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mathematics
statistics

A Pathway To Introductory Statistics 1st Edition Jay Lehmann - Solutions

Y = –2x + 4Determine the slope and the y-intercept. Then use the slope and the y-intercept to graph the equation by hand.
Y = –3x + 5Determine the slope and the y-intercept. Then use the slope and the y-intercept to graph the equation by hand.
Y = x + 1Determine the slope and the y-intercept. Then use the slope and the y-intercept to graph the equation by hand.
Y = – x + 2Determine the slope and the y-intercept. Then use the slope and the y-intercept to graph the equation by hand.
Y = –3xDetermine the slope and the y-intercept. Then use the slope and the y-intercept to graph the equation by hand.
Y = 4xDetermine the slope and the y-intercept. Then use the slope and the y-intercept to graph the equation by hand.
Y = xDetermine the slope and the y-intercept. Then use the slope and the y-intercept to graph the equation by hand.
Y = – xDetermine the slope and the y-intercept. Then use the slope and the y-intercept to graph the equation by hand.
Y = – 3Determine the slope and the y-intercept. Then use the slope and the y-intercept to graph the equation by hand.
Y = – 2Determine the slope and the y-intercept. Then use the slope and the y-intercept to graph the equation by hand.
Y = 0Determine the slope and the y-intercept. Then use the slope and the y-intercept to graph the equation by hand.
Y = 1Determine the slope and the y-intercept. Then use the slope and the y-intercept to graph the equation by hand.
Graphs of four linear equations are shown in Fig. 93. State whether m and b are positive, negative, zero, or undefined for the y = mx + b form of each equation.
Graphs of four linear equations are shown in Fig. 94. State the signs of the constants m and b for the y = mx + b form of each equation.
Graph by hand an equation of the form y = mx + b that meets the given criteria for m and b. Also, find an equation of each graph.M = 0 and b = 0
M = 2/3, (0,1)
M = 3/5, (0, 2)
Let n be the number (in thousands) of postal employees at t years since 2010. For the period 2010–2014, a reasonable model is n = - 31t + 586.a. Graph the model by hand.b. Estimate the number of postal employees in 2014.
Let n be the number of firefighters who died on duty in the year that is t years since 2010. For the period 2010–2014, a reasonable model is n = -2t + 83.a. Graph the model by hand.b. Estimate the number of firefighters who died on duty in 20 13.
A study was based on the records of 6789 patients in 369 hospitals in which the patients’ hearts stopped because of conditions that could have been reversed by an electrical shock from a defibrillator. Let p be the percentage of patients who survived at least until being discharged from the
Let H be the price (in dollars) of a hot dog, and let S be the price (in dollars) of a soft drink, both at a Major League Baseball (MLB) stadium. For hot dog prices between $1 and $6.25, inclusive, a reasonable model is S = 0.8H + 0.4.a. Graph the model by hand.b. Predict the price of a hot dog at
For monthly recordings since 1909, let B be the mean sea level at The Battery, New York, and let G be the mean sea level at Galveston, Texas, both in feet. For mean sea levels at The Battery between -1.5 and 0.9 feet, inclusive, a reasonable model is G = 1.43B + 0.46.a. What is the slope? What does
For the 60 players picked in the 2014 draft for NBA basket- ball, let h be the height (in inches) of a player and let w be the weight (in pounds) of a player. For heights between 72 and 87 inches, inclusive, a reasonable model is w = 6.54h - 301.81.a. What is the slope? What does it mean in this
Google’s revenue was $29 billion in 2010, and it increased by about $9 billion per year until 2014. Let r be the annual revenue (in billions of dollars) at t years since 2010.a. Identify the explanatory and response variables.b. Find the slope and the r-intercept of a linear model.c. Find an
M = 5/2, (0, 4)
As of February 1, a garage band knows 5 songs. Each week, the band members learn 2 more songs. Let n be the number of songs that the band knows at t weeks since February 1.a. Identify the explanatory and response variables.b. Find the slope and the n-intercept of a linear model.c. Find an equation
A student’s saving account has balance of $4700 on September 1. Each month for 6 months, the balance declines by $650. Let B be the balance (in dollars) at t months since September 1.a. Why is there a linear association between t and B?b. Find the slope of a linear model. What does it mean in
A person owns a Coleman RoadTrip LXE Propane Grill with a tank that holds 16.4 ounces of propane. The person always sets the burner on high, which uses 0.13 ounce of propane per minute (Source: Coleman). Let p be the number of ounces of propane that remain in the tank after t minutes of cooking
For fall semester 2014, part-time students at Centenary College paid $575 per credit (unit or hour) for tuition and paid a mandatory part-time student fee of $15 per semester (Source: Centenary College). Let T be the total cost (in dollars) of tuition and the fee when taking c credits of courses.a.
