تكلم مع الذكاء الاصطناعي
Deck 6: Integration
ملء الشاشة (f)
سؤال
Find 
. Round your answer to the nearest integer.
A)
B)
C)
D)
E)
. Round your answer to the nearest integer.A)
B)
C)
D)
E)
سؤال
Suppose an investment is expected to generate income at the rate of 
dollars/year for the next 6 years. Find the present value of this investment if the prevailing interest rate is 8% / year compounded continuously. Round your answer to the nearest dollar.
A) $950,930
B) $953,042
C) $951,802
D) $957,375
dollars/year for the next 6 years. Find the present value of this investment if the prevailing interest rate is 8% / year compounded continuously. Round your answer to the nearest dollar.A) $950,930
B) $953,042
C) $951,802
D) $957,375
سؤال
A certain country's income distribution is described by the function 
Compute 
and 
.
A)
B)
C)
D)
E)
Compute and .A)
B)
C)
D)
E)
سؤال
سؤال
The management of the Titan Tire Company has determined that the quantity demanded x of their Super Titan tires/week is related to the unit price p by the relation 
where p is measured in dollars and x is measured in units of a thousand. Titan will make x units of the tires available in the market if the unit price is 
dollars. Determine the consumers' surplus and the producers' surplus when the market unit price is set at the equilibrium price. Round your answers to the nearest dollar.
A) CS = $337,012 , PS = $174,988
B) CS = $343,476 , PS = $168,524
C) CS = $341,333 , PS = $170,667
D) CS = $342,567 , PS = $169,433
where p is measured in dollars and x is measured in units of a thousand. Titan will make x units of the tires available in the market if the unit price is dollars. Determine the consumers' surplus and the producers' surplus when the market unit price is set at the equilibrium price. Round your answers to the nearest dollar.A) CS = $337,012 , PS = $174,988
B) CS = $343,476 , PS = $168,524
C) CS = $341,333 , PS = $170,667
D) CS = $342,567 , PS = $169,433
سؤال
سؤال
سؤال
The demand function for a certain make of replacement cartridges for a water purifier is given by 
where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the market price is set at $5/cartridge. Round your answer to the nearest dollar.
A) $16,333
B) $16,800
C) $16,667
D) $16,886
where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the market price is set at $5/cartridge. Round your answer to the nearest dollar.A) $16,333
B) $16,800
C) $16,667
D) $16,886
سؤال
In a study conducted by a certain country's Economic Development Board, it was found that the Lorentz curve for the distribution of income of college teachers was described by the function 
and that of lawyers by the function 
Compute the coefficient of inequality for each Lorentz curve. Round your answer to four decimal places. Which profession has a more equitable income distribution?
A)
,
, college teachers
B)
,
, college teachers
C)
,
, college teachers
D)
,
, college teachers
and that of lawyers by the function Compute the coefficient of inequality for each Lorentz curve. Round your answer to four decimal places. Which profession has a more equitable income distribution?A)
, , college teachersB)
, , college teachersC)
, , college teachersD)
, , college teachers سؤال
سؤال
سؤال
A firm purchased a 16-year franchise for a computer outlet store that is expected to generate income at the rate of 
dollars per year. If the prevailing interest rate is 10% per year compounded continuously, find the present value of the franchise.
A) $1,114,979
B) $2,250,532
C) $4,660,006
D) $3,192,414
E) $1,756,632
dollars per year. If the prevailing interest rate is 10% per year compounded continuously, find the present value of the franchise.A) $1,114,979
B) $2,250,532
C) $4,660,006
D) $3,192,414
E) $1,756,632
سؤال
A certain country's income distribution is described by the function 
Sketch the Lorentz curve for this function. Compute 
and 
and interpret your results.
A)
;
The lowest 10 percent of the people receive 1.5 percent of the total income.
The lowest 30 percent of the people receive 10.1 percent of the total income.
B)
;
The lowest 10 percent of the people receive 1.5 percent of the total income.
The lowest 30 percent of the people receive 10.1 percent of the total income.
C)
;
The lowest 30 percent of the people receive 1.5 percent of the total income.
The lowest 10 percent of the people receive 10.1 percent of the total income.
Sketch the Lorentz curve for this function. Compute and and interpret your results.A)
; The lowest 10 percent of the people receive 1.5 percent of the total income.The lowest 30 percent of the people receive 10.1 percent of the total income.
B)
; The lowest 10 percent of the people receive 1.5 percent of the total income.The lowest 30 percent of the people receive 10.1 percent of the total income.
C)
; The lowest 30 percent of the people receive 1.5 percent of the total income.The lowest 10 percent of the people receive 10.1 percent of the total income.
سؤال
The demand function for a certain brand of compact disc is given by 
The supply function for the compact discs of is given by 
where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the producers' surplus if the wholesale market price is set at the equilibrium price. Round your answer to the nearest dollar.
A) $11,894
B) $11,667
C) $11,792
D) $11,346
The supply function for the compact discs of is given by where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the producers' surplus if the wholesale market price is set at the equilibrium price. Round your answer to the nearest dollar.A) $11,894
B) $11,667
C) $11,792
D) $11,346
سؤال
سؤال
It is known that the quantity demanded of a certain make of portable hair dryer is x hundred units/week and the corresponding wholesale unit price is 
dollars. Determine the consumers' surplus if the wholesale market price is set at $20/unit. Round your answer to the nearest dollar.
