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A Pathway To Introductory Statistics 1st Edition Jay Lehmann - Solutions
The number of U.S. patent applications was 520 thousand in 2010, and it increased by about 21.7 thousand per year until 2014. Let n be the number of patent applications (in thousands) during the year that is t years since 2010.a. Find an equation of a model.b. Estimate the number of patent
Substitute 0.9 for P(E OR F), 0.4 for P(E), and 0.7 for P(F) in the formula P1E OR F2 = P (E) + P (F) - P (E AND F), and then solve for P(E AND F).
The First Amendment says: €œCongress shall make no law respecting an establishment of religion or prohibiting the free exercise thereof, or abridging the freedom of speech or of the press, or the right of the people peaceably to assemble, and to petition the government for a redress of
Determine the slope and the y-intercept of the line 2x - 3y = 12. Use the slope and the y-intercept to graph the equation by hand.
3(2x + 1) ≤ 4 (x + 2) – 1Describe the solution set as an inequality, in interval notation, and on a graph.
½ < 3 – 5/2x ≤ 13Describe the solution set as an inequality, in interval notation, and on a graph.
The Internal Revenue Service (IRS) standard mileage rate is a way of computing an automobile expense deduction on a tax return. Mileage rates for businesses are provided in Table 36 for various years.Let M = f1t2 be the standard mileage rate (in cents per mile) at t years since 2000.a. Construct a
8 – 2 (3t – 1) = 7t
A student thinks that if a line has slope 2 and contains the point64. (3, 5), then the equation of the line is y = 2x + 5, because the slope is 2 (the coefficient of x) and the y-coordinate of (3, 5) is 5 (the constant term). What would you tell the student?
Consider the line that contains the points (-2, -6) and (4,3).a. Find an equation of the line.b. Sketch the line on a coordinate system.
Consider the line that contains the points (-3, 4) and (6, -2).a. Find an equation of the line.b. Sketch the line on a coordinate system.
Decide whether it is possible for a line to have the indicated number of x-intercepts. If it is possible, find an equation of such a line. If it is not possible, explain why not.a. no x-interceptsb. exactly one x-interceptc. exactly two x-interceptsd. an infinite number of x-intercepts
Decide whether it is possible for a line to have the indicated number of y-intercepts. If it is possible, find an equation of such a line. If it is not possible, explain why not.a. no y-interceptsb. exactly one y-interceptc. exactly two y-interceptsd. an infinite number of y-intercepts
Let E be the enrollment (in thousands of students) at a college t years after the college opens. Some pairs of values of t and E are listed in Table 2.a. Construct a scatterplot.b. Describe the four characteristics of the association.c. Find an equation that describes the association between t and
Let s be a person€™s savings (in thousands of dollars) at t years since 2000. Some pairs of values of t and s are listed in Table 3.a. Construct a scatterplot.b. Describe the four characteristics of the association.c. Find an equation that describes the association between t and s.d. Graph the
a. Use each of the following forms to find an equation of the line that contains the points (2, 1) and (4, 7). Write each result in slope–intercept form. i. Slope–intercept form ii. point–slope form b. Compare the results you found in parts (ai) and (aii).
a. Use each of the following forms to find an equation of the line that contains the points 1-4, 32 and 12, -52. Write each result in slope–intercept form. i. slope–intercept form ii. point–slope form b. Compare the results you found in parts (ai) and (aii).
a. Find an equation of a line with slope -2.b. Find an equation of a line with y-intercept (0, 4).c. Find an equation of a line that contains the point (3, 5).d. Determine whether there is a line that has slope -2 and y-intercept (0, 4) and contains the point (3, 5). Explain.
a. Graph y = 2x - 3 by hand.b. Choose two points that lie on the graph. Then use the two points to find an equation of the line that contains them. Compare your equation with the equation y = 2x - 3.
Find an equation of the line that contains the points (3, 7) and (4, 9). After finding the slope, you used one of the points to complete the process. Now use the other point to complete the process. Did you get the same result? Why does this makes sense?
The enrollments in an elementary algebra course at the College of San Mateo are shown in Table 13 for various Tuesdays leading up to the first day of class on Tuesday, January 17.Let E be the enrollment in the elementary algebra course at t weeks since November 22.a. Construct a scatterplot.b.
