ch. 12 - Agriculture The following list of numbers...Ch. 12 - Sheet Metal Trades The following data represent...Ch. 12 - Prob. 8FPSCh. 12 - Prob. 9FPS
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