A) $5,093
B) $5,217
C) $4,975
D) $4,661
dollars. Determine the consumers' surplus if the wholesale market price is set at $20/unit. Round your answer to the nearest dollar.A) $5,093
B) $5,217
C) $4,975
D) $4,661
سؤال
The quantity demanded 
(in units of a hundred) of the miniature cameras per week is related to the unit price 
(in dollars) by 
and the quantity 
(in units of a hundred) that the supplier is willing to make available in the market is related to the unit price 
(in dollars) by 
If the market price is set at the equilibrium price, find the consumers' surplus and the producers' surplus. Please round the answers to the nearest dollar.
A) The consumers' surplus: $26,704, the producers' surplus: $142,718
B) The consumers' surplus: $142,718, the producers' surplus: $26,704
C) The consumers' surplus: $18,333, the producers' surplus: $20,000
D) The consumers' surplus: $20,000, the producers' surplus: $18,333
E) The consumers' surplus: $44,040, the producers' surplus: $21,478
(in units of a hundred) of the miniature cameras per week is related to the unit price (in dollars) by and the quantity (in units of a hundred) that the supplier is willing to make available in the market is related to the unit price (in dollars) by If the market price is set at the equilibrium price, find the consumers' surplus and the producers' surplus. Please round the answers to the nearest dollar.A) The consumers' surplus: $26,704, the producers' surplus: $142,718
B) The consumers' surplus: $142,718, the producers' surplus: $26,704
C) The consumers' surplus: $18,333, the producers' surplus: $20,000
D) The consumers' surplus: $20,000, the producers' surplus: $18,333
E) The consumers' surplus: $44,040, the producers' surplus: $21,478
سؤال
The demand function for a certain brand of compact disc is given by 
where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the wholesale market price is set at $2/disc. Round your answer to the nearest dollar.
A) $16,346
B) $16,790
C) $16,880
D) $16,667
where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the wholesale market price is set at $2/disc. Round your answer to the nearest dollar.A) $16,346
B) $16,790
C) $16,880
D) $16,667
سؤال
سؤال
Find 
. Round your answer to the nearest integer.
A) 866,981
B) 912,104
C) 854,636
D) 851,747
. Round your answer to the nearest integer.A) 866,981
B) 912,104
C) 854,636
D) 851,747
سؤال
سؤال
In a study conducted by a certain country's Economic Development Board, it was found that the Lorentz curve for the distribution of income of stockbrokers was described by the function 
and that of high school teachers by the function 
Compute the coefficient of inequality for each Lorentz curve. Round your answers to the nearest hundredth. Which profession has a more equitable income distribution?
A)
,
, stockbrokers
B)
,
, teachers
C)
,
, stockbrokers
D)
,
, stockbrokers
and that of high school teachers by the function Compute the coefficient of inequality for each Lorentz curve. Round your answers to the nearest hundredth. Which profession has a more equitable income distribution?A)
, , stockbrokersB)
, , teachersC)
, , stockbrokersD)
, , stockbrokers سؤال
In a study conducted by a certain country's Economic Development Board, it was found that the Lorentz curve for the distribution of income of stockbrokers was described by the function 
and that of high school teachers by the function 
Compute the coefficient of inequality for each Lorentz curve. Round your answers to the nearest hundredth.
The coefficient of inequality for stockbrokers is __________.
The coefficient of inequality for teachers is __________.
Which profession has a more equitable income distribution?
and that of high school teachers by the function Compute the coefficient of inequality for each Lorentz curve. Round your answers to the nearest hundredth.The coefficient of inequality for stockbrokers is __________.
The coefficient of inequality for teachers is __________.
Which profession has a more equitable income distribution?
سؤال
Suppose an investment is expected to generate income at the rate of 
dollars/year for the next 5 years. Find the present value of this investment if the prevailing interest rate is 0.05% / year compounded continuously. Round your answer to the nearest dollar.
$__________
dollars/year for the next 5 years. Find the present value of this investment if the prevailing interest rate is 0.05% / year compounded continuously. Round your answer to the nearest dollar.$__________
سؤال
سؤال
The demand function for a certain make of replacement cartridges for a water purifier is given by 
where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the market price is set at $1/cartridge. Round your answer to the nearest dollar.
CS = $__________
where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the market price is set at $1/cartridge. Round your answer to the nearest dollar.CS = $__________
سؤال
سؤال
Verify that 
.
. سؤال
The demand function for a certain brand of compact disc is given by 
The supply function for the compact discs is given by 
where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the producers' surplus if the wholesale market price is set at the equilibrium price. Round your answer to the nearest dollar.
$__________
The supply function for the compact discs is given by where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the producers' surplus if the wholesale market price is set at the equilibrium price. Round your answer to the nearest dollar.$__________
سؤال
سؤال
In a study conducted by a certain country's Economic Development Board, it was found that the Lorentz curve for the distribution of income of college teachers was described by the function 
and that of lawyers by the function 
Compute the coefficient of inequality for each Lorentz curve. Round your answer to four decimal places.
The coefficient of inequality for college teachers is __________.
The coefficient of inequality for lawyers is __________.
Which profession has a more equitable income distribution?
and that of lawyers by the function Compute the coefficient of inequality for each Lorentz curve. Round your answer to four decimal places.The coefficient of inequality for college teachers is __________.