For the spring semester 2014, California residents paid an enrollment fee of $46 per unit (credit or hour) at Santa Barbara City College. Students were also required to pay a $18 health fee each semester. Let T be the total cost (in dollars) of enrollment and health fees when taking M units of
A person drives her Toyota Prius® on a road trip. At the start of the trip, she fills up the 11.9-gallon tank with gasoline. During the trip, the cars uses about 0.02 gallon of gasoline per mile. Let G be the number of gallons of gasoline remaining in the tank after driving d miles.a. Why is there
Although the United States and Great Britain use the Fahrenheit (°F) temperature scale, most countries use the Celsius (°C) scale. The temperature reading 0°C is equivalent to the Fahrenheit reading 32°F. An increase of 1°C is equivalent to an increase of 1.8°F. Let F be the Fahrenheit
Digital music sales in the United States are shown in Table 31 for various years.Let s be the annual U.S. digital music sales (in billions of dollars) at t years since 2005.a. Use technology to construct a scatterplot.b. Describe the four characteristics of the association. Compute and interpret r
The numbers of countries that require picture warnings on cigarette packages are shown in Table 32 for various years.Let n be the number of countries that require picture warnings on cigarette packages at t years since 2000.a. Use technology to construct a scatterplot.b. Describe the four
The percentages of Americans who believe marriages between same-sex couples should be recognized by the law as valid are shown in Table 33 for various age groups.Let p be the percentage of Americans at age a years who believe marriages between same-sex couples should be recognized by the law as
M = –3/4, (0, –2)
In a study of adults who had received radiation to the brain to treat brain cancer when they were children, researchers found that the cancer survivors tended to develop mild cognitive deficits typically seen in older people. The percentages of childhood brain cancer survivors who have mild
In an attempt to raise the low graduation rates of college football and basketball players, Division I institutions require that prospective athletes must meet new grade point aver- age (GPA) standards (based on a maximum of 4.0) to play as freshmen, and enrolled athletes must meet these new
The mean selling prices for a Subaru Outback® of various ages are shown in Table 36.Let p be the mean price (in dollars) of a Subaru Outback of age a years.a. Use technology to construct a scatterplot.b. Describe the four characteristics of the association. Compute and interpret r as part of your
Amazon.com€™s revenues are shown in Table 37 for various years.Let r be Amazon.com€™s annual revenues (in billions of dollars) at t years since 2010. A model of the situation is r = 13.6t + 34.18.a. Use technology to construct a scatterplot, and graph the model on the same coordinate
Costco€™s net sales are shown in Table 38 for various years.Let n be Costco€™s annual net sales (in billions of dollars) at t years since 2005. A model of the situation is n = 8.7t + 34.4.a. Use technology to construct a scatterplot, and graph the model on the same coordinate system. Does
Use the slope and y-intercept of the line y = 2x - 1 to graph the equation y = 2x - 1 by hand. Then choose two points that lie on the graph, and show that both of the corresponding ordered pairs are solutions of the equation y = 2x - 1.
