Connect Math hosted by ALEKS Access Card 52 Weeks for Math in Our World
3rd Edition
ISBN: 9781259232848
Author: David Sobecki, Allan Bluman
Publisher: McGraw-Hill Education
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Chapter 12.8, Problem 17E
(a)
To determine
To draw: The
(b)
To determine
To find: The
(c)
To determine
To test: The significance of
(d)
To determine
To find: The equation of the regression line for the variables x and y as well as draw the line on the scatter plot when, r is significant.
(e)
To determine
To describe: The nature of the linear relationship for the given data sets, when it exist.
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This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one.
A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The
wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture.
A
B
A
B
at some instant, the piston will be tangent to the circle
(a) Express the x and y coordinates of point A as functions of t:
x= 2 cos(3πt)
and y= 2 sin(3t)
(b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds:
-cot(3πt)
sin(3лt)
(c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411-
4
-2 sin (3лt)
(d)…
5. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.AE.003.
y
y= ex²
0
Video Example
x
EXAMPLE 3
(a) Use the Midpoint Rule with n = 10 to approximate the integral
कर
L'ex²
dx.
(b) Give an upper bound for the error involved in this approximation.
SOLUTION
8+2
1
L'ex² d
(a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.)
dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)]
0.1 [0.0025 +0.0225
+
+ e0.0625 + 0.1225
e0.3025 + e0.4225
+ e0.2025
+
+ e0.5625 €0.7225 +0.9025]
The figure illustrates this approximation.
(b) Since f(x) = ex², we have f'(x)
=
0 ≤ f'(x) =
< 6e.
ASK YOUR TEACHER
and f'(x) =
Also, since 0 ≤ x ≤ 1 we have x² ≤
and so
Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final
answer to five decimal places.)
6e(1)3
e
24(
=
≈
1. Consider the following preference ballots:
Number of voters
Rankings 6 5 4 2
1st choice A DCB
DC
2nd choice B B D
3rd choice DCBD
4th choice CA
AAA
For each of the four voting systems we have studied, determine who would win the election
in each case. (Remember: For plurality with runoff, all but the top two vote-getters are
simultaneously eliminated at the end of round 1.)
Chapter 12 Solutions
Connect Math hosted by ALEKS Access Card 52 Weeks for Math in Our World
Ch. 12.1 - To study the number of credit hours taken by a...Ch. 12.1 - A health-food store recorded the type of vitamin...Ch. 12.1 - In one math class, the data below represent the...Ch. 12.1 - Prob. 4TTOCh. 12.1 - What are data?Ch. 12.1 - Define statistics.Ch. 12.1 - Explain the difference between a population and a...Ch. 12.1 - How is a random sample selected?Ch. 12.1 - How is a systematic sample selected?Ch. 12.1 - How is a stratified sample selected?
Ch. 12.1 - How is a cluster sample selected?Ch. 12.1 - Prob. 8ECh. 12.1 - Describe the difference between descriptive and...Ch. 12.1 - How do inductive and deductive reasoning play a...Ch. 12.1 - For Exercises 1116, classify each sample as...Ch. 12.1 - For Exercises 1116, classify each sample as...Ch. 12.1 - For Exercises 1116, classify each sample as...Ch. 12.1 - For Exercises 1116, classify each sample as...Ch. 12.1 - For Exercises 1116, classify each sample as...Ch. 12.1 - For Exercises 1116, classify each sample as...Ch. 12.1 - In Exercises 1722, decide if you think the method...Ch. 12.1 - In Exercises 172, decide if you think the method...Ch. 12.1 - In Exercises 1722, decide if you think the method...Ch. 12.1 - In Exercises 1722, decide if you think the method...Ch. 12.1 - In Exercises 1722, decide if you think the method...Ch. 12.1 - In Exercises 1722, decide if you