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mathematics
calculus with applications

Questions and Answers of Calculus With Applications

The total value of consumer durable goods (goods purchased by households for their nonbusiness use with a life expectancy of at least three years) has grown at an approximately linear rate in recent
The formulas for the least squares line were found by solving the system of equationsSolve the above system for b and m to show that nb + (2x)m = Συ (Σx)b + (Σx?)m = Σχν.
Find the slope of each line.y = 8
What six quantities are needed to compute a correlation coefficient?
For exercises, let f (x) = 7 – 5x and g(x) – 2x – 3.Find the following. g(2.5)
Find the slope of each line.The x-axis
What is marginal cost? Fixed cost?
Find the slope of each line.x = 5
For exercises, let f (x) = 7 – 5x and g(x) – 2x – 3.Find the following.g(1.5)
Determine whether each statement is true or false, and explain why.It is not possible to get a correlation coefficient of -1.5 for a set of data.
For exercises, let f (x) = 7 – 5x and g(x) – 2x – 3.Find the following.ƒ(-1)
Consider the following table of data.(a) Calculate the least squares line and the correlation coefficient.(b) Sketch a graph of the data.(c) Comparing your answers to parts (a) and (b), does a
Consider the following table of data.(a) Calculate the correlation coefficient.(b) Sketch a graph of the data.(c) Based on how closely the data fit a straight line, is your answer to part (a)
Consider the following table of data.(a) Calculate the least squares line and the correlation coefficient.(b) Repeat part (a), but this time delete the last point.(c) Draw a graph of the data, and
Determine whether each statement is true or false, and explain why.The lines 4x + 3y = 8 and 4x + y = 5 are parallel.
For exercises let f (x) = 7 – 5x and g(x) – 2x – 3.Find the following.ƒ(4)
The following problem is reprinted from the Actuarial Examination on Applied Statistical Methods.You are givenDetermine r2, the coefficient of determination for the regression of Y on X. Choose one
Find the slope of each line.y = 3x - 2
Determine whether each statement is true or false, and explain why.The lines y = 3x + 17 and y = -3x + 8 are perpendicular.
For exercises, let f (x) = 7 – 5x and g(x) – 2x – 3.Find the following.ƒ(2)
For the following table of data,(a) Draw a scatterplot.(b) Calculate the correlation coefficient.(c) Calculate the least squares line and graph it on the scatterplot.(d) Predict the y-value when x is
Determine whether each statement is true or false, and explain why.At the break-even point, the profit is 0.
Find the slope of each line.Through (4, 5) and (-1, 2)
Suppose a positive linear correlation is found between two quantities. Does this mean that one of the quantities increasing causes the other to increase? If not, what does it mean?
Determine whether each statement is true or false, and explain why.The graph of ƒ(x) = ax is a straight line that passes through the origin.
Determine whether each statement is true or false, and explain why.The slope of the graph of a linear function cannot be undefined.
A vertical line has a slope of 0.Determine whether each statement is true or false, and explain why.
Determine whether each statement is true or false, and explain why.A positive correlation coefficient between two variables means that an increase in one causes an increase in the other.
Determine whether each statement is true or false, and explain why.The equation y = 3x + 4 represents the equation of a line with slope 4.
Determine whether each statement is true or false, and explain why.The graph of ƒ(x) = -5 is a vertical line.
Any equation of the form y = mx + b represents a line, where m and b are constants.Determine whether each statement is true or false, and explain why.
Determine whether each statement is true or false, and explain why.Knowing Σx, Σy, Σx2, Σxy, and n is sufficient for calculating the correlation coefficient.
Determine whether each statement is true or false, and explain why.A given line can have more than one slope.
Determine whether each statement is true or false, and explain why.To find the x-intercept of the graph of a linear function, we solve y = ƒ(x) = 0, and to find the y-intercept, we evaluate ƒ(0).
Any line can be represented in the form y = mx + b.Determine whether each statement is true or false, and explain why.
Determine whether each statement is true or false, and explain why.Knowing Σx, Σy, Σx2, Σxy, and n is sufficient for calculating the least squares line.
The average monthly Social Security payments (in 2018 dollars) to Old-Age, Survivors, and Disability Insurance (OASDI) recipients for selected years are given in the following table.(a) Find an
More people are staying single longer in the United States. The following table gives the percent of never-married adults, age 15 and over, by gender, for the years 1998 and 2018. The growth has been
The following data show the connection between blood sugar levels and cholesterol levels for eight different patients.For the data given in the preceding table, Σx = 1394, Σy = 1607, Σxy =
Graph each equation.x = 4
Graph each equation.x + 5 = 0
A mathematician exploring the relationship between ratings of movies, their year of release, and their length discovered a paradox. Rather than list the data set of 100 movies in the original
A recent study found that “absolute income mobility,” defined as the percent of children who earn more than their parents, declined in a linear way in the 20th century. The following table of
Graph each equation.y + 8 = 0
Listed in the table below are the estimated 2018 populations (in millions) and the 2018 salary of the governor (in thousands of dollars) for ten randomly selected states. (a) Find the
Graph each equation.y = 2x
Graph each equation.y = -5x
Graph each equation.x + 4y = 0
Graph each equation.3x - 5y = 0
The sales of a small company were $27,000 in its second year of operation and $63,000 in its fifth year. Let y represent sales in the xth year of operation. Assume that the data can be approximated
The total cost for a bakery to produce 100 gourmet cupcakes is $126, while the total cost to produce 120 gourmet cupcakes is $144. Let y represent the total cost for x gourmet cupcakes. Assume that a
The table lists the annual cost (in 2019 dollars) of tuition and fees at private four-year colleges for selected years.(a) Sketch a graph of the data. Do the data appear to lie roughly along a
The following table shows the subscribership of cellular telephones in the United States (in millions) for selected years between 2006 and 2018. The World Almanac and Book of Facts 2020.(a) Plot
The time interval between a person’s initial infection with HIV and that person’s eventual development of AIDS symptoms is an important issue. The method of infection with HIV affects the time
To achieve the maximum benefit for the heart when exercising, your heart rate (in beats per minute) should be in the target heart rate zone. The lower limit of this zone is found by taking 70% of the
A study found that the peak vertical force on a trotting Shetland pony increased linearly with the pony’s speed, and that when the force reached a critical level, the pony switched from a trot to a
The following table lists the U.S. median age at first marriage for men and women. The age at which both groups marry for the first time seems to be increasing at a roughly linear rate in recent
Some scientists believe there is a limit to how long humans can live. One supporting argument is that during the past century, life expectancy from age 65 has increased more slowly than life
The table lists the distances (in megaparsecs where 1 megaparsec ≈ 3.1 × 1019 km) and velocities (in kilometers per second) of four galaxies moving rapidly away from Earth.(a) Plot the
The mortality rate for children under 5 years of age around the world has been declining in a roughly linear fashion in recent years. The rate per 1000 live births was 93 in 1990 and 39 in 2018.(a)
In 1950, there were 249,187 immigrants admitted to the United States. In 2017, the number was 1,127,167.(a) Assuming that the change in immigration is linear, write an equation expressing the number
In 1990, the Intergovernmental Panel on Climate Change (IPCC) predicted that the average temperature on Earth would rise 0.3ºC per decade in the absence of international controls on greenhouse
According to a Pew Research survey, the percentage of Americans aged 12 and older who had listened to online radio in the previous month increased from 27% in 2010 to 64% in 2018. During this same

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