Use the slope and y-intercept of the line y = -2x + 3 to graph the equation y = -2x + 3 by hand. Then choose two points that lie on the graph, and show that both of the corresponding ordered pairs are solutions of the equation y = -2x + 3.
Recall that we can describe some or all of the solutions of an equation in two variables with an equation, a table, a graph, or words.a. Describe the solutions of y = 1/2 x + 2 by using a graph.b. Describe the solutions of y = 1/2 x + 2 by using words.
M = –5/2, (0, 0)
Recall that we can describe some or all of the solutions of an equation in two variables with an equation, a table, a graph, or words. a. Describe the solutions of y = 1/3 x - 1 by using a graph. b. Describe three solutions of y = 1/3 x - 1 by using a table. c. Describe the solutions of y = 1/3 x -
A student tries to graph the equation y = - 3x + 1 (see Fig. 98).
A student tries to graph the equation y = 3/2 x - 1 (see Fig. 99).
A line passes through the point (-1, 1) and has a slope of 2.a. Sketch the line.b. Find an equation of the line.
A line passes through the point (1, 2) and has a slope of - 3.a. Sketch the line.b. Find an equation of the line.
Graphs of the equations y = mx + b and y = kx + c (where m, b, k, and c are constants) are sketched in Fig. 100.a. Which is greater, m or k? Explain.b. Which is greater, b or c? Explain.
Let p be the percentage of adults with income d dollars who own a Mercedes-Benz. A student says that if f is the name of the function that describes the association between d and p, then f (p) = d. What would you tell the student?
a. For f(x) = 4x, find f(3), f(5), and f(8). Is the equation f (3 + 52 = f13) + f (5) a true statement?b. For f (x) = x2, find f(2), f(3), and f(5). Is the equation f(2 + 3) = f (2) + f (3) a true statement?c. For f (x) = √x, find f(9), f(16), and f(25). Is f(9 + 16) = f (9) + f (16) a true
a. For f (x) = 3x + 2, find f (5) – f (4). Compare your result with the slope of the graph of f. b. For f (x) = 2x + 5, find f (7) – f (6). Compare your result with the slope of the graph of f.c. For f (x) = 4x + 1, find f (3) – f (2). Compare your result with the slope of the graph of f.d.
Recall that we can describe some or all of the input–output pairsof a function by means of an equation, a graph, a table, or words.a. Describe the input–output pairs of y = 3x - 2 by using a graph.b. Describe the input–output pairs of y = 3x - 2 by using words.
Recall that we can describe some or all of the input–output pairs of a function by means of an equation, a graph, a table, or wordsa. Describe the input–output pairs of y = - 3/2 x + 2byusing a graph.b. Describe the input–output pairs of y = - 3/2 x + 2byusing words.
H (-4)Evaluate h(x) = 3x –4 / 5x + 2at the given value of x.
Some ordered pairs of four relations are listed in Table 47. Which of these relations could be functions? Explain.
Find f (17.28). Let f (x) = -5.95x + 183.22. Round any results to the second decimal place.
Some ordered pairs of four relations are listed in Table 48.a. Which of the relations could be functions? Explain. b. Which could be linear functions? Explain.
Let n be the number of drive-in movie sites in the United States at t years since 2009. The function n = -4.9t + 381 models the situation well for the period 2009–2014.a. Rewrite the equation n = -4.9 t + 381 using the function name f.b. Find f (3). What does it mean in this situation?c. Find f
In Exercise 64 of Homework 7.3, you worked with the model n = - 2t + 83, where n is the number of firefighters who died on duty in the year that is t years since 2010 (Source: U.S. Fire Administration). The function models the situation well for the period 2010–2014.YearPassenger Vehicle Sales
In Exercise 75 of Homework 7.3, you found the equation G = - 0.02d + 11.9, where G is the number of gallons of gasoline remaining in a Toyota Prius tank after driving d miles.a. Rewrite the equation G = -0.02d + 11.9 using the function name f.b. Find f (450). What does it mean in this situation?c.
