Numerical Analysis
10th Edition
ISBN: 9781305253667
Author: Richard L. Burden, J. Douglas Faires, Annette M. Burden
Publisher: Cengage Learning
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Textbook Question
Chapter 4.1, Problem 23ES
In Exercise 9 of Section 3.4, data were given describing a car traveling on a straight road. That problem asked to predict the position and speed of the car when t = 10 seconds. Use the following times and positions to predict the speed at each time listed.
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Students have asked these similar questions
In Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a
random sample of 1014 adults aged 18 and over. One of the questions was, "How many
cups of coffee, if any, do you drink on an average day?" The following table shows the
results obtained (Gallup website, August 6, 2012).
Number of Cups
per Day
0
1
2
3
4 or more
Number of
Responses
365
264
193
91
101
Define a random variable x = number of cups of coffee consumed on an average day. Let
x=4 represent four or more cups.
a. Develop a probability distribution for x.
b. Compute the expected value of x.
c. Compute the variance of x.
d. Suppose we are only interested in adults who drink at least one cup of coffee on an
average day. For this group, let y = the number of cups of coffee consumed on an
average day. Compute the expected value of y and compare it to the expected value of x.
Ten major college football bowl games were played in January 2010, with the University
of Alabama beating the University of Texas 37 to 21 to become the national champion
of college football. The results of the 10 bowl games follow (USA Today, January 8, 2010).
Bowl Game
Score
Outback
Gator
Auburn 38 Northwestern 35
Florida State 33 West Virginia 21
Capital One
Penn State 19 LSU 17
Rose
Ohio State 26 Oregon 17
Florida 51 Cincinnati 24
Sugar
Cotton
Alamo
Fiesta
Mississippi State 21 Oklahoma State 7
Texas Tech 41 Michigan State 31
Boise State 17 TCU 10
Orange
Iowa 24 Georgia Tech 14
Championship
Alabama 37 Texas 21
Predicted
Point Margin
Actual
Point Margin
5
3
1
12
3
-2
14
3
9
-4
-3
4
229740706
14
10
10
16
The predicted winning point margin was based on Las Vegas betting odds approximately
one week before the bowl games were played. For example, Auburn was predicted to beat
Northwestern in the Outback Bowl by five points. The actual winning point margin for Au-
burn was three points. A…
In 2007 the New York Times reported that the median annual household income in the United
States was $55,500 (New York Times website, August, 21, 2013). Answer the following
questions based on the following sample of 14 household incomes for 2013 ($1000s).
49.4
52.2
52.4
53.4
51.3
52.1
48.7
64.5
51.6
46.5
52.9
52.5
52.1
51.2
a.
What is the median household income for the sample data for 2013?
b. Based on the sample data, estimate the percentage change in the median household
income from 2007 to 2013.
c. Compute the first and third quartiles.
Chapter 4 Solutions
Numerical Analysis
Ch. 4.1 - Use the forward-difference formulas and...Ch. 4.1 - The data in Exercise 1 were taken from the...Ch. 4.1 - Use the most accurate three-point formula to...Ch. 4.1 - Use the most accurate three-point formula to...Ch. 4.1 - The data in Exercise 5 were taken from the...Ch. 4.1 - The data in Exercise 6 were taken from the...Ch. 4.1 - Prob. 9ESCh. 4.1 - Use the formulas given in this section to...Ch. 4.1 - The data in Exercise 9 were taken from the...Ch. 4.1 - Prob. 12ES