The coefficient of inequality for lawyers is __________.
Which profession has a more equitable income distribution?
سؤال
The quantity demanded 
(in units of a hundred) of the miniature cameras per week is related to the unit price 
(in dollars) by 
and the quantity 
(in units of a hundred) that the supplier is willing to make available in the market is related to the unit price 
(in dollars) by 
If the market price is set at the equilibrium price, find the consumers' surplus and the producers' surplus. Please round the answers to the nearest dollar.
The consumers' surplus: $__________
The producers' surplus: $__________
(in units of a hundred) of the miniature cameras per week is related to the unit price (in dollars) by and the quantity (in units of a hundred) that the supplier is willing to make available in the market is related to the unit price (in dollars) by If the market price is set at the equilibrium price, find the consumers' surplus and the producers' surplus. Please round the answers to the nearest dollar.The consumers' surplus: $__________
The producers' surplus: $__________
سؤال
The management of the Titan Tire Company has determined that the quantity demanded x of their Super Titan tires/week is related to the unit price p by the relation 
where p is measured in dollars and x is measured in units of a thousand. Titan will make x units of the tires available in the market if the unit price is 
dollars. Determine the consumers' surplus and the producers' surplus when the market unit price is set at the equilibrium price. Round your answers to the nearest dollars.
CS = $__________
PS = $__________
where p is measured in dollars and x is measured in units of a thousand. Titan will make x units of the tires available in the market if the unit price is dollars. Determine the consumers' surplus and the producers' surplus when the market unit price is set at the equilibrium price. Round your answers to the nearest dollars.CS = $__________
PS = $__________
سؤال
سؤال
سؤال
The demand function for a certain brand of compact disc is given by 
where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the wholesale market price is set at $4/disc. Round your answer to the nearest dollar.
$__________
where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the wholesale market price is set at $4/disc. Round your answer to the nearest dollar.$__________
سؤال
سؤال
It is known that the quantity demanded of a certain make of portable hair dryer is x hundred units/week and the corresponding wholesale unit price is 
dollars. Determine the consumers' surplus if the wholesale market price is set at $10/unit. Round your answer to the nearest dollar.
$__________
dollars. Determine the consumers' surplus if the wholesale market price is set at $10/unit. Round your answer to the nearest dollar.$__________
سؤال
A firm purchased a 11-year franchise for a computer outlet store that is expected to generate income at the rate of 
dollars per year. If the prevailing interest rate is 9% per year compounded continuously, find the present value of the franchise. Please round the answer to the nearest dollar.
$__________
dollars per year. If the prevailing interest rate is 9% per year compounded continuously, find the present value of the franchise. Please round the answer to the nearest dollar.$__________
سؤال
Find the area of the shaded region. 
A) A = 23.6 sq units.
B) A = 19.9 sq units.
C) A = 18.1 sq units.
D) A = 21.3 sq units.
A) A = 23.6 sq units.
B) A = 19.9 sq units.
C) A = 18.1 sq units.
D) A = 21.3 sq units.
سؤال
Sketch the region completely enclosed by the graphs of the given functions f and g. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the area of the region enclosed by these graphs and the vertical lines 
and 
. 
A)
B)
C) 12
D)
E)
and . A)
B)
C) 12
D)
E)
سؤال
Sketch the graph and find the area of the region bounded by the graph of the function f and lines y = 0, x = a and x = b. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Sketch the graph and find the area of the region bounded below by the graph of the given function and above by the x-axis from x = a to x = b. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Sketch the region completely enclosed by the graphs of the given functions f and g. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Sketch the graph and find the area of the region completely enclosed by the graphs of the given functions f and g. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Sketch the graphs of the functions f and g and find the area of the region enclosed by these graphs and the vertical lines x = a and x = b. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Sketch the graphs of the functions f and g and find the area of the region enclosed by these graphs and the vertical lines x = a and x = b. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Find the area of the shaded region. 
A) A = 10 sq units.
B) A = 13 sq units.
C) A = 9 sq units.
D) A = 12 sq units.
A) A = 10 sq units.
B) A = 13 sq units.
C) A = 9 sq units.
D) A = 12 sq units.
سؤال
Sketch the graph of the region bounded by the graph of the function f and lines y = 0, x = a and x = b. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Sketch the region completely enclosed by the graphs of the given functions f and g. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Find the area of the shaded region. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the area of the region bounded below by the graph of the function and above by the 
-axis from 
to 
. 
A)
B)
C)
D)
E)
-axis from to . A)
B)
C)
D)
E)
سؤال
Find the area of the shaded region. 
A) A = 4 ln 2 sq units.
B) A = 5 ln 2 sq units.
C) A = ln 4 sq units.
D) A = 2 ln 2 sq units.
A) A = 4 ln 2 sq units.
B) A = 5 ln 2 sq units.
C) A = ln 4 sq units.
D) A = 2 ln 2 sq units.
سؤال
Sketch the graph and find the area of the region bounded by the graph of the function f and lines y = 0, x = a and x = b. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Sketch the graphs of the functions f and g and find the area of the region enclosed by these graphs and the vertical lines x = a and x = b. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Find the area of the region bounded by the graph of the function 
and the lines 
, 
, and 
. 