In Example 10 of Section 7.3, we found the model B = -5.9E + 212, where B is the boiling point (in degrees Fahrenheit) at an elevation of E thousand meters.a. Rewrite the equation B = - 5.9E + 212 using the function name f.b. Find f (5). What does it mean in this situation?c. Find f (0). What does
The percentages of total donations that went to the 10 colleges and universities that received the most in donations are shown in Table 50 for various years.Let p be the percentage of total donations that went to the 10 colleges and universities that received the most in donations at t years since
The annual sales of passenger vehicles in China are shown in Table 51 for various years.Let s be the annual passenger vehicle sales (in millions) in China at t years since 2000.a. Use technology to construct a scatterplot.b. Use technology to graph the model s = 1.86t - 8.26 on the scatterplot.
The labor force is made up of people at least 16 years of age who are either employed or actively looking for work.The participation rate is the percentage of people at least 16 years of age who are in the labor force. The unemployment rate is the percentage of the labor force who are unemployed.
The percentages of elementary and secondary school- teachers who are union members are shown in Table 53 for various years.Let p be the percentage of teachers who are union members at t years since 1995.a. Use technology to construct a scatterplot.b. Use technology to graph the model p = -0.43t +
The percentages of U.S. teenagers with driver€™s licenses are shown in Table 54 for various ages.Let p = f (a) be the percentage of teenagers at age a years who have driver€™s licenses.a. Use technology to construct a scatterplot.b. Describe the four characteristics of the association.
Credit scores measure financial responsibility. Mean credit scores of Americans are shown in Table 55 for various age groups.Let c = f (a) be the mean credit score (in points) of adults at a years of age.a. Use technology to construct a scatterplot.b. Describe the four characteristics of the
The numbers of women and people who live alone are shown in Table 56 for various years.Let W(t) be the number of women who live alone and P(t) be the number of people who live alone, both in millions, at t years since 1990. Reasonable models are W (t) = 0.18t + 13.94 and P1t2 = 0.43t + 22.84.a.
Mean annual U.S. per-person consumption of chicken and red meat (in pounds per person) is described for various years in Table 57.Let C(t) be the mean annual per-person consumption of chicken and R(t) be the mean annual per-person consumption of red meat, both in pounds per person, at t years since
To measure the strength of stitching in knitted jerseys, re- searchers applied pressure perpendicular to the fabric until it burst. The bursting strength is the pressure applied just before the fabric bursts. Figure 122 shows a scatterplot that compares the lengths of stitches with the bursting
Figure 123 shows a scatterplot that compares the distances and times for randomly selected Delta Air Lines flights de- parting from Hartsfield-Jackson International Airport in Atlanta, Georgia.Let f(d) be the airborne time (in minutes) for a flight that traveled d miles.a. By inspecting the
The mean number of viewers of Fox prime-time TV shows was 9.1 million viewers in 2010 and decreased by about 0.8 million viewers until 2014.. Let f(t) be the mean number (in millions) of Fox prime-time viewers at t years since 2010.a. Find an equation of f.b. Find f(3). What does it mean in this
The median age of buyers of Harley-Davidson motorcycles was 48.7 years in 2010 and increased by 0.31 year each year until 2014. Let f(t) be the median age (in years) of buyers at t years since 2010.a. Find an equation of f.b. Find f(4). What does it mean in this situation?c. Find f(0). What does it
The number of U.S. brewery openings was 154 openings in 2010 and increased by about 12.4 openings per year until 2014. Let f(t) be the number of brewery openings in the year that is t years since 2010.a. Find an equation of f.b. What is the slope? What does it mean in this situation?c. Find f 132 -
Annual sales of echinacea were $132 million in 2009 and de- creased by about $6.9 million per year until 2014. Let f(t) be the annual echinacea sales (in millions of dollars) at t years since 2009.a. Find an equation of f.b. What is the slope? What does it mean in this situation?c. Find f (3) - f