think the method...Ch. 12.1 - At a college financial aid office students who...Ch. 12.1 - A questionnaire about how students primarily get...Ch. 12.1 - Twenty-five fans of reality TV were asked to rate...Ch. 12.1 - A small independent developer of apps for...Ch. 12.1 - The ages of the signers of the Declaration of...Ch. 12.1 - The percentage of traffic fatalities in which at...Ch. 12.1 - The data shown are the cigarette taxes per pack in...Ch. 12.1 - The acreage (in thousands of acres) of the 39 U.S....Ch. 12.1 - The heights in feet above sea level of the major...Ch. 12.1 - During the 1998 baseball season. Mark McGwire and...Ch. 12.1 - The data (in millions of dollars) are the values...Ch. 12.1 - Twenty-nine executives reported the number of...Ch. 12.1 - The National Insurance Crime Bureau reported that...Ch. 12.1 - Prob. 36ECh. 12.1 - The data shown represent the percentage of...Ch. 12.1 - Prob. 38ECh. 12.1 - For Exercises 3944, decide whether descriptive or...Ch. 12.1 - For Exercises 3944, decide whether descriptive or...Ch. 12.1 - For Exercises 3944, decide whether descriptive or...Ch. 12.1 - For Exercises 3944, decide whether descriptive or...Ch. 12.1 - For Exercises 3944, decide whether descriptive or...Ch. 12.1 - Prob. 44ECh. 12.1 - In addition to the four basic sampling methods,...Ch. 12.1 - For the data in Exercise 33, draw a stem and leaf...Ch. 12.1 - Prob. 51ECh. 12.1 - Prob. 52ECh. 12.2 - The frequency distribution below represents...Ch. 12.2 - Prob. 2TTOCh. 12.2 - Prob. 3TTOCh. 12.2 - Prob. 4TTOCh. 12.2 - Prob. 5TTOCh. 12.2 - Describe how to draw a bar graph and a pie chart...Ch. 12.2 - Explain why bar graphs and pie charts are...Ch. 12.2 - How are histograms and frequency polygons similar?...Ch. 12.2 - Describe the purpose of a time series graph.Ch. 12.2 - Draw a bar graph for the number of transplants of...Ch. 12.2 - The data below show the number of students...Ch. 12.2 - Draw a bar graph for the number of registered...Ch. 12.2 - Prob. 8ECh. 12.2 - The number of students at one campus who had a 4.0...Ch. 12.2 - In an insurance company study of the causes of...Ch. 12.2 - In a survey of 100 college students, the numbers...Ch. 12.2 - Prob. 12ECh. 12.2 - For 108 randomly selected college applicants, the...Ch. 12.2 - Prob. 14ECh. 12.2 - Thirty cars and trucks were tested by the EPA for...Ch. 12.2 - Prob. 16ECh. 12.2 - The data below represent the number of people...Ch. 12.2 - Prob. 18ECh. 12.2 - The following data represent the number of...Ch. 12.2 - Prob. 20ECh. 12.2 - The data below are the avenge daily temperatures...Ch. 12.2 - The data below are the average daily temperatures...Ch. 12.2 - The number of employed registered nurses tin...Ch. 12.2 - Prob. 24ECh. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - Prob. 27ECh. 12.2 - Prob. 28ECh. 12.2 - Prob. 29ECh. 12.2 - Prob. 30ECh. 12.2 - Prob. 31ECh. 12.2 - Prob. 32ECh. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - Prob. 35ECh. 12.2 - Make up your own frequency polygon problem: using...Ch. 12.3 - To test a customers Internet connection, a tech...Ch. 12.3 - Prob. 2TTOCh. 12.3 - Prob. 3TTOCh. 12.3 - Prob. 4TTOCh. 12.3 - Prob. 5TTOCh. 12.3 - Prob. 6TTOCh. 12.3 - Prob. 7TTOCh. 12.3 - The number of earthquakes worldwide measuring at...Ch. 12.3 - Prob. 9TTOCh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Which of the measures of average can be used to...Ch. 12.3 - In Questions 710, describe some strengths and...Ch. 12.3 - In Questions 710, describe some strengths and...Ch. 12.3 - In Questions 710, describe some strengths and...Ch. 12.3 - In Questions 710, describe some strengths and...