A)
B)
C)
D)
E)
and the lines , , and . A)
B)
C)
D)
E)
سؤال
Sketch the graphs of the functions f and g and find the area of the region enclosed by these graphs and the vertical lines x = a and x = b. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Sketch the graph and find the area of the region bounded by the graph of the function f and lines y = 0, x = a and x = b. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Sketch the graph and find the area of the region bounded below by the graph of the given function and above by the x-axis from x = a to x = b. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Evaluate the given definite integral. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Evaluate the given definite integral. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Because of the increasingly important role played by coal as a viable alternative energy source, the production of coal has been growing at the rate of 
billion metric tons/year t years from 1970 (which corresponds to t = 0). Had it not been for the energy crisis, the rate of production of coal since 1970 might have been only 
billion metric tons/year t years from 1970. Determine how much additional coal was produced between 1970 and the end of the century as an alternate energy source. Round your answer to one decimal place.
__________ billion metric tons
billion metric tons/year t years from 1970 (which corresponds to t = 0). Had it not been for the energy crisis, the rate of production of coal since 1970 might have been only billion metric tons/year t years from 1970. Determine how much additional coal was produced between 1970 and the end of the century as an alternate energy source. Round your answer to one decimal place.__________ billion metric tons
سؤال
Evaluate the given definite integral. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The area of the region bounded by the graphs of ![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The area of the region bounded by the graphs of and and the vertical lines x = 0 and x = 6 is given by </strong> A) True. Since f and g are continuous functions and on the interval [0, 6], then the area of the region bounded above by y = f(x) and below by y = g(x) on [0, 6] is given by B) False. Since f and g are continuous functions and on the interval [0, 6], then the area of the region bounded above by y = g(x) and below by y = f(x) on [0, 6] is given by <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB6026/11eaa8b1_da77_71b6_b1b6_6925f3b68e0f_TB6026_11.jpg)
and ![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The area of the region bounded by the graphs of and and the vertical lines x = 0 and x = 6 is given by </strong> A) True. Since f and g are continuous functions and on the interval [0, 6], then the area of the region bounded above by y = f(x) and below by y = g(x) on [0, 6] is given by B) False. Since f and g are continuous functions and on the interval [0, 6], then the area of the region bounded above by y = g(x) and below by y = f(x) on [0, 6] is given by <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB6026/11eaa8b1_da77_98c7_b1b6_4f244b3c6f37_TB6026_11.jpg)
and the vertical lines x = 0 and x = 6 is given by ![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The area of the region bounded by the graphs of and and the vertical lines x = 0 and x = 6 is given by </strong> A) True. Since f and g are continuous functions and on the interval [0, 6], then the area of the region bounded above by y = f(x) and below by y = g(x) on [0, 6] is given by B) False. Since f and g are continuous functions and on the interval [0, 6], then the area of the region bounded above by y = g(x) and below by y = f(x) on [0, 6] is given by <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB6026/11eaa8b1_da77_98c8_b1b6_19a2ee48ab40_TB6026_11.jpg)
A) True. Since f and g are continuous functions and![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The area of the region bounded by the graphs of and and the vertical lines x = 0 and x = 6 is given by </strong> A) True. Since f and g are continuous functions and on the interval [0, 6], then the area of the region bounded above by y = f(x) and below by y = g(x) on [0, 6] is given by B) False. Since f and g are continuous functions and on the interval [0, 6], then the area of the region bounded above by y = g(x) and below by y = f(x) on [0, 6] is given by <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB6026/11eaa8b1_da77_bfd9_b1b6_77ff5ee95e7e_TB6026_11.jpg)
on the interval [0, 6], then the area of the region bounded above by y = f(x) and below by y = g(x) on [0, 6] is given by
![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The area of the region bounded by the graphs of and and the vertical lines x = 0 and x = 6 is given by </strong> A) True. Since f and g are continuous functions and on the interval [0, 6], then the area of the region bounded above by y = f(x) and below by y = g(x) on [0, 6] is given by B) False. Since f and g are continuous functions and on the interval [0, 6], then the area of the region bounded above by y = g(x) and below by y = f(x) on [0, 6] is given by <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB6026/11eaa8b1_da77_e6ea_b1b6_27068666240e_TB6026_11.jpg)
B) False. Since f and g are continuous functions and![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The area of the region bounded by the graphs of and and the vertical lines x = 0 and x = 6 is given by </strong> A) True. Since f and g are continuous functions and on the interval [0, 6], then the area of the region bounded above by y = f(x) and below by y = g(x) on [0, 6] is given by B) False. Since f and g are continuous functions and on the interval [0, 6], then the area of the region bounded above by y = g(x) and below by y = f(x) on [0, 6] is given by <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB6026/11eaa8b1_da78_0dfb_b1b6_67ae04b1a8a1_TB6026_11.jpg)
on the interval [0, 6], then the area of the region bounded above by y = g(x) and below by y = f(x) on [0, 6] is given by
![<strong>Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The area of the region bounded by the graphs of and and the vertical lines x = 0 and x = 6 is given by </strong> A) True. Since f and g are continuous functions and on the interval [0, 6], then the area of the region bounded above by y = f(x) and below by y = g(x) on [0, 6] is given by B) False. Since f and g are continuous functions and on the interval [0, 6], then the area of the region bounded above by y = g(x) and below by y = f(x) on [0, 6] is given by <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB6026/11eaa8b1_da78_0dfc_b1b6_5f9d7eb5ea1e_TB6026_11.jpg)
and and the vertical lines x = 0 and x = 6 is given by A) True. Since f and g are continuous functions and
on the interval [0, 6], then the area of the region bounded above by y = f(x) and below by y = g(x) on [0, 6] is given byB) False. Since f and g are continuous functions and
on the interval [0, 6], then the area of the region bounded above by y = g(x) and below by y = f(x) on [0, 6] is given by سؤال
In an endeavor to curb population growth in a certain country, the government has decided to launch an extensive propaganda campaign. Without curbs, the government expects the rate of population growth to have been 
thousand people per year 
years from now, over the next 
years. However, successful implementation of the proposed campaign is expected to result in a population growth rate of 
thousand people per year 
years from now, over the next 
years. Assuming that the campaign is mounted, how many fewer people will there be in that country 
years from now then there would have been if no curbs had been imposed?