The percentages of births outside marriage in the United States are shown in Table 14 for various years.Let p be the percentage of births outside marriage in the United States at t years since 1900.a. Construct a scatterplot.b. Describe the four characteristics of the association. Compute and
Repeat Exercise 11, but let p be the percentage of births outside marriage in the United States at t years since 1970. Compare the slope of your model with the slope of the model you found in Exercise 11. Compare the p-intercepts. Explain why your comparisons make sense.Repeat exercise 11The
Table 15 lists world record times for the women€™s 400-meter run.Let r be the record time (in seconds) at t years since 1900.a. Construct a scatterplot.b. Describe the four characteristics of the association. Compute and interpret r as part of your analysis.c. Find an equation of a linear
Table 16 lists world record times for the men€™s 400-meter run.Let r be the record time (in seconds) at t years since 1900.a. Construct a scatterplot.b. Describe the four characteristics of the association. Compute and interpret r as part of your analysis.c. Find an equation of a linear
In Exercises 13 and 14, you found equations for the women’s and men’s 400-meter run record times. Equations that model the data well arer = -0.27t + 70.45………………….(women’s model)r = -0.053t + 48.08……………………(men’s model)where r represents the record time (in
The mean annual U.S. per-person consumptions of milk and soft drinks are shown in Table 17 for various years.a. Let M(t) be the mean annual per-person consumption of milk and S(t) be the mean annual per-person consumption of soft drinks, both in gallons per person, in the year that is t years since
The percentages of American adults whose favorite sport is racing are shown in Table 18 for various years.Let p be the percentage of American adults whose favorite sport is racing at t years since 2000.a. Construct a scatterplot.b. Describe the four characteristics of the association. Compute and
Worldwide sales of Alfa Romeo cars are shown in Table 19 for various years.Let s be the annual worldwide sales (in thousands) of Alfa Romeo cars at t years since 2000.a. Construct a scatterplot.b. Describe the four characteristics of the association. Compute and interpret r as part of your
The numbers of conflicts in New York City involving police firearm discharges are shown in Table 20 for various years.Let f (t) be the number of conflicts in New York City involving police firearm discharges in the year that is t years since 2000.a. Construct a scatterplot.b. Describe the four
The percentages of households that consist of married couples with children are shown in Table 21 for various years.Let f (t) be the percentage of households that consist of married couples with children at t years since 1980.a. Construct a scatterplot.b. Describe the four characteristics of the
A runner€™s stride rate is the number of steps per second. The average stride rates of the top female runners are shown in Table 22 for various speeds.Let f (v) be the mean stride rate of a woman running at v feet per second.a. Construct a scatterplot.b. Describe the four characteristics of the
The percentages of Americans who have been diagnosed with diabetes are shown in Table 23 for various age groups.Let f(a) be the percentage of Americans at age a years who have been diagnosed with diabetes at some point in their lives.a. Construct a scatterplot.b. Find an equation of f.c. Find f
Five human subjects were injected with various concentrations of LSD, and with each concentration they solved as many simple arithmetic problems that they could in three minutes. Their work was recorded as the percentage of the number of problems they could do before being injected with LSD. The
Fibromyalgia (FMS) and chronic fatigue syndrome (CFS) are two illnesses that often coexist. Patients who have both illnesses tend to suffer from fatigue, poor sleep, lack of mental clarity, and body aches. Researchers randomly assigned 69 patients with both FMS and CFS and 3 patients with only FMS
To enroll in intermediate algebra, a student at the College of San Mateo (CSM) must score at least 21 points (out of 50) on a placement test. Using four semesters of data, the CSM Mathematics Department computed the percentages of students who succeeded in intermediate algebra (grade of A, B, or C)
The €œcrime index€ refers to the number of incidents of crime. The numbers of burglaries, aggravated assaults, and all types of crime per 100,000 Americans are shown in Table 27 for various years.a. Let A be the crime index of aggravated assaults for the year that is t years since 1990. Can
The percentages of the workforce in unions and the percent- ages of worker hours lost due to strikes are compared by the scatterplot in Fig. 15 for the 50 states, except Alaska and Nebraska. Let U be the percentage of a state€™s workforce in unions and L be the percentage of the state€™s
Figure 16 displays a scatterplot that compares the mean lengths and mean heights of 51 types of dinosaurs. Let L be the mean length and H be the mean height, both in meters, of a dinosaur.a. Describe the four characteristics of the association.b. Imagine the line that contains the two red dots,
The lengths of cruise ships and the sizes of the crews are compared by the scatterplot shown in Fig. 17. Let S be the crew size (in hundreds) for a cruise ship with length L hundred feet.a. Describe the four characteristics of the association.b. For the scatterplot, imagine a reasonable linear
True or False: It is more desirable to find a linear model that contains several, but not all, data points than it is to find a linear model that does not contain any data points but comes close to all data points.