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 1122, find the mean, median, mode,...Ch. 12.3 - For Exercises 2330, find the mean of the data set....Ch. 12.3 - For Exercises 2330, find the mean of the data set....Ch. 12.3 - For Exercises 2330, find the mean of the data set....Ch. 12.3 - Prob. 26ECh. 12.3 - For Exercises 2330, find the mean of the data set....Ch. 12.3 - Prob. 28ECh. 12.3 - For Exercises 2330, find the mean of the data set....Ch. 12.3 - For Exercises 2330, find the mean of the data set....Ch. 12.3 - For these situations, state which measure of...Ch. 12.3 - For Exercises 3338, describe which measure of...Ch. 12.3 - For Exercises 3338, describe which measure of...Ch. 12.3 - For Exercises 3338, describe which measure of...Ch. 12.3 - For Exercises 3338, describe which measure of...Ch. 12.3 - For Exercises 3338, describe which measure of...Ch. 12.3 - For Exercises 3338, describe which measure of...Ch. 12.3 - Prob. 39ECh. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Prob. 42ECh. 12.3 - Prob. 43ECh. 12.3 - Prob. 44ECh. 12.3 - Prob. 45ECh. 12.3 - Prob. 46ECh. 12.3 - Prob. 47ECh. 12.3 - Prob. 48ECh. 12.4 - The monthly average high temperatures from January...Ch. 12.4 - Prob. 2TTOCh. 12.4 - Prob. 3TTOCh. 12.4 - Prob. 4TTOCh. 12.4 - Name three measures of variation.Ch. 12.4 - What is the range?Ch. 12.4 - Why is the range not usually the best measure...Ch. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12.4 - Prob. 6ECh. 12.4 - For Exercises 710, discuss the relative sizes of...Ch. 12.4 - For Exercises 710, discuss the relative sizes of...Ch. 12.4 - For Exercises 710, discuss the relative sizes of...Ch. 12.4 - Prob. 10ECh. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - For Exercises 1126, find the range, variance, and...Ch. 12.4 - The three data sets have the same mean and range,...Ch. 12.4 - Prob. 28ECh. 12.5 - The weights in pounds for the 12 members of a...Ch. 12.5 - Prob. 2TTOCh. 12.5 - Prob. 3TTOCh. 12.5 - Prob. 4TTOCh. 12.5 - Prob. 5TTOCh. 12.5 - If your score in your math class puts you in the...Ch. 12.5 - Does a score in the 90th percentile mean that you...Ch. 12.5 - Explain what quartiles are.Ch. 12.5 - Prob. 4ECh. 12.5 - What does the portion inside the box in a box plot...Ch. 12.5 - What is meant by the term outlier? How can you...Ch. 12.5 - The scores for 20 students on a 50-point math test...Ch. 12.5 - The heights (in inches) of the 12 students in a...Ch. 12.5 - In a class of 500 students, Carvetas rank was 125....Ch. 12.5 - In a class of 400 students, Johns rank was 80....Ch. 12.5 - In a charity marathon to raise money for AIDS...Ch. 12.5 - An investor decides to buy stock only in companies...Ch. 12.5 - On an exam, Angela scored in the 20th percentile....Ch. 12.5 - Out of 600 applicants to a graduate program at an...Ch. 12.5 - Eldrick finished at the 77th percentile of a mens...Ch. 12.5 - Tinas application for a nursing position is ranked...Ch. 12.5 - Leas percentile rank on an exam in a class of 600...Ch. 12.5 - In an English class of 30 students, Audrelias...Ch. 12.5 - The Bowling Green State University mens basketball...Ch. 12.5 - A pro golfer is ranked 48th out of 230 players...Ch. 12.5 - In an evening statistics class, the ages of 20...Ch. 12.5 - Twenty subjects in a psychology class experiment...Ch. 12.5 - For Exercises 2328, find the values for Q1, Q2,...Ch. 12.5 - For Exercises 2328, find the values for Q1, Q2,...Ch. 12.5 - For Exercises 2328, find the values for Q1, Q2,...Ch. 12.5 - For Exercises 2328, find the values for Q1, Q2,...Ch. 12.5 - For Exercises 2328, find the values for Q1, Q2,...Ch. 12.5 - For Exercises 2328, find the values for Q1, Q2,...Ch. 12.5 - In Problems 2932, draw a box plot for the data,...Ch. 12.5 - Prob. 30ECh. 12.5 - In Problems 2932, draw a box plot for the data,...Ch. 12.5 - In Problems 2932, draw a box plot for the data,...Ch. 12.5 - Is it possible to score 90% on a test and have a...Ch. 12.5 - Prob. 34ECh. 12.5 - Prob. 35ECh. 12.5 - Prob. 36ECh. 12.5 - Prob. 37ECh. 12.5 - Prob. 38ECh. 12.6 - A standard test of intelligence is scaled so that...Ch. 12.6 - Prob. 2TTOCh. 