Please round your answer to the nearest whole number.
__________ thousand people
thousand people per year years from now, over the next years. However, successful implementation of the proposed campaign is expected to result in a population growth rate of thousand people per year years from now, over the next years. Assuming that the campaign is mounted, how many fewer people will there be in that country years from now then there would have been if no curbs had been imposed?Please round your answer to the nearest whole number.
__________ thousand people
سؤال
Evaluate the given definite integral. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
The area of the region bounded by the graphs of
and 
and the vertical lines x = 0 and x = 4 is given by 
The area of the region bounded by the graphs of
and and the vertical lines x = 0 and x = 4 is given by سؤال
Find the area of the region completely enclosed by the graphs of the given functions 
and 
. 
A)
B)
C)
D)
E)
and . A)
B)
C)
D)
E)
سؤال
Find the area of the shaded region. 
سؤال
Find the area of the shaded region. Round your answer to one decimal place. 
سؤال
Find the area of the shaded region. 
سؤال
In tests conducted by Auto Test Magazine on two identical models of the Phoenix Elite - one equipped with a standard engine and the other with a turbo-charger - it was found that the acceleration of the former is given by 
ft/sec, t seconds after starting from rest at full throttle, whereas the acceleration of the latter is given by 
ft/sec. How much faster is the turbo-charged model moving than the model with the standard engine at the end of a 10-second test run at full throttle?
__________ ft/sec
ft/sec, t seconds after starting from rest at full throttle, whereas the acceleration of the latter is given by ft/sec. How much faster is the turbo-charged model moving than the model with the standard engine at the end of a 10-second test run at full throttle?__________ ft/sec
سؤال
In tests conducted by Auto Test Magazine on two identical models of the Phoenix Elite - one equipped with a standard engine and the other with a turbo-charger - it was found that the acceleration of the former is given by 
ft/sec, t sec after starting from rest at full throttle, whereas the acceleration of the latter is given by 
ft/sec. How much faster is the turbo-charged model moving than the model with the standard engine at the end of a 10-second test run at full throttle?
A) 65 ft/sec
B) 58 ft/sec
C) 75 ft/sec
D) 70 ft/sec
ft/sec, t sec after starting from rest at full throttle, whereas the acceleration of the latter is given by ft/sec. How much faster is the turbo-charged model moving than the model with the standard engine at the end of a 10-second test run at full throttle?A) 65 ft/sec
B) 58 ft/sec
C) 75 ft/sec
D) 70 ft/sec
سؤال
Find the area of the shaded region. 
سؤال
Evaluate the given definite integral. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
In an endeavor to curb population growth in a certain country, the government has decided to launch an extensive propaganda campaign. Without curbs, the government expects the rate of population growth to have been 
thousand people per year 
years from now, over the next 
years. However, successful implementation of the proposed campaign is expected to result in a population growth rate of 
thousand people per year 
years from now, over the next 
years. Assuming that the campaign is mounted, how many fewer people will there be in that country 
years from now then there would have been if no curbs had been imposed? Please round your answer to the nearest integer number of thousands.
A)
thousand people
B)
thousand people
C)
thousand people
D)
thousand people
E)
thousand people
thousand people per year years from now, over the next years. However, successful implementation of the proposed campaign is expected to result in a population growth rate of thousand people per year years from now, over the next years. Assuming that the campaign is mounted, how many fewer people will there be in that country years from now then there would have been if no curbs had been imposed? Please round your answer to the nearest integer number of thousands.A)
thousand peopleB)
thousand peopleC)
thousand peopleD)
thousand peopleE)
thousand people سؤال
Because of the increasingly important role played by coal as a viable alternative energy source, the production of coal has been growing at the rate of 
billion metric tons/year t years from 1990 (which corresponds to t = 0). Had it not been for the energy crisis, the rate of production of coal since 1990 might have been only 
billion metric tons/year t years from 1990. Determine how much additional coal was produced between 1990 and the end of the century as an alternate energy source.
A) 13.6 billion metric tons
B) 0.6 billion metric tons
C) 4.7 billion metric tons
D) 7.9 billion metric tons
billion metric tons/year t years from 1990 (which corresponds to t = 0). Had it not been for the energy crisis, the rate of production of coal since 1990 might have been only billion metric tons/year t years from 1990. Determine how much additional coal was produced between 1990 and the end of the century as an alternate energy source.A) 13.6 billion metric tons
B) 0.6 billion metric tons
C) 4.7 billion metric tons
D) 7.9 billion metric tons
سؤال
Evaluate the definite integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate the given definite integral. 
