Using and Understanding Mathematics: A Quantitative Reasoning Approach plus NEW MyMathLab with Pearson eText -- Access Card Package (6th Edition) (Bennett Science & Math Titles)
6th Edition
ISBN: 9780321923219
Author: Jeffrey O. Bennett, William L. Briggs
Publisher: PEARSON
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Chapter 5.B, Problem 33E
Bias. Identify at least one potential source of bias in the followrng studies. Explain why the bias would or would not affect your view of the study.
33. Planned Parenthood members are surveyed to determine whether American adults prefer abstinence, counseling and education, or morning-after pills for high school students.
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(c) Let
6
0 0
A =
-10 4 8
5 1 2
(i) Find the characteristic polynomial of A and factorise it.
(ii) Determine all eigenvalues of A and find bases for the corresponding
eigenspaces.
(iii) Is A diagonalisable? Give reasons for your answer.
Drapers' Bank offers loans and deposits with interest rate 5% compounded monthly.
(a)
If you deposit £5,000 in a Drapers' Bank account, how much money will be in your account 4 years from now? Enter your answer correct to the
nearest pound.
Answer:
(b) What is the effective interest rate of a Drapers' Bank account? Enter your answer as a percentage correct to 3 significant digits.
Answer:
(c)
Drapers' Bank gives you a loan of £60,000 to start a new company under the condition that you pay back the loan in monthly instalments of EC to
be paid at the end of each month over the next 5 years, starting at the end of this month. Determine the value of C and enter it correct to the nearest pound.
Answer:
most 2, and let
Let P2 denote the vector space of polynomials of degree at
D: P2➡ P2
be the transformation that sends a polynomial p(t) = at² + bt+c in P2 to its derivative
p'(t)
2at+b, that is,
D(p) = p'.
(a) Prove that D is a linear transformation.
(b) Find a basis for the kernel ker(D) of the linear transformation D and compute its
nullity.
(c) Find a basis for the image im(D) of the linear transformation D and compute its
rank.
(d) Verify that the Rank-Nullity Theorem holds for the linear transformation D.
(e) Find the matrix representation of D in the standard basis (1,t, t2) of P2.
Chapter 5 Solutions
Using and Understanding Mathematics: A Quantitative Reasoning Approach plus NEW MyMathLab with Pearson eText -- Access Card Package (6th Edition) (Bennett Science & Math Titles)
Ch. 5.A - You conduct a poll in which you randomly select...Ch. 5.A - Results of the poll described in question 1 would...Ch. 5.A - When we say that a sample is representative of the...Ch. 5.A - Consider an experiment designed to test whether...Ch. 5.A - The experiment described in question 4 is a....Ch. 5.A - The purpose of a placebo is a. to prevent...Ch. 5.A - Prob. 7QQCh. 5.A - An experiment is single-blind if a. it lacks a...Ch. 5.A - Poll X predicts that Powell will receive 49% of...Ch. 5.A - A survey reveals that 12% of Americans believe...