When a golfer hits the ball at the starting point, the shot is called a drive and the driving distance is the distance that the ball travels. The fairway is the closely mown area that runs from the starting point almost all the way to the hole. The fairway accuracy is the percentage of drives in
Three students are to find a linear model for the data in Table 28. Student A uses points (1, 5.9) and (2, 6.4), student B uses points (3, 9.0) and (4, 11.0), and student C uses points (5, 12.1) and (6, 15.5). Which student seems to have made the best choice of points?
Three students are to find a linear model for the data in Table 29. Student A uses points (3, 13.8) and (4, 10.1), student B uses points (6, 7.8) and (7, 4.3), and student C uses points (5, 9.1) and (8, 3.1). Which student seems to have made the best choice of points? Explain.
Consider the scatterplot of data and the graph of the model y = mx + b in the indicated figure. Sketch the graph of a linear model that describes the data better. Then explain how you would adjust the values of m and b of the original model so it would describe the data better.
Consider the scatterplot of data and the graph of the model y = mx + b in the indicated figure. Sketch the graph of a linear model that describes the data better. Then explain how you would adjust the values of m and b of the original model so it would describe the data better.
The prices of ski rental packages from Gold Medal Sports® are shown in Table 12 for various numbers of days.Let p be the price (in dollars) of a ski rental package for n days.a. Construct a scatterplot.b. Describe the four characteristics of the association. Compute and interpret r as part of your
See Fig. 66.
The ages and prices of 6 Ford Taurus sedans at dealer- ships in the Nashville area are shown in Table 36.Let x be the age (in years) and y be the price (in thousands ofdollars), both for a Ford Taurus sedan.a. Construct a scatterplot.b. Find the linear regression equation.c. The equation of the
The prices of hot dogs and soft drinks at 5 randomly selected Major League Baseball stadiums are shown in Table 37.Let x be the price of a hotdog and y be the price of a soft drink, both in dollars, at a Major League Baseball stadium.a. Construct as catterplot, treating x as the explanatory
The percentages of teens who have cell phones are shown in Table 38 for various ages.Let p be the percentage of teens at age a years who have cell phones.a. Construct a scatterplot.b. Find the linear regression equation.c. The equation of the line that contains the data points (13, 54) and (17, 79)
The percentages of Americans who have been diagnosed with diabetes are shown in Table 39 for various age groups.Let y be the percentage of Americans at age x years who have been diagnosed with diabetes at some point in their lives.a. Construct a scatterplot.b. Find the linear regression equation.c.
A racquetball is dropped from various heights, and the bounce height is recorded each time (see Table 40).Let f(x) be the bounce height (in inches) of the racquetball after it is dropped from an initial height of x inches.a. Construct a scatterplot.b. Find the linear regression equation for f. Does
The heights of objects and the lengths of their shadows are shown in Table 41.Let x be the height (in inches) of an object and f(x) be the length (in inches) of the object€™s shadow.a. Construct a scatterplot.b. Find the linear regression equation for f. Does the graph of f come close to the
Mean gasoline prices in Michigan are shown in Table 42 for various years.Let f (x) be the mean gasoline price (in dollars) at x years since 2000.a. Construct a scatterplot.b. Find the linear regression equation for f. Does the graph of f come close to the data points?c. Find f (13). What does it
Due to inflation, an item that cost $10,000 in 1980 cost $28,486 in 2015. Costs comparable to $10,000 in 1980 are shown in Table 43 for various years.Let f(x) be the cost (in dollars) at x years since 1980 that is comparable to $10,000 in 1980.a. Construct a scatterplot.b. Find the linear
The number of cases and deaths from Ebola in some African countries as of October 14, 2014, are shown in Table 44.Let y be the number of Ebola deaths in a country that has had x Ebola cases.a. What is the explanatory variable? Explain.b. Construct a scatterplot.c. Find the linear regression
The rate at which a cricket chirps depends on the temperature of the surrounding air. You can estimate the air temperature by counting chirps! Some data randomly selected from the study€™s data are provided in Table 45.Let y be the number of chirps a cricket makes in 13 seconds when the
If you could stop time and live forever in good health at a particular age, what age would you choose? The mean ideal ages chosen by various age groups are shown in Table 46.Let y be the mean ideal age (in years) chosen by people whose actual age is x years.a. Construct a scatterplot.b. Find the