A)
B)
C)
D)
A)
B)
C)
D)
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ملء الشاشة (f)
Deck 6: Integration
1
Find . Round your answer to the nearest integer.
A)
B)
C)
D)
E)
. Round your answer to the nearest integer.A)
B)
C)
D)
E)
2
Suppose an investment is expected to generate income at the rate of dollars/year for the next 6 years. Find the present value of this investment if the prevailing interest rate is 8% / year compounded continuously. Round your answer to the nearest dollar.
A) $950,930
B) $953,042
C) $951,802
D) $957,375
dollars/year for the next 6 years. Find the present value of this investment if the prevailing interest rate is 8% / year compounded continuously. Round your answer to the nearest dollar.A) $950,930
B) $953,042
C) $951,802
D) $957,375
$953,042
3
A certain country's income distribution is described by the function Compute and .
A)
B)
C)
D)
E)
Compute and .A)
B)
C)
D)
E)
4
Aiso deposits $110/month in a savings account paying 8% / year compounded continuously. Estimate the amount that will be in his account after 15 years.
A) $37,048
B) $36,139
C) $38,282
D) $42,603
A) $37,048
B) $36,139
C) $38,282
D) $42,603
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5
The management of the Titan Tire Company has determined that the quantity demanded x of their Super Titan tires/week is related to the unit price p by the relation where p is measured in dollars and x is measured in units of a thousand. Titan will make x units of the tires available in the market if the unit price is dollars. Determine the consumers' surplus and the producers' surplus when the market unit price is set at the equilibrium price. Round your answers to the nearest dollar.
A) CS = $337,012 , PS = $174,988
B) CS = $343,476 , PS = $168,524
C) CS = $341,333 , PS = $170,667
D) CS = $342,567 , PS = $169,433
where p is measured in dollars and x is measured in units of a thousand. Titan will make x units of the tires available in the market if the unit price is dollars. Determine the consumers' surplus and the producers' surplus when the market unit price is set at the equilibrium price. Round your answers to the nearest dollar.A) CS = $337,012 , PS = $174,988
B) CS = $343,476 , PS = $168,524
C) CS = $341,333 , PS = $170,667
D) CS = $342,567 , PS = $169,433
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6
Estimate the present value of an annuity if payments are $500 monthly for 19 years and the account earns interest at the rate of 8% / year compounded continuously. Round your answer to the nearest dollar.
A) $56,454
B) $57,363
C) $62,918
D) $58,597
A) $56,454
B) $57,363
C) $62,918
D) $58,597
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7
A state lottery commission pays the winner of the "Million Dollar" lottery 10 annual installments of $40,000 each. If the prevailing interest rate is 5% / year compounded continuously, find the present value of the winning ticket. Round your answer to the nearest dollar.
A) $316,918
B) $310,454
C) $316,009
D) $314,775
A) $316,918
B) $310,454
C) $316,009
D) $314,775
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8
The demand function for a certain make of replacement cartridges for a water purifier is given by where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the market price is set at $5/cartridge. Round your answer to the nearest dollar.
A) $16,333
B) $16,800
C) $16,667
D) $16,886
where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the market price is set at $5/cartridge. Round your answer to the nearest dollar.A) $16,333
B) $16,800
C) $16,667
D) $16,886
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9
In a study conducted by a certain country's Economic Development Board, it was found that the Lorentz curve for the distribution of income of college teachers was described by the function and that of lawyers by the function Compute the coefficient of inequality for each Lorentz curve. Round your answer to four decimal places. Which profession has a more equitable income distribution?
A) ,
, college teachers
B) ,
, college teachers
C) ,
, college teachers
D) ,
, college teachers
and that of lawyers by the function Compute the coefficient of inequality for each Lorentz curve. Round your answer to four decimal places. Which profession has a more equitable income distribution?A)
, , college teachersB)
, , college teachersC)
, , college teachersD)
, , college teachers فتح الحزمة
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10
Sinclair wishes to supplement his retirement income by $200 per month for the next 12 years. He plans to obtain a reverse annuity mortgage (RAM) on his home to meet this need. Estimate the amount of the mortgage he will require if the prevailing interest rate is 12% per year compounded continuously.
A) $14,068
B) $15,261
C) $15,451
D) $29,552
E) $12,541
A) $14,068
B) $15,261
C) $15,451
D) $29,552
E) $12,541
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11
Find the amount of an annuity if $300 per month is paid into it for a period of 17 years, earning interest at the rate of 9% per year compounded continuously.
A) $144,727
B) $118,909
C) $245,790
D) $179,614
E) $179,511
A) $144,727
B) $118,909
C) $245,790
D) $179,614
E) $179,511
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12
A firm purchased a 16-year franchise for a computer outlet store that is expected to generate income at the rate of dollars per year. If the prevailing interest rate is 10% per year compounded continuously, find the present value of the franchise.
A) $1,114,979
B) $2,250,532
C) $4,660,006
D) $3,192,414
E) $1,756,632
dollars per year. If the prevailing interest rate is 10% per year compounded continuously, find the present value of the franchise.A) $1,114,979
B) $2,250,532
C) $4,660,006
D) $3,192,414
E) $1,756,632
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13
A certain country's income distribution is described by the function Sketch the Lorentz curve for this function. Compute and and interpret your results.
A)
;
The lowest 10 percent of the people receive 1.5 percent of the total income.
