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Q:
Find the least squares regression line for the points (1,0) , (3,3) , (8,6).
A) B) C) D) E) none of the above
Q:
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. A linear regression model with a positive correlation will have a slope that is greater than 0.A) TrueB) False
Q:
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. When the correlation coefficient is , the model is a good fit.A) FalseB) True
Q:
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. Data that are modeled by have a positive correlation.A) TrueB) False; The data modeled by have a positive correlation.
Q:
An agronomist used four test plots to determine the relationship between the wheat yield (in bushels per acre) and the amount of fertilizer(in pounds per acre). The results are shown in the table. (a) Use the regression capabilities of a graphing utility or a spreadsheet to find the least squares regression line for the data.
(b) Estimate the yield for a fertilizer application of 160 pounds per acre.
A) B) C) D) E)
Q:
Use the regression capabilities of a graphing utility or a spreadsheet to find the least squares regression line for the given points. A) B) C) D) E)
Q:
Find the least squares regression line for the given points. Then plot the points and sketch the regression line. A) B) C) D) E)
Q:
Find the sum of the squared errors for the linear model and the quadratic model using the given points. A) ; B) ; C) ; D) ; E) ;
Q:
A rancher plans to use an existing stone wall and the side of a barn as a boundary for two adjacent rectangular corrals. Fencing for the perimeter costs 25 per foot. To separate the corrals, a fence that costs 20 per foot will divide the region. The total area of the two corrals is to be square feet. Use Lagrange multipliers to find the dimensions that will minimize the cost of the fencing. A) dimensions: feet by feetB) dimensions: feet by feetC) dimensions: feet by feetD) dimensions: feet by feetE) dimensions: feet by feet
Q:
A manufacturer has an order for 800 units of fine paper that can be produced at two locations. Let and be the numbers of units produced at the two plants. Find the number of units that should be produced at each plant to minimize the cost if the cost function is given by .
A) units and units
B) units and units
C) units and units
D) units and units
E) units and units
Q:
Use Lagrange multipliers to find the minimum distance from the circle to the point Round your answer to the nearest tenth.
A) 13.6
B) 107.0
C) 184.4
D) 7.8
E) 60.4
Q:
Use Lagrange multipliers to minimize the function subject to the following constraint. Assume that x, y, and z are positive.
A) 81
B) 243
C) 162
D) 486
E) 729
Q:
A microbiologist must prepare a culture medium in which to grow a certain type of bacteria. The percent of salt contained in this medium is given by where and are the nutrient solutions to be mixed in the medium. For the bacteria to grow, the medium must be 13% salt. Nutrient solutions and cost $1, $2, and $3 per liter, respectively. How much of each nutrient solution should be used to minimize the cost of the culture medium?
A) B) C) D) E)
Q:
A rectangular box is resting on the -plane with one vertex at the origin. The opposite lies in the plane Find the dimensions that maximize the volume. (Hint: Maximize subject to the constraint ).
A) 15 units 12 units 5 units
B) 11 units 9 units 5 units
C) 10 units 9 units 6 units
D) 15 units 10 units 6 units
E) 12 units 11 units 7 units
Q:
Use Lagrange multipliers to find the given extremum. In each case, assume that andare positive.
Maximize Constraints A) B) C) D) E)
Q:
Use Lagrange multipliers to find the given extremum. Assume that and are positive. Minimize Constraint A) B) C) D) E)
Q:
Use Lagrange multipliers to find the given extremum. In each case, assume that and are positive.
Maximize Constraint A) B) C) D) E)
Q:
Use Lagrange multipliers to maximize the function subject to the following constraint: Assume that x, y, and z are positive.
A) B) C) D) E) no absolute maximum
Q:
A company manufactures two types of sneakers: running shoes and basketball shoes. The total revenue from x1 units of running shoes and y1 units of basketball shoes is:
,
where x1 and x2 are in thousands of units. Find x1 and x2 so as to maximize the revenue.