Ch. 5.A - 1. Why do we say that the term statistics has two...Ch. 5.A - 2. Define the terms populatíon, sample, population...Ch. 5.A - Describe the five basic steps in a statistical...Ch. 5.A - Why is a so important that a statistical study use...Ch. 5.A - Prob. 5ECh. 5.A - Prob. 6ECh. 5.A - What is a placebo? Describe the placebo effect and...Ch. 5.A - What is meant by the margin of error in a survey...Ch. 5.A - In my experimental study, I used a sample that was...Ch. 5.A - I followed all the guidelines for sample selection...Ch. 5.A - I wanted to test the effects of vitamin C on...Ch. 5.A - I don’t believe the results of the experiment...Ch. 5.A - Prob. 13ECh. 5.A - By choosing my sample carefully, I can make a good...Ch. 5.A - Population and Sample. For the following studies,...Ch. 5.A - 15–20: Population and Sample. For the following...Ch. 5.A - 15–20: Population and Sample. For the following...Ch. 5.A - 15–20: Population and Sample. For the following...Ch. 5.A - Population and Sample. For the following studies,...Ch. 5.A - Population and Sample. For the following studies,...Ch. 5.A - Steps in a Study. Describe how you would apply the...Ch. 5.A - Prob. 22ECh. 5.A - Prob. 23ECh. 5.A - Steps in a Study. Describe how you would apply the...Ch. 5.A - Prob. 25ECh. 5.A - Prob. 26ECh. 5.A - Representative Sample? You want to determine the...Ch. 5.A - Representative Sample? You want to determine the...Ch. 5.A - Identify the Sampling Method. Identify the...Ch. 5.A - Identify the Sampling Method. Identify the...Ch. 5.A - Identify the Sampling Method. Identify the...Ch. 5.A - 29–34: Identify the Sampling Method. Identify the...Ch. 5.A - Identify the Sampling Method. Identify the...Ch. 5.A - Identify the Sampling Method. Identify the...Ch. 5.A - Type of Study. Determine whether the following...Ch. 5.A - Type of Study. Determine whether the following...Ch. 5.A - Type of Study. Determine whether the following...Ch. 5.A - Type of Study. Determine whether the following...Ch. 5.A - Type of Study. Determine whether the following...Ch. 5.A - Type of Study. Determine whether the following...Ch. 5.A - What Type of Study? What type of statistical study...Ch. 5.A - What Type of Study? What type of statistical study...Ch. 5.A - What Type of Study? What type of statistical study...Ch. 5.A - Prob. 44ECh. 5.A - Prob. 45ECh. 5.A - Prob. 46ECh. 5.A - Margin of Error. The following summaries of...Ch. 5.A - Prob. 48ECh. 5.A - Margin of Error. The following summaries of...Ch. 5.A - Margin of Error. The following summaries of...Ch. 5.A - Prob. 51ECh. 5.A - Prob. 52ECh. 5.A - Prob. 53ECh. 5.A - Prob. 54ECh. 5.A - Real Studies. Consider the following statistical...Ch. 5.A - Real Studies. Consider the following statistical...Ch. 5.A - Prob. 57ECh. 5.A - Prob. 58ECh. 5.A - Prob. 59ECh. 5.A - Prob. 60ECh. 5.A - Statistics in the News. Select three news stories...Ch. 5.A - 62. Statistics in Your Major. Write two to three...Ch. 5.A - Prob. 63ECh. 5.A - Prob. 64ECh. 5.A - 65. Poor Sampling. Find a new article about a...Ch. 5.A - 66. Good Sampling. Find a recent news article that...Ch. 5.A - 67. Margin of Error. Find a report of a recent...Ch. 5.A - Prob. 68ECh. 5.A - Prob. 69ECh. 5.B - You read about an issue that was the subject of an...Ch. 5.B - A study conducted by the oil company Exxon Mobil...Ch. 5.B - Consider a study designed to learn about the...Ch. 