The lowest 30 percent of the people receive 10.1 percent of the total income.
B)
;
The lowest 10 percent of the people receive 1.5 percent of the total income.
The lowest 30 percent of the people receive 10.1 percent of the total income.
C)
;
The lowest 30 percent of the people receive 1.5 percent of the total income.
The lowest 10 percent of the people receive 10.1 percent of the total income.
Sketch the Lorentz curve for this function. Compute and and interpret your results.A)
; The lowest 10 percent of the people receive 1.5 percent of the total income.The lowest 30 percent of the people receive 10.1 percent of the total income.
B)
; The lowest 10 percent of the people receive 1.5 percent of the total income.The lowest 30 percent of the people receive 10.1 percent of the total income.
C)
; The lowest 30 percent of the people receive 1.5 percent of the total income.The lowest 10 percent of the people receive 10.1 percent of the total income.
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14
The demand function for a certain brand of compact disc is given by The supply function for the compact discs of is given by where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the producers' surplus if the wholesale market price is set at the equilibrium price. Round your answer to the nearest dollar.
A) $11,894
B) $11,667
C) $11,792
D) $11,346
The supply function for the compact discs of is given by where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the producers' surplus if the wholesale market price is set at the equilibrium price. Round your answer to the nearest dollar.A) $11,894
B) $11,667
C) $11,792
D) $11,346
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15
The Armstrongs wish to establish a custodial account to finance their children's education. If they deposit $600 monthly for 10 years in a savings account paying 6% / year compounded continuously, how much will their savings account be worth at the end of this period? Round your answer to the nearest dollar.
A) $99,877
B) $98,654
C) $100,786
D) $94,327
A) $99,877
B) $98,654
C) $100,786
D) $94,327
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16
It is known that the quantity demanded of a certain make of portable hair dryer is x hundred units/week and the corresponding wholesale unit price is dollars. Determine the consumers' surplus if the wholesale market price is set at $20/unit. Round your answer to the nearest dollar.
A) $5,093
B) $5,217
C) $4,975
D) $4,661
dollars. Determine the consumers' surplus if the wholesale market price is set at $20/unit. Round your answer to the nearest dollar.A) $5,093
B) $5,217
C) $4,975
D) $4,661
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17
The quantity demanded (in units of a hundred) of the miniature cameras per week is related to the unit price (in dollars) by and the quantity (in units of a hundred) that the supplier is willing to make available in the market is related to the unit price (in dollars) by If the market price is set at the equilibrium price, find the consumers' surplus and the producers' surplus. Please round the answers to the nearest dollar.
A) The consumers' surplus: $26,704, the producers' surplus: $142,718
B) The consumers' surplus: $142,718, the producers' surplus: $26,704
C) The consumers' surplus: $18,333, the producers' surplus: $20,000
D) The consumers' surplus: $20,000, the producers' surplus: $18,333
E) The consumers' surplus: $44,040, the producers' surplus: $21,478
(in units of a hundred) of the miniature cameras per week is related to the unit price (in dollars) by and the quantity (in units of a hundred) that the supplier is willing to make available in the market is related to the unit price (in dollars) by If the market price is set at the equilibrium price, find the consumers' surplus and the producers' surplus. Please round the answers to the nearest dollar.A) The consumers' surplus: $26,704, the producers' surplus: $142,718
B) The consumers' surplus: $142,718, the producers' surplus: $26,704
C) The consumers' surplus: $18,333, the producers' surplus: $20,000
D) The consumers' surplus: $20,000, the producers' surplus: $18,333
E) The consumers' surplus: $44,040, the producers' surplus: $21,478
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18
The demand function for a certain brand of compact disc is given by where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the wholesale market price is set at $2/disc. Round your answer to the nearest dollar.
A) $16,346
B) $16,790
C) $16,880
D) $16,667
where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the wholesale market price is set at $2/disc. Round your answer to the nearest dollar.A) $16,346
B) $16,790
C) $16,880
D) $16,667
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19
Estimate the present value of an annuity if payments are $1,500 monthly for 12 years and the account earns interest at the rate of 9% per year compounded continuously.
A) $105,563
B) $86,116
C) $129,803
D) $132,081
E) $104,177
A) $105,563
B) $86,116
C) $129,803
D) $132,081
E) $104,177
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20
Find . Round your answer to the nearest integer.
A) 866,981
B) 912,104
C) 854,636
D) 851,747
. Round your answer to the nearest integer.A) 866,981
B) 912,104
C) 854,636
D) 851,747
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21
Estimate the present value of an annuity if payments are $700 monthly for 19 years and the account earns interest at the rate of 5% / year compounded continuously. Round your answer to the nearest dollar.
$__________
$__________
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22
In a study conducted by a certain country's Economic Development Board, it was found that the Lorentz curve for the distribution of income of stockbrokers was described by the function and that of high school teachers by the function Compute the coefficient of inequality for each Lorentz curve. Round your answers to the nearest hundredth. Which profession has a more equitable income distribution?
A) ,
, stockbrokers
B) ,
, teachers
C) ,
, stockbrokers
D) ,
, stockbrokers
and that of high school teachers by the function Compute the coefficient of inequality for each Lorentz curve. Round your answers to the nearest hundredth. Which profession has a more equitable income distribution?A)
, , stockbrokersB)
, , teachersC)
, , stockbrokersD)
, , stockbrokers فتح الحزمة
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23
In a study conducted by a certain country's Economic Development Board, it was found that the Lorentz curve for the distribution of income of stockbrokers was described by the function and that of high school teachers by the function Compute the coefficient of inequality for each Lorentz curve. Round your answers to the nearest hundredth.
