Mathematics for Elementary Teachers with Activities (5th Edition)
5th Edition
ISBN: 9780134392790
Author: Beckmann, Sybilla
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 16.2, Problem 3P
Explain your answers to the following:
a. How many 9-digit numbers are there that use only the digits 1, 2, 3,..., 8, 9? (Repetitions are allowed, so, for example, 123211114 is allowed.)
b. How many 9-digit numbers are there that use each of the digits 1, 2, 3,..., 8, 9 exactly once?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
(b) An otherwise fair six-sided die has been tampered with in an attempt to
cheat at a dice game. The effect is that the 1 and 6 faces have a
different probability of occurring than the 2, 3, 4 and 5 faces.
Let θ be the probability of obtaining a 1 on this biased die. Then the
outcomes of rolling the biased die have the following probability mass
function.
Table 1 The p.m.f. of outcomes of rolls of a biased die
Outcome 1 2 3 4 5 6
Probability θ
1
4
(1 − 2θ)
1
4
(1 − 2θ)
1
4
(1 − 2θ)
1
4
(1 − 2θ) θ
(i) By consideration of the p.m.f. in Table 1, explain why it is
necessary for θ to be such that 0 < θ < 1/2. [2]
(ii) The value of θ is unknown. Data from which to estimate the value
of θ were obtained by rolling the biased die 1000 times. The result
of this experiment is shown in Table 2.
Table 2 Outcomes of 1000 independent rolls of a biased die
Outcome 1 2 3 4 5 6
Frequency 205 154 141 165 145 190
Show that the likelihood of θ based on these data is
L(θ) = C θ395 (1 − 2θ)
605
,…
Problem: The probability density function of a random variable is given by the exponential
distribution
Find the probability that
f(x) = {0.55e-0.55 x 0 < x, O elsewhere}
a. the time to observe a particle is more than 200 microseconds.
b. the time to observe a particle is less than 10 microseconds.
How to solve it explain it step by step please
Chapter 16 Solutions
Mathematics for Elementary Teachers with Activities (5th Edition)
Ch. 16.1 - Some games have spinners. When the arrow in a...Ch. 16.1 - a. Draw a spinner such that the probability of...Ch. 16.1 - a. Draw a 4-color spinner (red, green, yellow,...Ch. 16.1 - Write a paragraph discussing the following: a....Ch. 16.1 - A family math night at school features the...Ch. 16.1 - There are 50 small balls in a tub. Some balls are...Ch. 16.1 - In a classroom, there are l00 plastic fish in a...Ch. 16.1 - There is a bag filled with 4 red blocks and 16...Ch. 16.1 - Write several paragraphs in which you describe and...Ch. 16.2 - A bakery makes 4 different kinds of cake. Each...
Ch. 16.2 - Allie and Betty want to know how many 3-letter...Ch. 16.2 - Explain your answers to the following: a. How many...Ch. 16.2 - In all 3 parts in this problem, explain your...Ch. 16.2 - Most Georgia car license plates currently use the...Ch. 16.2 - a. A 40-member club will elect a president and...Ch. 16.2 - A dance club has 10 women and 10 men. In each of...Ch. 16.2 - A pizza parlor problem. How many different large...Ch. 16.2 - A pizza parlor offers lo different toppings to...Ch. 16.3 - A children’s game has a spinner that is equally...Ch. 16.3 - A children’s game has a spinner that is equally...Ch. 16.3 - A children’s game has a spinner that is equally...Ch. 16.3 - A children’s game has a spinner that is equally...Ch. 16.3 - A children’s game has a spinner that is equally...Ch. 16.3 - Determine the probability of spinning a blue...Ch. 16.3 - Determine the probability of spinning a blue...Ch. 16.3 - Determine the probability of spinning a red...Ch. 16.3 - Suppose you have a penny, a nickel, a dime, and a...Ch. 16.3 - You have a bag containing 2 yellow and 3 blue...Ch. 16.3 - There are 3 plastic bears in a bag. The teacher...Ch. 16.3 - There are 4 black marbles and 5 red marbles in a...Ch. 16.3 - Suppose you have 100 light bulbs and one of them...Ch. 16.3 - A game at a fund-raiser: There are 20 rubber ducks...Ch. 16.3 - You are making up a game for a fund-raiser. You...Ch. 16.3 - a. A waitress is serving 5 people at a table. She...Ch. 16.3 - Prob. 17PCh. 16.3 - Prob. 18PCh. 16.4 - A children’s game has a spinner that is equally...Ch. 16.4 - Suppose you flip a coin and roll a number cube...Ch. 16.4 - Use fraction arithmetic to solve problem 1 on page...Ch. 16.4 - Use fraction arithmetic to solve problem 3 on page...Ch. 16.4 - Use fraction arithmetic to solve problem 6 on page...Ch. 16.4 - Prob. 6PCh. 16.4 - Use fraction arithmetic to solve problem 8 on page...Ch. 16.4 - There are 3 boxes, one of which contains 2...Ch. 16.4 - A game consists of spinning a spinner and then...Ch. 16.4 - Prob. 10PCh. 16.4 - Prob. 11PCh. 16.4 - Prob. 12PCh. 16.4 - Prob. 13PCh. 16.4 - Prob. 14PCh. 16.4 - Suppose you have 2 boxes, 50 black pearls and 50...Ch. 16.4 - Due to its high population, China has a stringent...Ch. 16.4 - The Pretty Flower Company starts plants from seed...Ch. 16.4 - Suppose that ¡n a survey of a large, random group...Ch. 16.4 - Suppose that 1% of the population has a certain...