The percentages of Americans who gamble online are shown in Table 47 for various age groups.Let y be the percentage of Americans who gamble online at age x years.a. Construct a scatterplot.b. Find the linear regression equation. Graph it on the scatterplot.c. Construct a residual plot.d. Find the
In Exercise 33 on page 620 you found the linear regression equation = 0.55x + 15.90, where y is the mean ideal age (in years) chosen by people whose actual age is x years.a. Use the model to predict the mean ideal age chosen by 25-year-olds.b. What is the slope? What does it mean in this
In Exercise 34 you found the linear regression equation = 0.57x - 6.68, where y is the percentage of Americans who gamble online at age x years.a. Use the model predict the percentage of 30-year-old Americans who gamble online.b. What is the slope? What does it mean in this situation?c. Use the
Mean scores on tests that evaluate general knowledge and vocabulary, and mean scores on tests that evaluate memory and information-processing speed are shown in Table 48 for various ages. (The higher the mean score, the better the mental function will be. The mean score for everyone in the study is
Mean scores on tests that evaluate general knowledge and vocabulary, and mean scores on tests that evaluate memory and information-processing speed are shown in Table 48 for various ages. (The higher the mean score, the better the mental function will be. The mean score for everyone in the study is
The levels of rainfall in Tuscola County, Michigan, and the numbers of murders by pushing from high places in the United States are shown in Table 49 for various years.Let x be the level of rainfall (in mm) in Tuscola County, Michigan, and y be the number of murders by pushing from high places in
The total revenues of skiing facilities and the numbers of people who died from becoming tangled in their bedsheets are shown in Table 50 for various years.Let x be the total revenue (in billions of dollars) of skiing facilities, and let y be the number of fatalities from people be- coming tangled
If you are driving and spot an object in the road, the distance it will take you to stop is equal to the sum of the following:• The reaction distance is the distance you will continue to travel before you hit the brakes.• The braking distance is the distance you will travel as you are
Refer to Exercise 41 for a description of reaction and braking distances. Let R be the reaction distance and let B be the braking distance, both in feet, when driving at s miles per hour.a. Find the stopping distances (in feet) for the driving speeds 20, 30, 40, 50, 60, 70, and 80, all in miles per
Refer to Exercise 41 for a description of reaction and braking distances. Let R be the reaction distance, B be the braking distance, and D be the stopping distance, all in feet, when driving at s miles per hour.a. The residual plot for using the regression line to model the association between s
Table 52 compares the SAT scores and acceptance rates of applicants to 10 of the most selective U.S. colleges and universities. The data do not include students who participated in the early-decision application process.For students who score x points, let y be the percentage of applicants who are
The residual plot in Fig. 79 describes the residuals for using the regression line to describe the association between the percentage of people who voted for President Obama in the 2008 presidential election and the percentage of people who voted for him in the 2012 presidential election, where the
The scatterplot and the model in Fig. 81 describe the association between the percentage of children who receive free or reduced-fee lunches at school and the percentage of people who wear bicycle helmets, for each of 12 neighborhoods.A residual plot is shown in Fig. 82.a. The researchers
The scatterplot and the model in Fig. 84 describe the association between the years and the winning times for the men€™s Olympic 100-meter run. Let y be the winning time (in seconds) for the men€™s Olympic 100-meter run at x years since 0 a.d.a. The linear regression equation is =
The numbers of commercial airline boardings on domestic flights are shown in Table 53 for various years.Let n be the number (in millions) of commercial airline boardings on domestic flights for the year that is t years since 1990.a. Construct a scatterplot.b. Identify the outlier. Explain how the
Access the data about roller coasters, which are available at MyMathLab and at the Pearson Downloadable Student Resources for Math & Stats website.a. Construct a pie chart for the countries and a pie chart for the states. Are all the roller coasters in the world included in the data set? If no,
When a golfer hits a golf ball at the starting point, the shot is called a drive and the driving distance is the distance that the ball travels. The fairway is the closely mown area that runs from the starting point almost all the way to the hole. The fairway accuracy is the percentage of drives in
If the regression line is used to model some data pairs, explain why it is impossible for all the dots in the residual plot to be above the zero residual line.