5.B - The show American Idol selects winners based on...Ch. 5.B - Consider an experiment in which you measure the...Ch. 5.B - Consider a survey in which 1000 people are asked...Ch. 5.B - Imagine that a survey of randomly selected people...Ch. 5.B - You want to know whether people prefer Smith or...Ch. 5.B - A self-selected survey is one in which a. the...Ch. 5.B - If a statistical study is carefully conducted tn...Ch. 5.B - Prob. 1ECh. 5.B - Prob. 2ECh. 5.B - Prob. 3ECh. 5.B - Prob. 4ECh. 5.B - The TV survey got more than 1 million...Ch. 5.B - Thc survey of religious beliefs suffered from...Ch. 5.B - My experiment proved beyond a doubt that vitamin C...Ch. 5.B - Everyone who jogs for exercise should try the new...Ch. 5.B - Should You Believe This Study? Based solely on the...Ch. 5.B - Should You Believe This Study? Based solely on the...Ch. 5.B - Prob. 11ECh. 5.B - 9–20: Should You Believe This Study? Based solely...Ch. 5.B - Should You Believe This Study? Based solely on the...Ch. 5.B - Should You Believe This Study? Based solely on the...Ch. 5.B - Should You Believe This Study? Based solely on the...Ch. 5.B - Should You Believe This Study? Based solely on the...Ch. 5.B - Prob. 17ECh. 5.B - Should You Believe This Study? Based solely on the...Ch. 5.B - Should You Believe This Study? Based solely on the...Ch. 5.B - Prob. 20ECh. 5.B - 21–26: Should You Believe This Claim? Based solely...Ch. 5.B - Should You Believe This Claim? Based solely on the...Ch. 5.B - Prob. 23ECh. 5.B - Prob. 24ECh. 5.B - Prob. 25ECh. 5.B - Should You Believe This Claim? Based solely on the...Ch. 5.B - Prob. 27ECh. 5.B - Prob. 28ECh. 5.B - Prob. 29ECh. 5.B - Prob. 30ECh. 5.B - Prob. 31ECh. 5.B - Prob. 32ECh. 5.B - Bias. Identify at least one potential source of...Ch. 5.B - Prob. 34ECh. 5.B - 35. Its All in the Wording. Princeton Survey...Ch. 5.B - Prob. 36ECh. 5.B - Prob. 37ECh. 5.B - Stat-Bytes. Much like sound bytes of news stories,...Ch. 5.B - Prob. 39ECh. 5.B - Prob. 40ECh. 5.B - Prob. 41ECh. 5.B - Prob. 42ECh. 5.B - Accurate Headlines? Consider the following...Ch. 5.B - 43–44: Accurate Headlines? Consider the following...Ch. 5.B - 45. What is the Question? Discuss the differences...Ch. 5.B - 46. Exercise and Dementia. A recent study in the...Ch. 5.B - Prob. 47ECh. 5.B - Prob. 48ECh. 5.B - Prob. 49ECh. 5.B - Prob. 50ECh. 5.C - Prob. 1QQCh. 5.C - For the class described in question 1, what was...Ch. 5.C - Prob. 3QQCh. 5.C - The sizes of the wedges in a pie chart tell you a....Ch. 5.C - You have a table listing ten tourist attractions...Ch. 5.C - In the table of tourist attractions and visitors...Ch. 5.C - You have a list of the GPAs of 100 college...Ch. 5.C - You have a list of the average gasoline price for...Ch. 5.C - A histogram is a. a graph that shows how some...Ch. 5.C - You have a histogram and you want to convert it...Ch. 5.C - Prob. 1ECh. 5.C - Prob. 2ECh. 5.C - Prob. 3ECh. 5.C - Prob. 4ECh. 5.C - Prob. 5ECh. 5.C - 6. What two types of graphs are most common when...Ch. 5.C - I made a frequency table with two columns, one...Ch. 5.C - The relative frequency of B grades in our class...Ch. 5.C - Prob. 9ECh. 5.C - Prob. 10ECh. 5.C - Prob. 11ECh. 5.C - Your pie chart must be wrong, because when I added...Ch. 5.C - Prob. 13ECh. 5.C - I rearranged the bars on my histogram the tallest...Ch. 5.C - Prob. 15ECh. 5.C - Frequency Tables. Make