Pearson eText for Mathematics for Elementary Teachers with Activities -- Instant Access (Pearson+)
5th Edition
ISBN: 9780137442812
Author: Sybilla Beckmann
Publisher: PEARSON+
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Chapter 16.3, Problem 9P
Suppose you have a penny, a nickel, a dime, and a quarter in a bag. You shake the bag and dump out the coins. What is the probability that exactly 2 coins will land heads up and 2 coins will land heads down? Is the probability 50% or not? Solve this problem by drawing a tree diagram that shows all the possible outcomes when you dump the coins out. Explain.
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2. Consider the ODE
u' = ƒ (u) = u² + r
where r is a parameter that can take the values r = −1, −0.5, -0.1, 0.1. For each value of r:
(a) Sketch ƒ(u) = u² + r and determine the equilibrium points.
(b) Draw the phase line.
(d) Determine the stability of the equilibrium points.
(d) Plot the direction field and some sample solutions,i.e., u(t)
(e) Describe how location of the equilibrium points and their stability change as you increase the
parameter r.
(f) Using the matlab program phaseline.m generate a solution for each value of r and the initial
condition u(0) = 0.9. Print and turn in your result for r = −1. Do not forget to add a figure caption.
(g) In the matlab program phaseline.m set the initial condition to u(0) = 1.1 and simulate the ode
over the time interval t = [0, 10] for different values of r. What happens? Why? You do not need to
turn in a plot for (g), just describe what happens.
The following are suggested designs for group sequential studies. Using PROCSEQDESIGN, provide the following for the design O’Brien Fleming and Pocock.• The critical boundary values for each analysis of the data• The expected sample sizes at each interim analysisAssume the standardized Z score method for calculating boundaries.Investigators are evaluating the success rate of a novel drug for treating a certain type ofbacterial wound infection. Since no existing treatment exists, they have planned a one-armstudy. They wish to test whether the success rate of the drug is better than 50%, whichthey have defined as the null success rate. Preliminary testing has estimated the successrate of the drug at 55%. The investigators are eager to get the drug into production andwould like to plan for 9 interim analyses (10 analyzes in total) of the data. Assume thesignificance level is 5% and power is 90%.Besides, draw a combined boundary plot (OBF, POC, and HP)
4. Solve the system of equations and express your solution using vectors.
2x1 +5x2+x3 + 3x4 = 9
-x2+x3 + x4 = 1
-x1-6x2+3x3 + 2x4
= -1
Chapter 16 Solutions
Pearson eText for Mathematics for Elementary Teachers with Activities -- Instant Access (Pearson+)
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...
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