The ratios of the median wealth of upper-income house- holds to the median wealth of middle-income households are shown in Table 62 for various years.Let y be the ratio of the median wealth of upper-income households to the median wealth of middle-income house- holds at x years since 1990.a.
The percentages of American adults in favor of banning smoking in public places are shown in Table 63 for various years.Let y be the percentage of American adults who favor banning smoking in public places at x years since 2000.a. Construct a scatterplot.b. Use two points to find an equation of a
The ages and prices of 9 Chevrolet Impala sedans at dealerships in Fort Myers, Florida, are shown in Table 64.Let x be the age (in years) and let y be the price (in thousands of dollars), both for a Chevrolet Impala sedan.a. Construct a scatterplot of the data.b. Find the linear regression
An ERCP is a medical procedure used most often to treat tumors or gallstones. The numbers of ERCP procedures in the United States are shown in Table 65 for various years.Let y be the number (in thousands) of ERCP procedures in the year that is x years since 2010.a. Construct a scatterplot of the
Researchers studied the impact on children€™s future incomes due to moving to wealthier neighborhoods. For each child in the study, researchers computed the percentile of the child€™s future income (at age 24 years) for incomes between the poorer neighborhood and the wealthier neigh-
The mean prices of high school lunches are shown in Table 69 for various years.Let y be the mean price (in dollars) of high school lunches at x years since 2000.a. Construct a scatterplot.b. Describe the four characteristics of the association. Compute and interpret r as part of your analysis.c.
The mean numbers of viewers of American Idol are shown in Table 70 for various years.Let y be the mean number (in millions) of viewers in the year that is x years since 2000.a. Construct a scatterplot.b. Find the linear regression equation. Graph it on the scatterplot.c. Construct a residual
Consider the scatterplot of data and the graph of the model = mx + b in Fig. 92. Sketch a linear model that describes the data better, and then explain how you would adjust the values of m and b of the original model so that it would describe the data better.
The percentages of Fortune 500 companies that still offer traditional pensions to new hires are shown in Table 67 for various years.Let f (x) be the percentage of Fortune 500 companies that offer traditional pensions to new hires at x years since 1990.a. Construct a scatterplot.b. Use two points to
The force f(L) (in pounds) you must exert on a wrench handle of length L inches to loosen a bolt is described by the equation f(L) = 720L-1. a. Simplify the right-hand side of the equation. b. Find f(12). What does your result mean in this situation?
If a person plays an electric guitar outside, the sound level f(d) (in decibels) at a distance d yards from the amplifier is described by the equation f(d) = 5760d-2. a. Simplify the right-hand side of the equation. b. Find f(8). What does your result mean in this situation?
The amount of light f(d) (in milliwatts per square centimeter) of a 50-watt light bulb at a distance d centimeters from the bulb is described by the equation f(d) = 8910d-2. a. Simplify the right-hand side of the equation. b. Find f(80). What does your result mean in this situation?
The mean costs (in current dollars) of tuition, fees, room, and board at four-year public colleges are shown in Table 4 for various years.Table 4Mean Costs (in Current Dollars) of Tuition, Fees, Room, and BoardYear Mean Cost (dollars)1975 ………………………… 16461980
The revenues of Amazon are shown in Table 5 for various years.Table 5Annual Revenues of AmazonYearRevenue (billions of dollars)2001 ………………………………….. 3.122003 ………………………………….. 5.262005 ………………………………….. 8.492007
a. Simplify (b/c)-2. b. Simplify (b/c)-n. c. Use your result from part (b) to simplify (b/c)-5 in one step.
It is common to confuse expressions such as 22, 2-1, 2(-1), (1/2)2, (1/2)-1, -22, (-2)2 and 1/2. List these numbers from least to greatest. Are there any “ties”?
Simplify each expression.a. b-1b. (b-1)-1c. ((b-1)-1)-1d. (((b-1)-1)-1)-1e.
(7b-4c-1)-2 (2b3c-2)5 Simplify.
18b5c3d-7 / 24b-6c3d-2 Simplify.
(16b-2c)(25b4c-5) / 15b5c-1)(8b-7c-2) Simplify.
(3bc-2)-2 / (3b-3c)-1 Simplify.
(2bc-7/5b-1c-2)3 Simplify.
(8b-2c2/12b-5c-3)-3 Simplify.
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