A) B) C) D) E)
Q:
The sum of the length (denote by z) and the girth (perimeter of a cross section) of packages carried by a delivery service cannot exceed 72 inches. Find the dimensions of the rectangular package of largest volume that may be sent.
A) x = 9, y = 9, z = 24
B) x = 6, y = 6, z = 48
C) x = 12 , y = 12 , z = 24
D) x = 4.8, y = 7.2, z = 48
E) x = 2.4, y = 14.4, z = 38.4
Q:
Find three positive numbers x, y, and z whose sum is 33 and the sum of the squares is a maximum.
A) x = y = z = 11
B) x = 5.5, y = 5.5, z = 22
C) x = 8.25, y = 8.25, z = 16.5
D) x = 4.4, y = 6.6, z = 11
E) x = 2.2, y = 13.2, z = 17.6
Q:
Find three positive numbers x, y, and z whose sum is 15 and product is a maximum.
A) x = 2.5, y = 2.5, z = 10
B) x = y = z = 5
C) x = 3.75, y = 3.75, z = 7.5
D) x = 2, y = 3, z = 5
E) x = 1, y = 6, z = 8
Q:
Find the critical points of the function , and, from the form of the function, determine whether a relative maximum or a relative minimum occurs at each point.
A) relative minima at , , , where and are arbitrary real numbers
B) relative maxima at , , , where and are arbitrary real numbers
C) relative minimum at D) relative maximum at E) no relative extrema
Q:
Find the critical points of the function , and, from the form of the function, determine whether a relative maximum or a relative minimum occurs at each point.
A) relative minimum at B) relative maximum at C) relative minimum at D) relative maximum at E) no relative extrema
Q:
Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function at the critical point .
Given: A) at B) at C) at D) at
Q:
Examine the function given below for relative extrema and saddle points. A) The function has a saddle point at .
B) The function has a relative maximum at .
C) The function has a relative minimum at .
D) The function has a saddle point at .
E) The function has a relative maximum at .
Q:
Examine the function given below for relative extrema and saddle points. A) The function has a relative maximum at.
B) The function has a relative minimum at.
C) The function has a saddle point at.
D) The function has a relative maximum at.
E) The function has a relative minimum at.
Q:
Examine the function for relative extrema and saddle points.
A) saddle point: ; relative minimum: B) relative minimum: ; relative maximum: C) saddle points: , D) saddle point: ; relative minimum: E) relative minimum: ; relative maximum:
Q:
Examine the function for relative extrema.
A) relative at B) relative at C) relative at D) relative at E) no relative extrema
Q:
Examine the function for relative extrema.
A) relative maximum at B) saddle point at C) relative maximum at D) relative minimum at E) relative maximum at
Q:
Test for relative extrema and saddle points. A) saddle point at B) saddle point at C) saddle point at D) relative minimum at E) relative minimum at
Q:
The utility function is a measure of utility (or satisfaction) derived by a person from the consumption of two products x and y. Suppose the utility function is . Determine the marginal utility of product x.
A) B) C) D) E)
Q:
The value of an investment of $18,000 after t years in an account for which the interest rate 100r% is compounded continuously is given by the function dollars. Write the partial derivative A) B) C) D) E)
Q:
A company manufactures two types of wood-burning stoves: a freestanding model and a fireplace-insert model. The cost function for producing x freestanding and y fireplace-insert stoves is . Find the marginal costs (and ) when and . Round your answers to two decimal places.
A) B) C) D) E)
Q:
Find the four second partial derivatives. Observe that the second mixed partials are equal. A) B) C) D) E)
Q:
Find the slopes of the surface in the x- and y- directions at the point .