12.6 - Find the area under the standard normal...Ch. 12.6 - Find the area under the standard normal...Ch. 12.6 - Prob. 5TTOCh. 12.6 - What is the distinguishing characteristic of a...Ch. 12.6 - Prob. 2ECh. 12.6 - What does the area under a portion of a normal...Ch. 12.6 - Explain what the empirical rule says.Ch. 12.6 - What percentage of the area under a normal curve...Ch. 12.6 - Why does it make sense that the total area under a...Ch. 12.6 - Prob. 7ECh. 12.6 - Prob. 8ECh. 12.6 - Prob. 9ECh. 12.6 - Prob. 10ECh. 12.6 - For Exercises 1116, the data set described is...Ch. 12.6 - Prob. 12ECh. 12.6 - For Exercises 1116, the data set described is...Ch. 12.6 - Prob. 14ECh. 12.6 - For Exercises 1116, the data set described is...Ch. 12.6 - Prob. 16ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 18ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 20ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 22ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 24ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 26ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 28ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 30ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 32ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 34ECh. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - For Exercises 1738, find the area under the...Ch. 12.6 - Prob. 38ECh. 12.6 - As we know from Chapter 11, the probability of an...Ch. 12.6 - As we know from Chapter 11, the probability of an...Ch. 12.6 - As we know from Chapter 11, the probability of an...Ch. 12.6 - As we know from Chapter 11, the probability of an...Ch. 12.6 - Prob. 43ECh. 12.6 - Prob. 44ECh. 12.6 - Find two z values, one positive and one negative...Ch. 12.7 - Based on data compiled by the World Health...Ch. 12.7 - The Statistical Abstract also indicates that of...Ch. 12.7 - The mean for a reading test given nationwide is...Ch. 12.7 - The ages of 33 randomly selected inmates at a...Ch. 12.7 - Explain why the normal distribution can be used to...Ch. 12.7 - Given a data set, how could you decide if the...Ch. 12.7 - Describe the connection between area under a...Ch. 12.7 - Prob. 4ECh. 12.7 - The average hourly wage for all workers in the...Ch. 12.7 - Prob. 6ECh. 12.7 - The average cost for two people to go to a movie...Ch. 12.7 - Average sales for an online textbook distributor...Ch. 12.7 - A survey found that people keep their televisions...Ch. 12.7 - The average age of CEOs is 56 years. Assume the...Ch. 12.7 - The average life of a brand of automobile tires is...Ch. 12.7 - The average time a person spends in each visit to...Ch. 12.7 - The average amount of snow per season in Trafford...Ch. 12.7 - The average waiting time for a drive-in window at...Ch. 12.7 - The average time it takes college freshmen to...Ch. 12.7 - A brisk walk at 4 miles per hour burns an average...Ch. 12.7 - During September, the average temperature of...Ch. 12.7 - If the systolic blood pressure for a certain group...Ch. 12.7 - An IQ test has a mean of 100 and a standard...Ch. 12.7 - The average size (in square feet) of homes built...Ch. 12.7 - According to the National Association of Realtors,...Ch. 12.7 - The average price of Stephen King paperbacks sold...Ch. 12.7 - Refer to Exercise 5. If your buddy Earl gets a job...Ch. 12.7 - Refer to Exercise 9. If you buy a TV for your dorm...Ch. 12.7 - Refer to Exercise 12. Suppose that your grades...Ch. 12.7 - Refer to Exercise 20. When the one-hit wonder band...Ch. 12.7 - In Problems 2730, (a) construct a