frequency table for the...Ch. 5.C - Prob. 17ECh. 5.C - Qualitative versus Quantitative. Determine whether...Ch. 5.C - Prob. 19ECh. 5.C - Qualitative versus Quantitative. Determine whether...Ch. 5.C - Qualitative versus Quantitative. Determine whether...Ch. 5.C - Qualitative versus Quantitative. Determine whether...Ch. 5.C - 17–24: Qualitative versus Quantitative. Determine...Ch. 5.C - Qualitative versus Quantitative. Determine whether...Ch. 5.C - Binned Frequency Tables. Use the given bin sizes...Ch. 5.C - Binned Frequency Tables. Use the given bin sizes...Ch. 5.C - Largest States. Make a bar graph of the...Ch. 5.C - Prob. 28ECh. 5.C - Prob. 29ECh. 5.C - Pie Charts. Construct pie charts for the following...Ch. 5.C - Oscar-Winning Actors. The following frequcncy...Ch. 5.C - 32. Teacher Salaries. The following table shows...Ch. 5.C - 13. Cell Phone Subscriptions. The following table...Ch. 5.C - Prob. 34ECh. 5.C - Prob. 35ECh. 5.C - Prob. 36ECh. 5.C - Prob. 37ECh. 5.C - Prob. 38ECh. 5.C - Prob. 39ECh. 5.C - Prob. 40ECh. 5.C - Prob. 41ECh. 5.C - Prob. 42ECh. 5.C - Prob. 43ECh. 5.C - Alcohol-Related Motor Vehicle Fatalities. Figure...Ch. 5.C - Prob. 45ECh. 5.C - Prob. 46ECh. 5.C - Prob. 47ECh. 5.C - Prob. 48ECh. 5.C - 49. Bar Graph. Find a recent news article tha...Ch. 5.C - 50. Pie Chart. Find a recent news article that...Ch. 5.C - 51. Histogram. Find a recent news article that...Ch. 5.C - 52. Line Chart. Find a recent news article that...Ch. 5.C - 53. Making a Frequency Table. The following...Ch. 5.C - Prob. 54ECh. 5.C - Prob. 55ECh. 5.C - Prob. 56ECh. 5.C - Prob. 57ECh. 5.D - Prob. 1QQCh. 5.D - Prob. 2QQCh. 5.D - Consider Figure 5.16. According to this graph,...Ch. 5.D - Prob. 4QQCh. 5.D - Prob. 5QQCh. 5.D - Prob. 6QQCh. 5.D - Prob. 7QQCh. 5.D - Prob. 8QQCh. 5.D - 9. Consider Figure 5.22(a). Moving one tick mark...Ch. 5.D - 10. Consider Figure 5.23(a). In years where the...Ch. 5.D - Briefly describe the construction and use of...Ch. 5.D - What are geographical data? Briefly describe at...Ch. 5.D - What are three-dimensional graphics? Explain the...Ch. 5.D - What are infographics, and what is their goal?Ch. 5.D - Prob. 5ECh. 5.D - 6. What is an exponential scale? When is an...Ch. 5.D - Explain how a graph that shows percentage change...Ch. 5.D - Prob. 8ECh. 5.D - My bar chart contains more information than yours,...Ch. 5.D - 10. I used an exponential scale because the data...Ch. 5.D - Prob. 11ECh. 5.D - A graph showing the yearly rate of increase in the...Ch. 5.D - 13. Net Grain Production. Net grain production is...Ch. 5.D - Education and Earnings. Examine Figure 5.l2(a),...Ch. 5.D - 15. Education and Earnings. Examine Figure...Ch. 5.D - Gender and Test Scores. Consider the data...Ch. 5.D - Gender and Test Scores. Consider the data...Ch. 5.D - Prob. 18ECh. 5.D - College Costs Stack Plot. Answer the following...Ch. 5.D - College Degrees. Figure 5.26 shows the numbers of...Ch. 5.D - Federal Spending. Figure 5.27 shows the major...Ch. 5.D - Melanoma Mortality. Figure 5.28 shows the female...Ch. 5.D - Contour Maps. Consider the contour map in Figure...Ch. 5.D - Prob. 24ECh. 5.D - Prob. 25ECh. 5.D - Prob. 26ECh. 5.D - Prob. 27ECh. 5.D - Three-DimensionaI Pies. The pie charts in Figure...Ch. 5.D - Prob. 29ECh. 5.D - Prob. 30ECh. 5.D - Cell Phone Users. The following table shows the...Ch. 5.D - Prob. 32ECh. 5.D - World