Concept explainers
Focus Problem: Water Solve the focus problem at the beginning of this chapter.
The Yellowstone River starts in massive and beautiful Yellowstone Lake. Then it flows through prime trout fishing areas to the famous Yellowstone Falls. After it leaves the park, the river is an important source of water for wildlife, ranchers, farmers, and cities downstream. How much water does leave the park each year? The annual flow of the Yellowstone River (units
25.9 | 32.4 | 33.1 | 19.1 | 17.5 | 24.9 |
27.1 | 29.1 | 25.6 | 31.8 | ||
21.0 | 45.1 | 30.8 | 34.3 | 25.9 | 18.6 |
23.7 | 24.1 | 23.9 |
(a) Is there a "guaranteed" amount of water farmers, ranchers, and cities will get from the Yellowstone River each year?
(b) What is the “expected” annual How from the Yellowstone snowmelt? Find the mean, the median, and the
(c) Find the
(d) Find a 75% Chebyshev interval around the mean.
(e) Give a five-number summary of annual water How from the Yellowstone River and make a box-and-whisker plot. Interpret the five-number summary and the box-and-whisker plot. Where does the middle portion of the data lie? What is the
(f) The Madison River is a smaller but very important source of water flowing out of Yellowstone Park from a different drainage. Ten recent years of annual water flow data are shown below (units
3.83 | 3.81 | 4.01 | 4.84 | 5.81 | 5.50 | 4.31 | 5.81 | 4.31 | 4.67 |
Although smaller, is the Madison more reliable? Use the coefficient of variation to make an estimate.
(g) Interpretation Based on the data, would it be safe to allocate at least 27 units of Yellowstone River water each year for agricultural and domestic use? Why or why not?
Trending nowThis is a popular solution!
Chapter 3 Solutions
UNDERSTANDING BASIC STAT LL BUND >A< F
- An Aluminum Can The cost of making a can is determined by how much aluminum A, in square inches, is needed to make it. This in turn depends on the radius r and the height h of the can, both measured in inches. You will need some basic facts about cans. See Figure 2.107. The surface of a can may be modeled as consisting of three parts: two circles of radius r and the surface of a cylinder of radius r and height h. The area of each circle is r2. In what follows, we assume that the can must hold 15 cubic inches, and we will look at various cans holding the same volume. a. Explain why the height of any can that holds a volume of 15 cubic inches is given by h=15r2 b. Make a graph of the height h as a function of r, and explain what the graph is showing. c. Is there a value of r that gives the least height h? Explain. d. If A is the amount of aluminum needed to make the can, explain why A=2r2+2rh. e. Using the formula for h from part a, explain why we may also write A as A=2r2+30r.arrow_forwardWork The work W required to lift an object varies jointly with the object’s mass m and the height h that the object is lifted. The work required to lift a 120-kilogram object 1.8 meters is 2116.8 joules. Find the amount of work required to lift a 100-kilogram object 1.5 meters.arrow_forwardVelocity of a Ferris Wheel Use Figure 7 as a model of the Ferris wheel called Colossus that is built in St. Louis in 1986. The diameter of the wheel is 165 feet. A brochure that gives some statistics associated with Colossus indicates that it rotates at 1.5 revolutions per minute and also indicates that a rider on the wheel is traveling at 10 miles per hour. Explain why these two numbers, 1.5 revolutions per minute and 10 miles per hour, cannot both be correct.arrow_forward
- pH of calcium hydroxide Find the hydrogen ion concentration of a saturated solution of calcium hydroxide whose pH is 13.2arrow_forwardEXERCISE River flow The cross sectional area C, in square feet, of a river is given by the formula C=wd, where, w is the width of the river and d is the depth, both in feetSee Figure 5.58. The speed s of the flow, in feet per minute, is measured using a meter. The flow rate F, in cubic feet per minute, of the river is given by F=sC a Find a formula that gives F in terms of the variables w,d, and s. b Use the formula you found in part a to find the flow rate of the river that has a width of 23 feet, a depth of 2 feet, and flow speed of 24 feet per minute.arrow_forwardHeight of a Cliff To measure the height of an inaccessible cliff on the opposite side of a river, a surveyor makes the measurements shown in the figure at the left. Find the height of the cliff.arrow_forward
- Force If you have ever ridden on a chair lift at a ski area and had it stop, you know that the chair will pull down on the cable, dropping you down to a lower height than when the chair is in motion. Figure 19 shows a gondola that is stopped. Find the magnitude of the tension in the cable toward each end of the cable if the total weight of the gondola and its occupants is 1,850 pounds.arrow_forwardLinear and Angular Speed A computerized spin balance machine rotates a 25-inch diameter tire at 480 revolutions per minute. (a) Find the road speed (in miles per hour) at which the tire is being balanced. (b) At what rate should the spin balance machine be set so that the tire is being tested for 55 miles per hour?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning