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College Mathematics for Business Economics Life Sciences and Social Sciences 12th edition Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen - Solutions
write the equation of the line through each indicated point with the indicated slope. Write the final answer in the form y = mx + b. m = -6; (-4. 1)
write the equation of the line through each indicated point with the indicated slope. Write the final answer in the form y = mx + b. m = 4/3; (-6,2)
(A) Find the slope of the line that passes through the give, points.(B) Find the standard form of the equation of the Hue.(C) Find the slope-intercept form of the equation of the lint(1,2) and (3,5)
(A) Find the slope of the line that passes through the give, points.(B) Find the standard form of the equation of the Hue.(C) Find the slope-intercept form of the equation of the lint(2,3) and (-3,7)
(A) Find the slope of the line that passes through the give, points. (B) Find the standard form of the equation of the Hue. (C) Find the slope-intercept form of the equation of the lint (1,4) and (0,4)
(A) Find the slope of the line that passes through the give, points. (B) Find the standard form of the equation of the Hue. (C) Find the slope-intercept form of the equation of the lint (2.0) and (2,-3)
In problem sketch a graph of each equation in a rectangular coordinate system. y = x/2 + 1
A small company manufactures picnic tables. The weekly fixed cost is $1,200 and the variable cost is $45 per table. Find the total weekly cost of producing x picnic tables. How many picnic tables can be produced for a total weekly cost of $4,800?
A plant can manufacture 50 tennis rackets per day for a total daily cost of $3,855 and 60 tennis rackets per day for a total daily cost of $4,245. (A) Assuming that daily cost and production are linearly related, find the total daily cost of producing x tennis rackets. (B) Graph the total daily
A clothing store sells a shirt costing $20 for $33 and a jacket costing $60 for $93.(A) If the markup policy of the store is assumed to be linear, write an equation that expresses retail price R in terms of cost C (wholesale price).(B) What does a store pay for a suit that retails for $240?
A charter fishing company buys a new boat for $224,000 and assumes that it will have a trade-in value of $115,200 after 16 years.(A) Find a linear model for the depreciated value V of the boat t years after it was purchased.(B) What is the depreciated value of the tractor after 10 years?(C) When
The temperature at which water starts to boil is also linearly related to barometric pressure. Water boils at 212°F at a pressure of 29.9 in Hg (inches of mercury) and at 191°F at a pressure of 28.4 in Hg. (A) Find a relationship of the form T = mx + b, where T is degrees Fahrenheit and x is
The airspeed indicator on some aircraft is affected by the changes in atmospheric pressure at different altitudes. A pilot can estimate the true airspeed by observing the indicated airspeed and adding to it about 1.6% for every 1,000 feet of altitude. (A) A pilot maintains a constant reading of 200
The median household income divides the households into two groups: the half whose income is less than or equal to the median, and the half whose income is greater than the median. The median household income in the United States grew from about $30,000 in 1990 to about $48,000 in 2006. (Source:
The percentage of male cigarette smokers in the United States declined from 25.2% in 2001 to 23.9% in 2006.(A) Find a linear equation relating percentage of male smokers (m)to years since 2000 (t).(B) Find the year in which the percentage of male smokers falls below 20%.
At a price of $1.94 per bushel, the supply of corn is 9,800 million bushels and the demand is 9,300 million bushels. At a price of $1.82 per bushel, the supply is 9,400 million bushels and the demand is 9,500 million bushels.(A) Find a price-supply equation of the form p - mx + b.(B) Find a
Sketch a graph of equation in a rectangular coordinate system 8x - 3y = 24
The distance d between a fixed spring and the floor is a linear function of the weight w attached to the bottom of the spring. The bottom of the spring is 18 inches from the floor when the weight is 3 pounds, and 10 inches from the floor when the weight is 5 pounds. (A) Find a linear equation that
Table 4 lists U.S. crude oil production as a percentage of total U.S. energy production for selected years. Let x represent years since 1960 and y represent the corresponding percentage of oil production.(A) Find the equation of the line through (0, 35) and (40,17), the first and last data points
Table 6 lists U.S. fossil fuel consumption as a percentage of total energy consumption for selected years. A linear regression model for this data isy = -0.06x + 85.6where x represents years since 1985 and y represents the corresponding percentage of fossil fuel consumption.(A) Draw a scatter plot
Cigarette smoking. The data in Table 7 shows that the percentage of male cigarette smokers in the U.S. declined from 27.6% in 1997 to 23.9% in 2006. (A) Applying linear regression to the data for males in Table 7 produces the model m = -0.42t + 27.23 where m is percentage of male smokers and / is
Regression model for the graduate student enrollment in Table 8 is y = 0.033x + 1.27 where represents years since 1980 and y is graduate enrollment in millions of students. (A) Draw a scatter plot of the graduate enrollment data and a graph of the model on the same axes. (B) Predict the graduate
Table 10 contains the state population and the number of licensed drivers in the state (both in millions) for the states with population over 10 million in 2006. The regression model for this data is y = 0.60x + 1.15 where x is the state population and y is the number of licensed drivers in the
A linear regression model for the operating income data in Table 11 is I = 1.66t + 8.80 where I is operating income and / is time since 2000 in years. (A) Draw a scatter plot of the data and a graph of the model on the same axes. (B) Predict Wal-Mart's annual operating income for 2018.
Dr. J. D. Robinson also published the following estimate of the ideal body weight of a man: 52 kg + 1.9 kg for each inch over 5 ft (A) Find a linear model for Robinson's estimate of the ideal weight of a man using w for ideal body weight (in kilograms) and h for height over 5 ft (in inches). (B)
A linear regression model for the propylene glycol data in Table 12 is P = -0.54T + 34
The figure contains a scatter plot of 100 data points for black walnut trees and the linear regression model for this data.(A) Interpret the slope of the model.(B) What is the effect of a 1-in. increase in Dbh?(C) Estimate the height of a black walnut with a Dbh of 12 in. Round your answer to the
The figure shows a scatter plot and a linear regression model for the annual revenue data in Table 13.(A) Interpret the slope of the model.(B) Use the model to predict the annual revenue (to the nearest billion dollars) in 2020.
Table 15 lists average annual telephone expenditures (in dollars) per consumer unit on residential phone service and cellular phone service, and the figure contains a scatter plot and regression line for each data set.(A) Interpret the slope of each model. (B) Predict (to the nearest dollar) the
Find a linear regression model for the men's 200-meter backstroke data given in Table 16, where v is years since 1980 and y is winning time (in seconds). Do the same for the women's 200-meter backstroke data. (Round regression coefficients to four decimal places.) Do these models indicate that the
Table 18 contains price-supply data and price-demand data for soybeans. Find a linear regression model for the price-supply data where x is supply (in billions of bushels) and y is price (in dollars). Do the same for the price-demand data. (Round regression coefficients to two decimal places.) Find
In fresh water, the pressure at a depth of 34 ft is 2 atms, or 29.4 pounds per square inch. (A) Find a linear model that relates pressure P (in pounds per square inch) to depth d (in feet). (B) Interpret the slope of the model. (C) Find the pressure at a depth of 50 ft. (D) Find the depth at which
The US Army is considering a new parachute, the Advanced Tactical Parachute System (ATPS). A jump at 2,880 ft using the ATPS system lasts 180 sees. (A) Find a linear model relating altitude a (in feet) and time in the air t (in seconds). (B) Find the rate of descent for an ATPS system
The speed of sound through sea water is linearly related to the temperature of the water. If sound travels at 1,403 m/sec at 0°C and at 1,481 m/sec at 20°C, construct a linear model relating the speed of sound (s)and the air temperature (t). Interpret the slope of this model.
In Problem each equation specifies a function with independent variable x. Determine whether the function is linear, constant, or neither
In Problem the three points in the table are on the graph of the indicated function f. Do these three points provide sufficient information for you to sketch the graph of y = f(x)? Add more points to the table until you are satisfied that your sketch is a good representation of the graph of y =
In Problem determine which of the equation specify function with independent variable x. For those that do, find the domain. For those that do not, find a value of x to which there corresponds more than one value of y x - y2 = 1
In Problem determine which of the equation specify function with independent variable x. For those that do, find the domain. For those that do not, find a value of x to which there corresponds more than one value of y x2 + y = 10
In Problem determine which of the equation specify function with independent variable x. For those that do, find the domain. For those that do not, find a value of x to which there corresponds more than one value of y xy + y - x = 5
In Problem determine which of the equation specify function with independent variable x. For those that do, find the domain. For those that do not, find a value of x to which there corresponds more than one value of y x2 - y2 = 16
In Problem find and simplify expression if f(x) = x2 - 1 f(5 + h) - f (5)
In Problem find and simplify the following, assuming h ‰ 0 in (C).(A) f(x + h) - f(x)(B) f(x + h) - f(x)(C)f (x) = - 3x + 9
In Problem find and simplify the following, assuming h ‰ 0 in (C).(A) f(x + h) - f(x)(B) f(x + h) - f(x)(C)f (x) = 3x2 + 5x - 8)
In Problem find and simplify the following, assuming h ‰ 0 in (C).(A) f(x + h) - f(x)(B) f(x + h) - f(x)(C)f (x) = x(x + 40)
The area of a rectangle is 81 sq/in. Express the perimeter P(l) as a function of the length l,and state the domain of this function.
The perimeter of a rectangle is 160 m. Express the area Aiw)as a function of the width w, and state the domain of this function.
A company manufactures notebook computers. Its marketing research department, using statistical techniques, collected the data shown in Table 9, where p is the wholesale price per computer at which x thousand computers can be sold. Using special analytical techniquesP(x) = 2,000 - 60x 1
(A) Using the price-demand functionp(x)=2,000 - 60x 1 ‰¤ x ‰¤ 25from Problem 88, write the company's revenue function and indicate its domain.(B) Complete Table 11, computing revenues to the nearest thousand dollars.(C) Plot the points from part (B) and sketch a graph of the revenue
The financial department for the company in Problems 88 and 90 established the following cost function for producing and selling x thousand notebook computers:C(x) = 4,000 + 500x thousand dollars(A) Write a profit function for producing and selling x thousand notebook computers and indicate its
(A) Table 15 shows the volume of the box for some values of x between 1 and 2. Use these values to estimate to one decimal place the value of x between 1 and 2 that would produce a box with a volume of 65 cu/in. (B) Describe how you could refine this table to estimate x to two decimal places. (C)
A parcel delivery service will only deliver pack-ages with length plus girth (distance around) not exceeding 108 in. A rectangular shipping box with square ends x inches on a side is to be used.(A) If the full 108 in. is to be used, express the volume of the box V(x)in terms of x.(B) What is the
The percentage s of seats in the House of Representatives won by Democrats and the percentage v of votes cast for Democrats (when expressed as decimal fractions) are related by the equation5v - 2s = 1.4 0 (A) Express v as a function of s and find the percentage of votes required for the Democrats
In problem graph of the functions using the graph of functions f and g below.y = g(x) -1
In problem graph of the functions using the graph of functions f and g below.Given:y = g( x-1 )
In problem graph of the functions using the graph of functions f and g below.y = g( x-1 )
In problem graph of the functions using the graph of functions f and g belowy = f( x + 3 )
In problem graph of the functions using the graph of functions f and g belowy = f(x) + 3
In problem graph of the functions using the graph of functions f and g belowy = -g(x)
In problem graph of the functions using the graph of functions f and g belowy = 2f( x )
In problem indicate verbally how the graph of function is related to the graph of the one of the six basic functions in figure 1 on page 60.Sketch a graph of each function. h ( x ) = -|x -5|
In problem indicate verbally how the graph of function is related to the graph of the one of the six basic functions in figure 1 on page 60.Sketch a graph of each function. m ( x ) = ( x + 3 )2 + 4
In problem indicate verbally how the graph of function is related to the graph of the one of the six basic functions in figure 1 on page 60.Sketch a graph of each function. g ( x ) = -6 +3√x
In problem indicate verbally how the graph of function is related to the graph of the one of the six basic functions in figure 1 on page 60.Sketch a graph of each function. m ( x ) = -0.4x2
Graph in Problem is the result of applying a sapience of transformations to the graph of one of the six basic function in Figure 1 on page 60. Identify the basic function and describe the transformation verbally. Write an equation for the given graph.
Graph in Problem is the result of applying a sapience of transformations to the graph of one of the six basic function in Figure 1 on page 60. Identify the basic function and describe the transformation verbally. Write an equation for the given graph.
In Problem the graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g and graph g using -5 ≤ x ≤ 5 and -5 ≤ y ≤ 5. The graph of f(x) = 3√x is shifted 3 units to the left and 2 units up
In Problem the graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g and graph g using -5 < x < 5 and -5
In Problem the graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g and graph g using -5 ≤ x ≤ 5 and -5 ≤y ≤ 5. The graph of f(x) = x2 is reflected in the x axis and shifted to the left 2 units
Graph function in Problem
Graph function in problem
Graph function in Problem
Changing the order in a sequence of transformations may change the final result. Investigate the pair of transformations in Problem to determine if reversing their order can produce a different result. Support your conclusions with specific examples and/or mathematical arguments. Vertical shift;
Changing the order in a sequence of transformations may change the final result. Investigate the pair of transformations in Problem to determine if reversing their order can produce a different result. Support your conclusions with specific examples and/or mathematical arguments. Horizontal shift;
Changing the order in a sequence of transformations may change the final result. Investigate the pair of transformations in Problem to determine if reversing their order can produce a different result. Support your conclusions with specific examples and/or mathematical arguments. Horizontal shift;
The manufacturers of the DVD players in Problem 61 are willing to supply x players at a price of p(x) as given by the equation p(x)=4√x 9 ≤ x ≤ 289 (A) Describe how the graph of function p can be obtained from the graph of one of the basic functions in Figure 1 on page 60. (B) Sketch a
A company manufactures and sells in-line skates. Its financial department has established the price-demand function p(x)=190 - 0.013(x - 10)2 10 ≤ x ≤ 100 where p(x)is the price at which x thousand pairs of in-line skates can be sold. (A) Describe how the graph of function p can be obtained
Table 4 shows the electricity rates charged by Monroe Utilities in the winter months.(A) Write a piecewise definition of the monthly charge W(x)for a customer who uses x kWh in a winter month.(B) Graph W(x).
Table 6 shows a recent state income tax schedule for individuals filing a return in Kansas.(A) Write a piecewise definition for the tax due T(x)on an income of x dollars.(B) Graph T(x).(C) Find the tax due on a taxable income of $20,000. Of $35,000.
The average weight of a particular species of snake is given by w(x) = 463x3, 0.2 ≤ x ≤ 0.8, where x is length in meters and w(x)is weight in grams. (A) Describe how the graph of function w can be obtained from the graph of one of the basic functions in Figure 1, page 60. (B) Sketch a graph of
A production analyst has found that on average it takes a new person T(x)minutes to perform a particular assembly operation after x performances of the operation, where T(x)=10 - 10- 3√x ≤ 0 ≤ 125. (A) Describe how the graph of function T can be obtained from the graph of one of the basic
For the function indicated in Problem find each of the following to the nearest integer by referring to the graphs for Problems 9 and 10. (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range Function m in the figure for Problem 10
For the function indicated in Problem find each of the following to the nearest integer by referring to the graphs for Problems 9 and 10. (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range Function g in the figure for Problem 10
In Problem find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range g(x)=-(x+ 2)2 + 3
In Problem find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range n(x) = (x-4)2 - 3
In Problem find the vertex form for each quadratic function. Then find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range g(x) = x2 - 6x + 5
In Problem find the vertex form for each quadratic function. Then find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range s(x) = -4x2 -8x - 3
In problem find the vertex form for each quadratic function. Then find each of the following (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range v(x) = 0.5x2 + 4x + 10
Let g(x) = -0.6x2 + 3x + 4. Solve each equation graphically to two decimal places. (A) g(x) = -2 (B) g(x) = 5 (C) g(x) = 8
In Problem first write each function in vertex form; then find each of the following (to two decimal places): (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range n(x) = 0.20x2 - 1.6x -1
In Problem first write each function in vertex form; then find each of the following (to two decimal places): (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range n(x)=-0.15x2 - 0.90x + 3.3
Solve Problem Graphically to two decimal places using a graphing calculator. 7 + 3x - 2x2 = 0
In Problem complete the square and find the vertex form of each quadratic function. n(x)=-x2 + 8x - 9
Solve ProblemGraphically to two decimal places using a graphing calculator.3.4 + 2.9x - 1.1x2 ≥ 0
Solve ProblemGraphically to two decimal places using a graphing calculator.1.8x2 - 3.1x - 4.9 > 0
Given that f is a quadratic function with maximum f(x) = f(-3) = -5, find the axis, vertex, range, and A: intercepts.
In Problem, (A) Graph f and g in the same coordinate system. (B) Solve f(x) = g(x) algebraically to two decimal places. (C) Solve f(x) > g(x) using parts (A) and (B). (D) Solve f(x) < g(x) using parts (A) and (B). f(x) = -0.7x(x - 7) g(x)=0.5x + 3.5 0 ≤ x ≤ 7
In Problem, (A) Graph f and g in the same coordinate system. (B) Solve f(x) = g(x) algebraically to two decimal places. (C) Solve f(x) > g(x) using parts (A) and (B). (D) Solve f(x) < g(x) using parts (A) and (B). f(x) = -0.7x2 + 6.3x g(x)=1.1x + 4.8 0 ≤ x ≤ 9
In Problem, assume that a,b,c,h and k are constants with a ‰ 0 such thatax2 + bx + c = a(x - h)2 + kfor all real numbers xShow that
The table shows the retail market share of passenger cars from Ford Motor Company as a percentage of the U.S. market.A mathematical model for this data is given by f(x) = -0.0206x2 + 0.548x + 16.9 where .v = 0 corresponds to 1980. (A) Complete the following table. Round values of f(x) to (B) Sketch
The marketing research department for a company that manufactures and sells notebook computers established the following price-demand and revenue functions: p(x) = 2,000 - 60x Price-demand function R(x) = xp(x) Revenue function = A-(2,000 - 60x) where p(x)is the wholesale price in
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