histogram for...Ch. 12.7 - In Problems 2730, (a) construct a histogram for...Ch. 12.7 - In Problems 2730, (a) construct a histogram for...Ch. 12.7 - In Problems 2730, (a) construct a histogram for...Ch. 12.7 - Discuss whether or not you think each of the given...Ch. 12.7 - The number of incoming students at two campuses of...Ch. 12.7 - If a distribution of raw scores were plotted and...Ch. 12.7 - A researcher who is in charge of an educational...Ch. 12.7 - For the data provided in Exercise 27, find the...Ch. 12.7 - Prob. 38ECh. 12.8 - The data below represent the heights in feet and...Ch. 12.8 - Find the correlation coefficient for the data in...Ch. 12.8 - Prob. 3TTOCh. 12.8 - Find the equation of the regression line for the...Ch. 12.8 - Use the equation of the regression line found in...Ch. 12.8 - Describe what a scatter plot is and how one is...Ch. 12.8 - Explain what is meant when two variables are...Ch. 12.8 - Explain what is meant when two variables are...Ch. 12.8 - Prob. 4ECh. 12.8 - Prob. 5ECh. 12.8 - Prob. 6ECh. 12.8 - Describe the key difference between correlation...Ch. 12.8 - Prob. 8ECh. 12.8 - Prob. 9ECh. 12.8 - Prob. 10ECh. 12.8 - For the data sets in Exercises 1118, (a)Draw a...Ch. 12.8 - Prob. 12ECh. 12.8 - For the data sets in Exercises 1118, (a)Draw a...Ch. 12.8 - Prob. 14ECh. 12.8 - For the data sets in Exercises 1118, (a)Draw a...Ch. 12.8 - Prob. 16ECh. 12.8 - Prob. 17ECh. 12.8 - Prob. 18ECh. 12.8 - For the data sets in Exercises 1926, (a) Draw a...Ch. 12.8 - Prob. 20ECh. 12.8 - For the data sets in Exercises 1926, (a)Draw a...Ch. 12.8 - For the data sets in Exercises 1926, (a)Draw a...Ch. 12.8 - For the data sets in Exercises 1926, (a)Draw a...Ch. 12.8 - Prob. 24ECh. 12.8 - Prob. 25ECh. 12.8 - For the data sets in Exercises 1926, (a)Draw a...Ch. 12.8 - Prob. 27ECh. 12.8 - Prob. 28ECh. 12.8 - Prob. 29ECh. 12.8 - Design your own correlation problem. Think of two...Ch. 12.8 - Prob. 31ECh. 12.8 - Prob. 32ECh. 12.8 - Prob. 33ECh. 12.8 - Prob. 34ECh. 12.8 - Prob. 35ECh. 12.8 - Prob. 36ECh. 12.8 - Prob. 37ECh. 12.8 - Prob. 38ECh. 12.8 - Prob. 39ECh. 12.8 - Prob. 40ECh. 12 - A sporting goods store kept a record of sales of...Ch. 12 - The data set shown below represents the time in...Ch. 12 - During June, a local theater company recorded the...Ch. 12 - Construct a bar graph for the number of homicides...Ch. 12 - Draw a pie chart for the data in Exercies 4....Ch. 12 - Draw a histogram and frequency polygon for the...Ch. 12 - The data set shown below indicates how much Janine...Ch. 12 - The data below are the number of U.S. citizens (in...Ch. 12 - Twelve batteries were tested to see how many hours...Ch. 12 - In your own words, explain the difference between...Ch. 12 - The data below are the number of beds at the eight...Ch. 12 - Which data set do you think would have a greater...Ch. 12 - For the census data in Problem 8, (a)Find the...Ch. 12 - Find the quartiles for the data in Problem 8, then...Ch. 12 - Find the area under the standard normal...Ch. 12 - A doctor has treated 45 male patients this week....Ch. 12 - For a data set with 90 values that is normally...Ch. 12 - Prob. 18RECh. 12 - Prob. 19RECh. 12 - The average weight of an airline passengers...Ch. 12 - The average cost of Cheetah brand running shoes is...Ch. 12 - Prob. 22RECh. 12 - A study is done to see whether there is a...Ch. 12 - Prob. 24RECh. 12 - Prob. 1CTCh. 12 - Prob. 2CTCh. 12 - Prob. 3CTCh. 12 - The data (in millions of dollars) are the values...Ch. 12 - Prob. 5CTCh. 12 - Prob. 6CTCh. 12 - These temperatures were recorded in Pasadena for a...Ch. 12 - Prob. 8CTCh. 12 - Prob. 9CTCh. 12 - Prob. 10CTCh. 12 - A major brand of potato chips sells its product in...Ch. 12 - A study is conducted to determine the relationship...
