Concept explainers
Transportation The King Trucking Company has an order for three products for delivery.
The following table gives the particulars for the products.
If the carrier can carry 6000 cu ft, can carry 11,000 lb, and is insured for $36,900, how many units of each type can be carried?
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Chapter 3 Solutions
Mathematical Applications for the Management, Life, and Social Sciences
- Running In 1987, Canadian Ben Johnson set a world record in the 100-m sprint.The record was later taken away when he was found to have used an anabolic steroid to enhance his performance. His speed at various times in the race is given in the following table . Source: Information Graphics. Timesec Speedmph 0 0 1.84 12.9 3.80 23.8 6.38 26.3 7.23 26.3 8.96 26.0 9.83 25.7 a. Use the information in the table and left endpoints to estimate the distance that Johnson ran in miles. You will first need to calculate t for each interval. At the end, you will need to divide by 3600 the number of seconds in an hour, since the speed is in miles per hour. b. Repeat part a, using right endpoints. c. Wait a minute, we know that the distance Johnson ran is 100m. Divide this by 1609, the number of meters in a mile, to find how far Johnson ran in miles. Is your answer from part a or part b closer to the true answer? Briefly explain why you think this answer should be more accurate. d.arrow_forwardOTHER APPLICATIONS Car Accidents The tables in the next columns give the death rates, per million person trips, for male and female drivers for various ages and number of passengers. Male Drivers Number of Passengers Age 0 1 2 3 16 2.61 4.39 6.29 9.08 17 1.63 2.77 4.61 6.92 30-59 0.92 0.75 0.62 0.54 Female Drivers Number of Passengers Age 0 1 2 3 16 1.38 1.72 1.94 3.31 17 1.26 1.48 2.82 2.28 30-59 0.41 0.33 0.27 0.40 a. Write a matrix for death rate of male drivers. b. Write a matrix for death rate of female drivers. c. Use the matrices from parts a and b to write a matrix showing the difference between the death rates of males and females. d. Analyze the results of part c and make some suggestions on how to reduce the rates.arrow_forwardGrade Point Average In many universities students are given grade points for each credit unit according to the following scale: A4 points B3 points C2 points D1 points F0 points For example, a grade of A in a 3-unit earns 43=12 grade points and grade points and a grade of B in a 5-unit course earns 35=15 grade points. A student’s grade point average (GPA) for these two courses is the total number of grade points earned divided by the number of units; in this case the GPA is (12+15)/8=3.375 . (a) Find a formula for a GPA of a student who earns a grade A in a units of course work, B in b units; C in c units, D in d units, and F in f units. (b) Find a GPA of a student who has earned a grade of A in two-units courses. B in one 4-unit course, and C in three 3-unit courses.arrow_forward
- Grade Point Average In many universities students are given grade points for each credit unit according to the following scale: A 4 points B 3 points C 2 points D 1 point F 0 point For example, a grade of A in a 3-unit course earns 43=12 grade points and a grade of B in a 5-unit course earns 35=15 grade points. A students grade point average GPA for these two courses is the total number of grade points earned divided by the number of units; in this case the GPA is (12+15)8=3.375. a Find a formula for the GPA of a student who earns a grade of A in a units of course work, B in b units, C in c units, D in d units and F in f units. b Find the GPA of a student who has earned a grade of A in two 3-unit courses, B in one 4-unit courses and C in three 3-unit courses.arrow_forwardLIFE SCIENCE APPLICATIONS Body Surface Area The surface area of a human in square meters has been approximated by A(h,m)=0.024265h0.3964m0.5378, where h is the height in cm and m is the mass in kg. Find A for the following data. Source: The Journal of Pediatrics. a. Height, 178cm; mass, 72kg b. Height, 140cm; mass 65kg c. Height, 160cm; mass, 70kg d. Using your mass and height, find your own surface area. e. f.arrow_forwardBroadway The ordered pairs below give the starting year and gross ticket sales S (in millions of dollars) for each Broadway season in New York City from 1997 through 2014. 1997,558 2003,771 2009,1020 1998,588 2004,769 2010,1081 1999,603 2005,862 2011,1139 2000,666 2006,939 2012,1139 2001,643 2007,938 2013,1269 2002,721 2008,943 2014,1365 (a) Use a graphing utility to create a scatter plot of the data. Let t=7 represent 1997. (b) Use the regression feature of the graphing utility to find the equation of the least squares regression line that fits the data. (c) Use the graphing utility to graph the scatter plot you created in part (a) and the model you found in part (b) in the same viewing window. How closely does the model represent the data? (d) Use the model to predict the gross ticket sales during the season starting in 2021. (e) Interpret the meaning of the slope of the linear model in the context of the problem.arrow_forward
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