Ch. 4.1 - Use the following data and the knowledge that the...Ch. 4.1 - Prob. 14ESCh. 4.1 - Prob. 15ESCh. 4.1 - Prob. 16ESCh. 4.1 - Prob. 17ESCh. 4.1 - Prob. 18ESCh. 4.1 - Prob. 19ESCh. 4.1 - Prob. 20ESCh. 4.1 - Prob. 21ESCh. 4.1 - In a circuit with impressed voltage (t) and...Ch. 4.1 - In Exercise 9 of Section 3.4, data were given...Ch. 4.1 - Derive an O(h4) five-point formula to approximate...Ch. 4.1 - Use the formula derived in Exercise 24 and the...Ch. 4.1 - a. Analyze the round-off errors, as in Example 4,...Ch. 4.1 - Derive a method for approximating f (x0) whose...Ch. 4.1 - Consider the function e(h)=h+h26M, where M is a...Ch. 4.1 - Prob. 1DQCh. 4.1 - Prob. 2DQCh. 4.2 - Apply the extrapolation process described in...Ch. 4.2 - Add another line to the extrapolation table in...Ch. 4.2 - The following data give approximations to the...Ch. 4.2 - Prob. 6ESCh. 4.2 - Prob. 7ESCh. 4.2 - The forward-difference formula can be expressed as...Ch. 4.2 - Prob. 9ESCh. 4.2 - Prob. 10ESCh. 4.2 - Prob. 11ESCh. 4.2 - Prob. 12ESCh. 4.2 - Prob. 13ESCh. 4.3 - Approximate the following integrals using the...Ch. 4.3 - Approximate the following integrals using the...Ch. 4.3 - Find a bound for the error in Exercise 1 using the...Ch. 4.3 - Prob. 4ESCh. 4.3 - Repeat Exercise 1 using Simpsons rule. 1....Ch. 4.3 - Prob. 6ESCh. 4.3 - Prob. 7ESCh. 4.3 - Prob. 8ESCh. 4.3 - Prob. 9ESCh. 4.3 - Prob. 10ESCh. 4.3 - Prob. 11ESCh. 4.3 - Prob. 12ESCh. 4.3 - The Trapezoidal rule applied to 02f(x)dx gives the...Ch. 4.3 - Prob. 14ESCh. 4.3 - Approximate the following integrals using formulas...Ch. 4.3 - Prob. 17ESCh. 4.3 - Suppose that the data of Exercise 17 have...Ch. 4.3 - Prob. 19ESCh. 4.3 - Prob. 20ESCh. 4.3 - The quadrature formula...Ch. 4.3 - The quadrature formula...Ch. 4.3 - Find the constants c0, c1, and x1 so that the...Ch. 4.3 - Find the constants x0, x1, and c1 so that the...Ch. 4.3 - Prob. 25ESCh. 4.3 - Prob. 26ESCh. 4.3 - Prob. 27ESCh. 4.3 - Derive Simpsons Three-Eighths rule (the closed...Ch. 4.3 - Prob. 1DQCh. 4.3 - Prob. 2DQCh. 4.4 - Use the Composite Trapezoidal rule with the...Ch. 4.4 - Prob. 2ESCh. 4.4 - Use the Composite Simpsons rule to approximate the...Ch. 4.4 - Prob. 4ESCh. 4.4 - Prob. 5ESCh. 4.4 - Prob. 6ESCh. 4.4 - Prob. 7ESCh. 4.4 - Prob. 8ESCh. 4.4 - Prob. 9ESCh. 4.4 - Prob. 10ESCh. 4.4 - Determine the values of n and h required to...Ch. 4.4 - Repeat Exercise 11 for the integral 0x2cosxdx. 11....Ch. 4.4 - Determine the values of n and h required to...Ch. 4.4 - Repeat Exercise 13 for the integral 12xlnxdx. 13....Ch. 4.4 - Prob. 15ESCh. 4.4 - Prob. 17ESCh. 4.4 - A car laps a race track in 84 seconds. The speed...Ch. 4.4 - Prob. 19ESCh. 4.4 - Prob. 20ESCh. 4.4 - Prob. 21ESCh. 4.4 - Prob. 23ESCh. 4.4 - Prob. 24ESCh. 4.4 - Prob. 25ESCh. 4.4 - Prob. 26ESCh. 4.4 - Prob. 1DQCh. 4.4 - Prob. 2DQCh. 4.5 - Use Romberg integration to compute R3, 3 for the...Ch. 4.5 - Use Romberg integration to compute R3, 3 for the...Ch. 4.5 - Prob. 3ESCh. 4.5 - Prob. 4ESCh. 4.5 - Use the following data to approximate 15f(x)dx as...Ch. 4.5 - Prob. 9ESCh. 4.5 - Prob. 10ESCh. 4.5 - Prob. 11ESCh. 4.5 - Romberg integration for approximating 01f(x)dx...Ch. 4.5 - Prob. 15ESCh. 4.5 - Prob. 18ESCh. 4.5 - Prob. 19ESCh. 4.5 - Prob. 1DQCh. 4.5 - Prob. 4DQCh. 4.6 - Prob. 1ESCh. 4.6 - Prob. 2ESCh. 4.6 - Prob. 11ESCh. 4.6 - Prob. 12ESCh. 4.6 - Could Romberg integration replace Simpsons rule in...Ch. 4.7 - Approximate the following integrals using Gaussian...Ch. 4.7 - Approximate the following integrals using Gaussian...Ch. 4.7 - Repeat Exercise 1 with n = 3. 1. Approximate the...Ch. 4.7 - Repeat Exercise 2 with n = 3. 2. Approximate the...Ch. 4.7 - Repeat Exercise 1 with n = 4. 1. Approximate the...Ch. 4.7 - Repeat Exercise 2 with n = 4. 2. Approximate the...Ch. 4.7 - Repeat Exercise 1 with n = 5. 1. Approximate the...Ch. 4.7 - Repeat Exercise 2 with n = 5. 2. Approximate the...Ch. 4.7 - Describe the differences and similarities between...Ch. 4.7 - Prob. 2DQCh. 4.8 - Prob. 1DQCh. 4.8 - Prob. 2DQCh. 4.8 - Prob. 3DQCh. 4.8 - Prob. 4DQCh. 4.9 - Suppose a body of mass m is traveling vertically...Ch. 4.9 - The Laguerre polynomials {L0(x), L1(x) ...} form...Ch. 4.9 - Prob. 7ESCh. 4.9 - Prob. 8ESCh. 4.9 - Prob. 9ESCh. 4.9 - Prob. 1DQCh. 4.9 - Prob. 2DQ
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