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- Practice k Help ises A 96 Anewer The probability that you get a sum of at least 10 is Determine the number of ways that the specified event can occur when two number cubes are rolled. 1. Getting a sum of 9 or 10 3. Getting a sum less than 5 2. Getting a sum of 6 or 7 4. Getting a sum that is odd Tell whether you would use the addition principle or the multiplication principle to determine the total number of possible outcomes for the situation described. 5. Rolling three number cubes 6. Getting a sum of 10 or 12 after rolling three number cubes A set of playing cards contains four groups of cards designated by color (black, red, yellow, and green) with cards numbered from 1 to 14 in each group. Determine the number of ways that the specified event can occur when a card is drawn from the set. 7. Drawing a 13 or 14 9. Drawing a number less than 4 8. Drawing a yellow or green card 10. Drawing a black, red, or green car The spinner is divided into equal parts. Find the specified…arrow_forwardProblem 1.We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.(d) We assume that you sell the American put to a market participant A for the pricefound in (b). Explain how you act on the market…arrow_forwardWhat is the standard scores associated to the left of z is 0.1446arrow_forward
- 2. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.015. Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) ASK YOUR TEACHER 3 1 3 + dy, n = 6 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule Need Help? Read It Watch Itarrow_forwardThis question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. B A B at some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 2 cos(3πt) and y= 2 sin(3πt) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot (3πt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +41/1 (d) Express the slope of the rod…arrow_forwardConsider the proof below: Proposition: If m is an even integer, then 5m +4 is an even integer. Proof: We see that |5m+4=10n+4 = 2(5n+2). Therefore, 5m+4 is an even integer. **Note: you may assume the proof is valid, just poorly written. Based upon the Section 1.3 screencast and the reading assignment, select all writing guidelines that are missing in the proof. Proof begins by stating assumptions ✓ Proof has an invitational tone/uses collective pronouns Proof is written in complete sentences Each step is justified ☐ Proof has a clear conclusionarrow_forward
- Note: The purpose of this problem below is to use computational techniques (Excelspreadsheet, Matlab, R, Python, etc.) and code the dynamic programming ideas seen inclass. Please provide the numerical answer to the questions as well as a sample of yourwork (spreadsheet, code file, etc.).We consider an N-period binomial model with the following properties: N = 60, thecurrent stock price is S0 = 1000; on each period, the stock price increases by 0.5% whenit moves up and decreases by 0.3% when it moves down. The annual interest rate on themoney market is 5%. (Notice that this model is a CRR model, which means that thebinomial tree is recombining.)(a) Find the price at time t0 = 0 of a (European) call option with strike price K = 1040and maturity T = 1 year.(b) Find the price at time t0 = 0 of a (European) put option with strike price K = 1040and maturity T = 1 year.(c) We consider now, that you are at time t5 (i.e. after 5 periods, which represents 1month later). Assume that the stock…arrow_forward4. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.024. Find the approximations Tη, Mn, and S, to the integral computer algebra system.) ASK YOUR TEACHER PRACTICE ANOTHER 4 39 √ dx for n = 6 and 12. Then compute the corresponding errors ET, EM, and Es. (Round your answers to six decimal places. You may wish to use the sum command on a n Tn Mn Sp 6 12 n ET EM Es 6 12 What observations can you make? In particular, what happens to the errors when n is doubled? As n is doubled, ET and EM are decreased by a factor of about Need Help? Read It ' and Es is decreased by a factor of aboutarrow_forward6. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.001. ASK YOUR TEACHER PRACTICE ANOTHER Let I = 4 f(x) dx, where f is the function whose graph is shown. = √ ² F(x 12 4 y f 1 2 (a) Use the graph to find L2, R2 and M2. 42 = R₂ = M₂ = 1 x 3 4arrow_forward
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