Mathematics for Elementary Teachers with Activities, Loose-Leaf Version Plus MyLab Math -- Access Card Package (5th Edition)
5th Edition
ISBN: 9780134800196
Author: Sybilla Beckmann
Publisher: PEARSON
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Chapter 12.8, Problem 2P
Sarah is confused about the difference between the perimeter and the area of a
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(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 12 Solutions
Mathematics for Elementary Teachers with Activities, Loose-Leaf Version Plus MyLab Math -- Access Card Package (5th Edition)
Ch. 12.1 - You have a 5-foot-by-7-foot rectangular rug in...Ch. 12.1 - Draw a 3-cm-by-7-cm rectangle. Then discuss the...Ch. 12.1 - a. Explain how to decompose the large rectangle in...Ch. 12.1 - a. Explain how to decompose the large rectangle in...Ch. 12.1 - Draw a (fairly long) line segment and designate it...Ch. 12.2 - Make a shape that has area 25in2 but that has no...Ch. 12.2 - Flgure 12.14 shows the floor plan for a one-story...Ch. 12.2 - An area problem: The Johnsons are planning to...Ch. 12.2 - Figure 12.15 shows a design for an herb garden,...Ch. 12.2 - Figure 12.16 [g shows the floor plan for a modern,...
Ch. 12.2 - Use the moving and additivity principles to...Ch. 12.2 - Use the moving and additivity principles to...Ch. 12.3 - Use the moving and additivity principles to...Ch. 12.3 - For each triangle in Figure 12.31 , show the...Ch. 12.3 - Use a ruler and compass to draw three identical...Ch. 12.3 - Explain clearly in your own words why the...Ch. 12.3 - Explain clearly in your own words why the...Ch. 12.3 - Becky was asked to divide a rectangle into 4 equal...Ch. 12.3 - Explain how to use the additivity principle to...Ch. 12.3 - Determine the area of the shaded triangle that is...Ch. 12.3 - Determine the area of the shaded shape in Figure...Ch. 12.3 - Determine the area of the shaded triangle in...Ch. 12.3 - Determine the area of the shaded shape in Figure...Ch. 12.3 - Determine the area of the shaded shape in Figure...Ch. 12.3 - Given that the rectangle ABCD in Figure 12.41 has...Ch. 12.4 - Josie has two wooden beams that are 15 feet long...Ch. 12.4 - Figure 12.47 shows a shaded parallelogram inside a...Ch. 12.4 - In the text, we saw a way to explain why the area...Ch. 12.4 - Figure 12.49 shows a trapezoid. This problem will...Ch. 12.4 - Use the moving and additivity principles to...Ch. 12.4 - Find a formula for the area of a rhombus (see...Ch. 12.4 - Determine the areas (in square units) of the 4...Ch. 12.4 - Determine the area (in square units) of the...Ch. 12.4 - Determine the area of the shaded shapes in Figure...Ch. 12.4 - A rug company weaves rugs that are made by...Ch. 12.4 - Determine the area of the shaded region in Figure...Ch. 12.4 - Given that the shaded shape in Figure 12.58 is a...Ch. 12.4 - Figure 12.59 shows a map of some land. Determine...Ch. 12.5 - Figure 12.68 shows a triangle on a pegboard....Ch. 12.5 - Make a drawing to show the result of shearing the...Ch. 12.5 - Prob. 3PCh. 12.5 - Make a drawing to show the result of shearing the...Ch. 12.5 - a. Make a drawing to show the result of shearing...Ch. 12.5 - The boundary between the Johnson and the Zhang...Ch. 12.5 - Suppose that in a trapezoid ABCD, as in Figure...Ch. 12.5 - Prob. 8PCh. 12.6 - In your own words. discuss how the diameter and...Ch. 12.6 - Tim works on the following exercise: For each...Ch. 12.6 - A large running track is constructed to have...Ch. 12.6 - Suppose you have a large spool used for winding...Ch. 12.6 - Suppose that when pizza dough is rolled out it...Ch. 12.6 - Lauriann and Kinsey are in charge of the annual...Ch. 12.6 - Penguins huddle together to stay warm in very cold...Ch. 12.6 - Jack has a truck that requires tires that are 26...Ch. 12.6 - Let r units denote the radius of each circle in...Ch. 12.7 - Suppose that you have a map on which 1 inch...Ch. 12.7 - Suppose that you have a map on which 1 inch...Ch. 12.7 - Suppose that you have a map on which 1 inch...Ch. 12.8 - Suppose that a student in your class wants to know...Ch. 12.8 - Sarah is confused about the difference between the...Ch. 12.8 - Describe a concrete way to demonstrate that many...Ch. 12.8 - Anya wants to draw many different rectangles that...Ch. 12.8 - On graph paper, draw 4 different rectangles that...Ch. 12.8 - Which of the lengths that follow could be the...Ch. 12.8 - a. Without using a calculator, fund the lengths...Ch. 12.8 - Draw 4 different rectangles, all of which have a...Ch. 12.8 - Draw 4 different rectangles, all of which have...Ch. 12.8 - A forest has a perimeter of 210 mi, but no...Ch. 12.8 - Bob wants to find the area of an irregular shape....Ch. 12.8 - Consider all rectangles whose area is 4 in2 ,...Ch. 12.9 - Jessica says she doesn‘t understand the...Ch. 12.9 - Town B is 380 km due south of town A. Town C is...Ch. 12.9 - What length ribbon will you need to stretch from...Ch. 12.9 - Rover the dog is on a 30-foot leash. One end of...Ch. 12.9 - Carmina and Antone measure that the distance...Ch. 12.9 - Use the Pythagorean theorem to help you determine...Ch. 12.9 - Assuming that the earth is a perfectly round,...
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- 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
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