
Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 1.5, Problem 4E
To determine
To calculate:To determine a best estimate for the depth (in meters) at which the temperature is 10-degree centigrade.
Expert Solution & Answer

Want to see the full answer?
Check out a sample textbook solution
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 1 Solutions
Numerical Analysis
Ch. 1.1 - Use the Intermediate Value Theorem to find an...Ch. 1.1 - Use the Intermediate Value Theorem to find an...Ch. 1.1 - Consider the equations in Exercise 1. Apply two...Ch. 1.1 - Consider the equations in Exercise 2. Apply two...Ch. 1.1 - Consider the equation x4=x3+10 . a. Find an...Ch. 1.1 - Suppose that the Bisection Method with starting...Ch. 1.1 - Prob. 1CPCh. 1.1 - Use the Bisection Method to find the root to eight...Ch. 1.1 - Use the Bisection Method to locate all solutions...Ch. 1.1 - Prob. 4CP
Ch. 1.1 - Prob. 5CPCh. 1.1 - Use the Bisection Method to calculate the solution...Ch. 1.1 - Use the Bisection Method to find the two real...Ch. 1.1 - The Hilbert matrix is the nn matrix whose ijth...Ch. 1.1 - Prob. 9CPCh. 1.1 - A planet orbiting the sun traverses an ellipse....Ch. 1.2 - Find all fixed points of the following gx . a. 3x...Ch. 1.2 - Find all fixed points of the following gx . x+63x2...Ch. 1.2 - Prob. 3ECh. 1.2 - Show that -1, 0, and 1 are fixed points of the...Ch. 1.2 - For which of the following gx is r=3 a fixed...Ch. 1.2 - For which of the following is a fixed...Ch. 1.2 - Use Theorem 1.6 to determine whether Fixed-Point...Ch. 1.2 - Use Theorem 1.6 to determine whether Fixed-Point...Ch. 1.2 - Find each fixed point and decide whether...Ch. 1.2 - Find each fixed point and decide whether...Ch. 1.2 - Express each equation as a fixed-point problem...Ch. 1.2 - Consider the Fixed-Point Iteration xgx=x20.24 ....Ch. 1.2 - (a) Find all fixed points of.
(b) To which of the...Ch. 1.2 - Which of the following three Fixed-Point...Ch. 1.2 - Which of the following three Fixed-Point...Ch. 1.2 - Which of the following three Fixed-Point...Ch. 1.2 - Check that and -1 are roots of. Isolate the term...Ch. 1.2 - Prove that the method of Example 1.6 will...Ch. 1.2 - Explore the idea of Example 1.6 for cube roots. Lf...Ch. 1.2 - Improve the cube root algorithm of Exercise 19 by...Ch. 1.2 - Prob. 21ECh. 1.2 - Prob. 22ECh. 1.2 - Assume that gx is continuously differentiable and...Ch. 1.2 - Assume that g is a continuously differentiable...Ch. 1.2 - Prob. 25ECh. 1.2 - Prove that a continuously differentiable function ...Ch. 1.2 - Prob. 27ECh. 1.2 - Prob. 28ECh. 1.2 - Prob. 29ECh. 1.2 - Prob. 30ECh. 1.2 - Prob. 31ECh. 1.2 - Find the set of all initial guesses for which the...Ch. 1.2 - Prob. 33ECh. 1.2 - Prob. 1CPCh. 1.2 - Prob. 2CPCh. 1.2 - Calculate the square roots of the following...Ch. 1.2 - Calculate the cube roots of the following numbers...Ch. 1.2 - Prob. 5CPCh. 1.2 - Prob. 6CPCh. 1.2 - Prob. 7CPCh. 1.3 - Find the forward and backward error for the...Ch. 1.3 - Find the forward and backward error for the...Ch. 1.3 - (a) Find the multiplicity of the root r=0 of...Ch. 1.3 - (a) Find the multiplicity of the root of.
(b)...Ch. 1.3 - Find the relation between forward and backward...Ch. 1.3 - Let be a positive integer. The equation defining...Ch. 1.3 - Let be the Wilkinson polynomial. (a) Prove that ...Ch. 1.3 - Let fx=xnaxn1 , and set gx=xn . (a) Use the...Ch. 1.3 - Prob. 1CPCh. 1.3 - Carry' out Computer Problem 1 for fx=sinx3x3 .Ch. 1.3 - Prob. 3CPCh. 1.3 - Prob. 4CPCh. 1.3 - Prob. 5CPCh. 1.3 - Prob. 6CPCh. 1.4 - Apply two steps of Newton’s Method with initial...Ch. 1.4 - Apply two steps of Newton’s Method with initial...Ch. 1.4 - Use Theorem 1.11 or 1.12 to estimate the error...Ch. 1.4 - Estimate
as in Exercise 3.
(a) ; ,
(b) ; ,
Ch. 1.4 - Consider the equation 8x412x3+6x2x=0 . For each of...Ch. 1.4 - Sketch a function f and initial guess for which...Ch. 1.4 - Let fx=x47x3+18x220x+8 . Does Newton’s Method...Ch. 1.4 - Prove that Newton’s Method applied to fx=ax+b...Ch. 1.4 - Show that applying Newton’s Method to fx=x2A...Ch. 1.4 - Find the Fixed-Point Iteration produced by...Ch. 1.4 - Use Newton’s Method to produce a quadratically...Ch. 1.4 - Suppose Newton’s Method is applied to the...Ch. 1.4 - (a) The function has a root at . If the error ...Ch. 1.4 - Let