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
- Not use ai pleasearrow_forward2.3 Vibration amplitude of a machine plotted against time shown in Fig. T2.3. is described by sin(0.8+) In(t + 2) x(t) = t + 0.5 Here, t is in seconds and x is in millimeters 0.6 0.4 0.2 ° -0.2 mmm -0.4 0 10 20 30 40 50 60 70 Time [s] Fig. T2.3: Machine vibration amplitude variation against time Obtain the vibration velocity as a function of time, x(t), if it is measured by a vibration velocity sensor.arrow_forwardO State Jordan's lemma. Calculate the following integrals using complex variable techniques. 2π do (i) 1+8 cos²0' I COS x dx x²-2x+5° Leave your answers in terms of real functions of real variables.arrow_forward
- Sketch to scale the orbit of Earth about the sun. Graph Icarus’ orbit on the same set of axesWhile the sun is the center of Earth’s orbit, it is a focus of Icarus’ orbit. There aretwo points of intersection on the graph. Based on the graph, what is the approximate distance between the two points of intersection (in AU)?arrow_forwardRefer to page 138 of the shared file for the numerical methods problem. Use Newton's method to approximate the solution of the given nonlinear system of equations. Start with an initial guess provided in the problem and iterate for at least two steps. Link: [https://drive.google.com/file/d/1RQ2OZk-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Show the Jacobian matrix, iteration formulas, and each step of the computation.arrow_forwardUnknown to a medical researcher, 7 out of 24 patients have a heart problem that will result in death if they receive the test drug. 5 patients are randomly selected to receive the drug and the rest receive a placebo. What is the probability that less than 4 patients will die? Express as a fraction or a decimal number rounded to four decimal places.arrow_forward
- Refer to page 128 for the heat equation problem. Solve the one-dimensional heat equation with the given initial and boundary conditions. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Use Fourier series or other appropriate methods.arrow_forwardGo to page 137 for the real analysis problem. Determine whether the given infinite series converges or diverges using appropriate convergence tests, such as the ratio test, root test, or comparison test. Justify your choice of test and provide clear steps. Link: [https://drive.google.com/file/d/1RQ2OZk-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Explain your reasoning and show all calculations.arrow_forwardRefer to page 132 of the document for the linear algebra problem. Solve the given nonhomogeneous system of equations using Gaussian elimination or matrix inverses, and express the general solution in parametric form. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Justify each step in the elimination process and interpret the solution.arrow_forward
- Tum to page 134 for the vector calculus problem. Verify Stokes' theorem by calculating the surface integral of the curl of a vector field over the given surface S and comparing it to the line integral of the same field over the boundary curve C. Link: [https://drive.google.com/file/d/1RQ2OZk-LSxpRyej KEMg1t2q15dbpVLCS/view? usp=sharing] Provide all detailed steps for calculating the curl, surface integral, and line integral.arrow_forwardThe Laplace equation problem is provided on page 136. Solve the two-dimensional Laplace equation on a rectangular region using the method of separation of variables with the specified boundary conditions. Link: [https://drive.google.com/file/d/1RQ2OZk-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Include all steps, separation constants, and final solution in series form.arrow_forwardThe dynamical systems problem is on page 127. Determine the stability of the fixed points of the given nonlinear system using linearization techniques. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Provide phase plane analysis if necessary.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Find number of persons in a part with 66 handshakes Combinations; Author: Anil Kumar;https://www.youtube.com/watch?v=33TgLi-wp3E;License: Standard YouTube License, CC-BY
Discrete Math 6.3.1 Permutations and Combinations; Author: Kimberly Brehm;https://www.youtube.com/watch?v=J1m9sB5XZQc;License: Standard YouTube License, CC-BY
How to use permutations and combinations; Author: Mario's Math Tutoring;https://www.youtube.com/watch?v=NEGxh_D7yKU;License: Standard YouTube License, CC-BY
Permutations and Combinations | Counting | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=0NAASclUm4k;License: Standard Youtube License
Permutations and Combinations Tutorial; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=XJnIdRXUi7A;License: Standard YouTube License, CC-BY