A) slope in x-direction: 2 slope in y-direction: "17
B) slope in x-direction: "6 slope in y-direction: "8
C) slope in x-direction: "17 slope in y-direction: 2
D) slope in x-direction: "14 slope in y-direction: "14
E) slope in x-direction: "8 slope in y-direction: "6
Q:
For , find all values of x and y such that and simultaneously. A) B) C) (0,0)
D) Both B and C
E) Both A and B
Q:
Find the first partial derivatives with respect to x, y, and z. A) B) C) D) E)
Q:
Evaluate and for the function at the point . Round your answer to two decimal places.
A) 4.03 and 1.19
B) 3.53 and 1.19
C) 3.88 and 5.82
D) 4.03 and 0.69
E) 3.88 and 5.82
Q:
Evaluate and for the function at the point .
A) "25 and "50
B) "45 and "80
C) "25 and "80
D) 100 and "30
E) "25 and 70
Q:
If find A) B) C) D) E)
Q:
If find and A) B) C) D) E)
Q:
Describe the level curves for the function for the c-values given by .
A) B) C) D) E)
Q:
Sketch the level curves for the function below for the given values . A)B)C)D)E)
Q:
Describe the level curves of the function. Sketch the level curves for the given c-values.
, c = 0, 2, 4, 6
A) B) C) D) E)
Q:
Describe the domain and range of the function. A) domain: The disk range: The interval (0,4)
B) domain: The disk range: The interval [0,4]
C) domain: The disk range: The interval [0,4)
D) domain: The disk range: The interval [0,4]
E) domain: The disk range: The interval [0,4)
Q:
A manufacturer estimates the Cobb-Douglas production function to be given by
.
Estimate the production levels when and .
A) 135,540 units
B) 122,560 units
C) 131,601 units
D) 145,330 units
E) 112,745 units
Q:
Find the domain and range of the function. A) Domain: all point such that Range: B) Domain: all point such that Range: C) Domain: all point such that Range: D) Domain: all point such that Range: E) Domain: all point such that Range:
Q:
Evaluate the function at A) B) C) D) E)
Q:
Use the function to find A) B) C) D) E)
Q:
Evaluate the function at the given values of the independent variables. A) B) C) D) E)
Q:
Use the function to find A) B) C) D) E)
Q:
Because of the forces caused by its rotation, a planet is actually an oblate ellipsoid rather than a sphere. The equatorial radius is 3963 miles and the polar radius is 3953 miles. Find an equation of the ellipsoid. Assume that the center of a planet is at the origin and the xy- trace corresponds to the equator.
A) B) C) D) E)
Q:
Identify the quadric surface. A) The graph is an elliptic cone.
B) The graph is hyperboloid of two sheets.
C) The graph is a hyperboloid of one sheet.
D) The graph is an ellipsoid.
E) The graph is an elliptic paraboloid.
Q:
Identify the quadric surface. A) The graph is a hyperboloid of one sheet.
B) The graph is hyperboloid of two sheets.
C) The graph is an elliptic cone.
D) The graph is an elliptic paraboloid.
E) The graph is an ellipsoid.
Q:
Describe the trace of the surface given by the function below in the xz-plane.
A) circle
B) parabola
C) line
D) ellipse
E) hyperbola
Q:
Describe the trace of the surface given by the function below in the xy-plane. A) circle
B) ellipse
C) parabola
D) hyperbola
E) line
Q:
The two planes and are parallel.A) trueB) false
Q:
The two planes and are perpendicular.A) falseB) true
Q:
Find the intercepts of the plane given by .
A) The-intercept is. The-intercept is.
The-intercept is.
The-intercept is.
B) The-intercept is. The-intercept is.
The-intercept is.
The-intercept is.
C) The-intercept is. The-intercept is.
The-intercept is.
The-intercept is.
D) The-intercept is. The-intercept is.
The-intercept is.
The-intercept is.
E) The-intercept is. The-intercept is.
The-intercept is.
The-intercept is.
Q:
Sketch the graph of the plane given by y5.A)B)C)D)E)
Q:
Find the intercepts of the plane given by .