Population. Recast the population data in...Ch. 5.D - Prob. 34ECh. 5.D - HIV Distribution. Figure 5.36 displays the wealth...Ch. 5.D - Creating Graphics. Make a graphical display of the...Ch. 5.D - Prob. 37ECh. 5.D - Prob. 38ECh. 5.D - 36-40: Creating Graphics. Make a graphical display...Ch. 5.D - Prob. 40ECh. 5.D - Prob. 41ECh. 5.D - Prob. 42ECh. 5.D - Prob. 43ECh. 5.D - Prob. 44ECh. 5.D - Prob. 45ECh. 5.D - 46. Interactive Infographics. Find a few examples...Ch. 5.E - If X is correlated with Y, a. X causes Y. b....Ch. 5.E - Prob. 2QQCh. 5.E - If the points on a scatterplot fall on a nearly...Ch. 5.E - If the points on a scatterplot fall into a broad...Ch. 5.E - When can you rule out the possibility that changes...Ch. 5.E - What type of correlation would you expect between...Ch. 5.E - You have found a higher rate of birth defects...Ch. 5.E - Based on the data in Figure 5.38, abou how much...Ch. 5.E - Which of the following statements best describes...Ch. 5.E - A finding by a jury that a pcrson is guilty...Ch. 5.E - What is a correlation? Give three examples of...Ch. 5.E - What is a scatterplot, and how is one made? How...Ch. 5.E - Prob. 3ECh. 5.E - Describe the three general categories of...Ch. 5.E - 5. Briefly describe each of the six guidelines...Ch. 5.E - Briefly describe three levels of confidence in...Ch. 5.E - There is a strong negative correlation between the...Ch. 5.E - There is a strong positive correlation between the...Ch. 5.E - I found a nearly perfect positive correlation...Ch. 5.E - I found a nearly perfect negative correlation...Ch. 5.E - I had originally suspected that an increase in...Ch. 5.E - Prob. 12ECh. 5.E - Interpreting Scatterplots. Consider the following...Ch. 5.E - Prob. 14ECh. 5.E - Interpreting Scatterplots. Consider the following...Ch. 5.E - 13–16: Interpreting Scatterplots. Consider the...Ch. 5.E - Types of Correlation. For the following pairs of...Ch. 5.E - Types of Correlation. For the following pairs of...Ch. 5.E - Types of Correlation. For the following pairs of...Ch. 5.E - Types of Correlation. For the following pairs of...Ch. 5.E - 17–24: Types of Correlation. For the following...Ch. 5.E - Types of Correlation. For the following pairs of...Ch. 5.E - 17–24: Types of Correlation. For the following...Ch. 5.E - Types of Correlation. For the following pairs of...Ch. 5.E - Making Satterplots. Consider the following data...Ch. 5.E - Making Satterplots. Consider the following data...Ch. 5.E - Making Satterplots. Consider the following data...Ch. 5.E - Prob. 28ECh. 5.E - Making Satterplots. Consider the following data...Ch. 5.E - Making Satterplots. Consider the following data...Ch. 5.E - Federal Aid and Representation. For each of 31...Ch. 5.E - Correlation and Causality. Consider the following...Ch. 5.E - Correlation and Causality. Consider the following...Ch. 5.E - Correlation and Causality. Consider the following...Ch. 5.E - Correlation and Causality. Consider the following...Ch. 5.E - Correlation and Causality. Consider the following...Ch. 5.E - Prob. 37ECh. 5.E - 38. Identifying Causes: Headaches. You are trying...Ch. 5.E - 39. Smoking and Lung Cancer. There is a strong...Ch. 5.E - Prob. 40ECh. 5.E - Prob. 41ECh. 5.E - Prob. 42ECh. 5.E - Prob. 43ECh. 5.E - Prob. 44ECh. 5.E - Prob. 45ECh. 5.E - Prob. 46ECh. 5.E - Prob. 47ECh. 5.E - Prob. 48E
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