The percentage of the work force having manufacturing jobs was 10.1% in 2010 and decreased by about 0.43 percentage point per year until 2014. Let p = f (t) be the percentage of the workforce who have manufacturing jobs at t years since 2010.a. Find an equation of f. b. Find f(4). What does it mean
The number of households that watched the Miss Universe Pageant was 4.62 million in 2010 and decreased by about 0.13 million per year until 2014 (Source: Nielsen Media Research). Let n = f 1t2 be the number (in millions) of house- holds that watched the show at t years since 2010.a. Find an
A basement is flooded with 640 cubic feet of water. It takes 4 hours to pump out the water at a constant rate. Let f(t) be the number of cubic feet of water that remains in the basement after t hours of pumping.a. Find a linear equation off.b. Graph f by hand.c. What are the domain and range of the
It takes a person 5 minutes to eat all 12 ounces of ice cream in a cup at a constant rate. Let f(t) be the number of ounces of ice cream remaining in the cup t minutes after the person began eating the ice cream.a. Find a linear equation off.b. Graph f by hand.c. What are the domain and range of
M = 3, (0, – 4)Sketch the line that has the given slope and contains the given point.
M = 4/3, (0, 1)Sketch the line that has the given slope and contains the given point.
Y = –2/5 x –1Determine the slope and the y-intercept. Use them to graph the equation by hand.
Y = 2/3 xDetermine the slope and the y-intercept. Use them to graph the equation by hand.
X = –2Determine the slope and the y-intercept. Use them to graph the equation by hand.
Y = x + 2Determine the slope and the y-intercept. Use them to graph the equation by hand.
X = – 3Graph the equation by hand.
Y = 2Graph the equation by hand.
Recall that we can describe some or all of the solutions of an equation in two variables with an equation, a table, a graph, or words.a. Describe three solutions of y = -2x + 1 by using a table.b. Describe the solutions of y = -2x + 1 by using a graph.c. Describe the solutions of y = -2x + 1 by
Let c be the charge (in dollars) for a taxi ride for d miles inNew York City. A reasonable model is c = 2d + 2.5.a. Identify the explanatory and response variables.b. What is the slope? What does it mean in this situation?c. What is the c-intercept? What does it mean in this situation?d. Graph the
A person weighs 195 pounds when he starts a weight-loss program. For the first 6 months of being in the program, he steadily loses 4 pounds per month. Let w be his weight (in pounds) t months after he has started the program.a. Why is there an exact linear association?b. Find the slope and the
Revenues of the National Football League (NFL) are shown in Table 62 for various years.Let r be the NFL€™s annual revenue (in billions of dollars) at t years since 2000.a. Use technology to construct a scatterplot.b. Describe the four characteristics of the association. Compute and interpret r
Some ordered pairs for four relations are listed in Table 63. Which of these relations could be functions? Explain.
The mean monthly day-care cost was $972 in 2011, and it increased by approximately $45.60 per year for the period 2011–2014. Costs are based on a three- year-old attending a day-care center eight hours a day, five days a week. Let f(t) be the mean monthly cost (in dollars) at t years since
In a study of 43 blind individuals (with no eyesight), a grooved surface was pressed against the index finger of each of the individuals. An individual€™s threshold was defined to be the smallest distance between grooves in which the individual could correctly identify the grooves as being
Prepaid cards can be loaded with cash and used anywhere credit cards or debit cards are accepted. The total amounts of money loaded onto U.S. prepaid cards are shown in Table 61 for various years.Let p be the total amount of money (in billions of dollars) loaded onto prepaid cards at t years since
The percentages of American adults who are confident they will retire ahead of their schedule are described by the scatterplot and the model in Fig. 125 for various incomes (in thousands of dollars).a. Is the association positive, negative, or neither? What does that mean in this situation?b.
Y = 3/2x + 2Determine the slope and the y-intercept. Use them to graph the equation by hand.

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