The histogram below gives the length of service of members of the Department of Chemistry at a particular university. The classes, in years of service, are 0-4.9, 5-9.9, etc., and the vertical axis represents the number of faculty. What percent of the department faculty have less than 25 years of service?$ Note: You answer should represent a propotion in the form of percentage

The histogram below gives the length of service of members of the Department of Chemistry at a particular university. The classes, in years of service, are 0-4.9, 5-9.9, etc., and the vertical axis represents the number of faculty. What percent of the department faculty have less than 25 years of service?$ Note: You answer should represent a propotion in the form of percentage

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

ChapterP: Prerequisites

SectionP.6: The Rectangular Coordinate System And Graphs

Problem 46E: Exam Scores The table shows the mathematics entrance test scores x and the final examination scores...

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Grade 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.
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.
Exam Scores The table shows the mathematics entrance test scores x and the final examination scores y in an algebra course for a sample of 10 students. (a) Sketch a scatter plot of the data. (b) Find the entrance test score of any student with a final exam score in the 80s. (c) Does a higher entrance test score imply a higher final exam score? Explain.
Market Demand This is a continuation of Exercise 13. The following table shows the quantity D of wheat, in billions of bushels, that wheat consumers are willing to purchase in a year at a prince P, in dollars per bushel. D = quantity of wheat P = price 1.0 2.05 1.5 1.75 2.0 1.45 2.5 1.15 In economics, it is customary to plot D on the horizontal axis and P on the vertical axis, so we will think of D as a variable and of P as a function of D. a. Show that these data can be modeled by a linear function, and find its formula. b. Add the graph of the linear formula you found in part a, which is called the market demand curve, to your graph of the market supply curve from Exercise 13. c. Explain why the market demand curve should be decreasing. d. The equilibrium price is the price determined by the intersection of the market demand curve and the market supply curve. Find the equilibrium price determined by your graph in part b. 13. Market supply The following table shows the quantity S of wheat, in billions of bushels, that wheat supplies are willing to produce in a year and offer for sale at a price P, in dollars per bushel. S = quantity of wheat P = price 1.0 1.35 1.5 2.40 2.0 3.45 2.5 4.50 In economics, it is customary to plot S on the horizontal axis and P on the vertical axis, so we will think of S as a variable and of P as a function of S. a. Show that these data can be modeled by a linear function, and find its formula. b. Make a graph of the linear formula you found in part a. This is called the market supply curve. c. Explain why the market supply curve should be increasing. Hint: Think about what should happen when the price increases. d. How much wheat would suppliers be willing to produce in a year and offer for sale at a price of 3.90 per bushel?
Making Ice Our ice machine is making ice in preparation for the game that starts at 7:00 p.m. The machine is monitored, and the amount of ice is recorded at the end of each hour. The results are in the table below. Time 12:00 p.m. 1:00 p.m. 2:00 p.m. 3:00 p.m. Pounds of ice 200 273 346 419 a. Show that the data are linear. b. Let t denote the time in hours since noon, and let I denote the pounds of ice made. Find a linear model for I as a function of t. c. If 675 pounds of ice will be needed for the game tonight, will the ice machine produce enough ice by game time?