denote the Newton’s Method iteration for the...Ch. 1.4 - Each equation has one root. Use Newton’s Method to...Ch. 1.4 - Prob. 2CPCh. 1.4 - Apply Newton’s Method to find the only root to as...Ch. 1.4 - Carry out the steps of Computer Problem 3 for (a)...Ch. 1.4 - Prob. 5CPCh. 1.4 - Prob. 6CPCh. 1.4 - Consider the function fx=esin3x+x62x4x31 on the...Ch. 1.4 - Prob. 8CPCh. 1.4 - Prob. 9CPCh. 1.4 - Set fx=54x6+45x5102x469x3+35x2+16x4 . Plot the...Ch. 1.4 - The ideal gas law for a gas at low temperature and...Ch. 1.4 - Prob. 12CPCh. 1.4 - Prob. 13CPCh. 1.4 - Prob. 14CPCh. 1.4 - Prob. 15CPCh. 1.4 - Prob. 16CPCh. 1.4 - Consider the national population growth model...Ch. 1.5 - Prob. 1ECh. 1.5 - Apply two steps of the Method of False Position...Ch. 1.5 - Apply two steps of Inverse Quadratic Interpolation...Ch. 1.5 - A commercial fisher wants to set the net at a...Ch. 1.5 - Prob. 5ECh. 1.5 - If the Secant Method converges to, , and , then...Ch. 1.5 - Consider the following four methods for...Ch. 1.5 - Prob. 1CPCh. 1.5 - Use the Method of False Position to find the...Ch. 1.5 - Prob. 3CPCh. 1.5 - Prob. 4CPCh. 1.5 - Prob. 5CPCh. 1.5 - Prob. 6CPCh. 1.5 - Write a MATLAB function file for f . The...Ch. 1.5 - Plot f on , . You may use the @ symbol as...Ch. 1.5 - Reproduce Figure 1.15. The MATLAB commands and...Ch. 1.5 - Solve the forward kinematics problem for the...Ch. 1.5 - Prob. 5SACh. 1.5 - Find a strut length p2 , with the rest of the...Ch. 1.5 - Calculate the intervals in p2 , with the rest of...Ch. 1.5 - Prob. 8SA
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Evaluate the triple integral 3' 23 HIG 2 +3 f(x, y, z)dxdydz where f(x, y, z) = x + 2x-y ม u = v = and w = 2 2 3 Triple Integral Region R -2 x N 2 y 3arrow_forwardFind the volume of the solid bounded below by the circular cone z = 2.5√√√x² + y² and above by the sphere x² + y²+z² = 6.5z.arrow_forwardElectric charge is distributed over the triangular region D shown below so that the charge density at (x, y) is σ(x, y) = 4xy, measured in coulumbs per square meter (C/m²). Find the total charge on D. Round your answer to four decimal places. 1 U 5 4 3 2 1 1 2 5 7 coulumbsarrow_forward
- Let E be the region bounded cone z = √√/6 - (x² + y²) and the sphere z = x² + y² + z² . Provide an answer accurate to at least 4 significant digits. Find the volume of E. Triple Integral Spherical Coordinates Cutout of sphere is for visual purposes 0.8- 0.6 z 04 0.2- 0- -0.4 -0.2 04 0 0.2 0.2 x -0.2 04 -0.4 Note: The graph is an example. The scale and equation parameters may not be the same for your particular problem. Round your answer to 4 decimal places. Hint: Solve the cone equation for phi. * Oops - try again.arrow_forwardThe temperature at a point (x,y,z) of a solid E bounded by the coordinate planes and the plane 9.x+y+z = 1 is T(x, y, z) = (xy + 8z +20) degrees Celcius. Find the average temperature over the solid. (Answer to 4 decimal places). Average Value of a function using 3 variables z 1- y Hint: y = -a·x+1 * Oops - try again. xarrow_forwardFind the saddle pointsarrow_forward
- Problem #5 Section A of my math class has 110 students. Section B of my math class has 80 students. a). If I randomly select 15 students from the combined classes, in a way that the order of my selection does not matter, what is the probability that all 15 students can from Section A? b). If I randomly select 15 students from the combined classes, in a way that the order of my selection does not matter, what is the probability that all 15 students can from Section B? c). If I randomly select 15 students from the combined classes, in a way that the order of my selection does not matter, what is the probability that all 7 students come from section A and 8 students come from section B?arrow_forwardProblem #6 A special passcode to unlock your phone consists of 4 digits where repeated digits are not allowed. If someone were to randomly guess a 4 digit passcode, what is the probability that they guess your passcode on the first try?arrow_forwardProblem #3 If a card is picked at random from a standard 52-card deck, what is the probability of getting a black card or a queen?arrow_forward
- Problem #1 In the 2010 census, it was reported that the United States had a population of 310 million people. Of those, 74 million were under the age of 18. If you chose a person from the U.S. population at random, what is the probability they are under the age of 18? Problem #2 Given a set S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, if you were choosing a number at random what is the probability that you would choose an even number or a number larger than 7?arrow_forwardAnswer number twoarrow_forwardAnswer number onearrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education

Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education

Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON


Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON

Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,

Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
Use of ALGEBRA in REAL LIFE; Author: Fast and Easy Maths !;https://www.youtube.com/watch?v=9_PbWFpvkDc;License: Standard YouTube License, CC-BY
Compound Interest Formula Explained, Investment, Monthly & Continuously, Word Problems, Algebra; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=P182Abv3fOk;License: Standard YouTube License, CC-BY
Applications of Algebra (Digit, Age, Work, Clock, Mixture and Rate Problems); Author: EngineerProf PH;https://www.youtube.com/watch?v=Y8aJ_wYCS2g;License: Standard YouTube License, CC-BY