A) The-intercept is. The-intercept is. The-intercept is.
The-intercept is.
The-intercept is.
The-intercept is.
B) The-intercept is. The-intercept is. The-intercept is.
The-intercept is.
The-intercept is.
The-intercept is.
C) The-intercept is. The-intercept is. The-intercept is.
The-intercept is.
The-intercept is.
The-intercept is.
D) The-intercept is. The-intercept is. The-intercept is.
The-intercept is.
The-intercept is.
The-intercept is.
E) The-intercept is. The-intercept is. The-intercept is.
The-intercept is.
The-intercept is.
The-intercept is.
Q:
Sketch the trace of the intersection of plane z = 4 with the sphere: .A)B)C)D)E)
Q:
Sketch the yz-trace of the equation: A)B)C)D)E)
Q:
Find the center and radius of the sphere whose equation is . Round your answer to two decimal places, where applicable.
A) center:; radius: 2.89
B) center:; radius: 2.89
C) center:; radius: 8.35
D) center:; radius: 2.89
E) center:; radius: 8.35
Q:
Find the equation of the sphere that has the points and as endpoints of a diameter.
A) B) C) D) E)
Q:
Find the standard equation of the sphere whose center is and whose radius is 4.
A) B) C) D) E)
Q:
Find the center and radius of the sphere. A) Center: Radius: B) Center: Radius: C) Center: Radius: D) Center: Radius: E) Center: Radius:
Q:
Find the lengths of the sides of the triangle with the given vertices, and determine whether the triangle is a right triangle, an isosceles triangle, or neither. A) ; obtuse triangle
B) ; right triangle
C) ; right triangle
D) ; acute triangle
E) ; acute triangle
Q:
Find if the midpoint of the line segment joining the two points and is .
A) B) C) D) E)
Q:
Find the the distance between the two points and .
A) 1 units
B) 11 units
C) units
D) 3 units
E) 5 units
Q:
Find the coordinates of the point that is located two units behind of the yz-plane, seven units to the left of the xz-plane, and four units above of the xy-plane.
A) B) C) D) E)
Q:
Find the capitalized cost C of an asset forever. The capitalized cost is given by where is the original investment, t is the time in years, r = 12% is the annual interest rate compounded continuously, n is the total time in years over which the asset is capitalized, and is the annual cost of maintenance (measured in dollars). Round your answer to two decimal places.
A) $1,525,000.00
B) $1,275,000.00
C) $1,108,333.33
D) $1,299,218.75
E) $1,247,222.22
Q:
A business is expected to yield a continuous flow of profit at the rate of $1,000,000 per year. If money will earn interest at the nominal rate of 8% per year compounded continuously, what is the present value of the business forever?
A) $12,600,000
B) $12,510,000
C) $12,500,000
D) $1,250,000
E) $1,350,000
Q:
Suppose the mean height of American women between the ages of 30 and 39 is 68.5 inches, and the standard deviation is 2.7 inches. Use a symbolic integration utility to approximate the probability that a 30-to 39-year-old woman chosen at random is between 5 and 6 feet tall.
A) 0.1772
B) 0.9017
C) 0.5707
D) 0.8547
E) 0.4257
Q:
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. A) converges to 0
B) converges to 3
C) converges to D) diverges to E) diverges to
Q:
Evaluate the improper integral if it converges, or state that it diverges. A) B) C) D) E) diverges
Q:
Evaluate the improper integral if it converges, or state that it diverges. A) B) C) D) E) diverges
Q:
Decide whether the following integral is improper. A) noB) yes
Q:
A body assimilates a 16-hour cold tablet at a rate modeled by , where t is measured in milligrams per hour and t is the time in hours. Use Simpson's Rule with n = 16 to estimate the total amount of the drug absorbed into the body during the 16 hours.
A) 58.88
B) 34.88
C) 54.33
D) 46.88
E) 64.90