The coefficient of inequality for stockbrokers is __________.
The coefficient of inequality for teachers is __________.
Which profession has a more equitable income distribution?
and that of high school teachers by the function Compute the coefficient of inequality for each Lorentz curve. Round your answers to the nearest hundredth.The coefficient of inequality for stockbrokers is __________.
The coefficient of inequality for teachers is __________.
Which profession has a more equitable income distribution?
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24
Suppose an investment is expected to generate income at the rate of dollars/year for the next 5 years. Find the present value of this investment if the prevailing interest rate is 0.05% / year compounded continuously. Round your answer to the nearest dollar.
$__________
dollars/year for the next 5 years. Find the present value of this investment if the prevailing interest rate is 0.05% / year compounded continuously. Round your answer to the nearest dollar.$__________
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25
Find the amount of an annuity if $210 per month is paid into it for a period of 24 years, earning interest at the rate of 9% per year compounded continuously. Please round the answer to the nearest dollar.
$__________
$__________
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26
The demand function for a certain make of replacement cartridges for a water purifier is given by where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the market price is set at $1/cartridge. Round your answer to the nearest dollar.
CS = $__________
where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the market price is set at $1/cartridge. Round your answer to the nearest dollar.CS = $__________
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27
Aiso deposits $140 / month in a savings account paying 8% / year compounded continuously. Estimate the amount that will be in his account after 15 years.
$__________
$__________
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28
Verify that .
. فتح الحزمة
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29
The demand function for a certain brand of compact disc is given by The supply function for the compact discs is given by where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the producers' surplus if the wholesale market price is set at the equilibrium price. Round your answer to the nearest dollar.
$__________
The supply function for the compact discs is given by where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the producers' surplus if the wholesale market price is set at the equilibrium price. Round your answer to the nearest dollar.$__________
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30
A state lottery commission pays the winner of the "Million Dollar" lottery 10 annual installments of $50,000 each. If the prevailing interest rate is 5% / year compounded continuously, find the present value of the winning ticket. Round your answer to the nearest dollar.
$__________
$__________
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31
In a study conducted by a certain country's Economic Development Board, it was found that the Lorentz curve for the distribution of income of college teachers was described by the function and that of lawyers by the function Compute the coefficient of inequality for each Lorentz curve. Round your answer to four decimal places.
The coefficient of inequality for college teachers is __________.
The coefficient of inequality for lawyers is __________.
Which profession has a more equitable income distribution?
and that of lawyers by the function Compute the coefficient of inequality for each Lorentz curve. Round your answer to four decimal places.The coefficient of inequality for college teachers is __________.
The coefficient of inequality for lawyers is __________.
Which profession has a more equitable income distribution?
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32
The quantity demanded (in units of a hundred) of the miniature cameras per week is related to the unit price (in dollars) by and the quantity (in units of a hundred) that the supplier is willing to make available in the market is related to the unit price (in dollars) by If the market price is set at the equilibrium price, find the consumers' surplus and the producers' surplus. Please round the answers to the nearest dollar.
The consumers' surplus: $__________
The producers' surplus: $__________
(in units of a hundred) of the miniature cameras per week is related to the unit price (in dollars) by and the quantity (in units of a hundred) that the supplier is willing to make available in the market is related to the unit price (in dollars) by If the market price is set at the equilibrium price, find the consumers' surplus and the producers' surplus. Please round the answers to the nearest dollar.The consumers' surplus: $__________
The producers' surplus: $__________
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33
The management of the Titan Tire Company has determined that the quantity demanded x of their Super Titan tires/week is related to the unit price p by the relation where p is measured in dollars and x is measured in units of a thousand. Titan will make x units of the tires available in the market if the unit price is dollars. Determine the consumers' surplus and the producers' surplus when the market unit price is set at the equilibrium price. Round your answers to the nearest dollars.
CS = $__________
PS = $__________
where p is measured in dollars and x is measured in units of a thousand. Titan will make x units of the tires available in the market if the unit price is dollars. Determine the consumers' surplus and the producers' surplus when the market unit price is set at the equilibrium price. Round your answers to the nearest dollars.CS = $__________
PS = $__________
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34
The Armstrongs wish to establish a custodial account to finance their children's education. If they deposit $600 monthly for 8 years in a savings account paying 7% / year compounded continuously, how much will their savings account be worth at the end of this period? Round your answer to the nearest dollar.
$__________
$__________
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35
Sinclair wishes to supplement his retirement income by $450 per month for the next 15 years. He plans to obtain a reverse annuity mortgage (RAM) on his home to meet this need. Estimate the amount of the mortgage he will require if the prevailing interest rate is 11% per year compounded continuously. Please round the answer to the nearest dollar.
$__________
$__________
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36
The demand function for a certain brand of compact disc is given by where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the wholesale market price is set at $4/disc. Round your answer to the nearest dollar.
$__________
where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the wholesale market price is set at $4/disc. Round your answer to the nearest dollar.$__________
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37
Estimate the present value of an annuity if payments are $1,400 monthly for 14 years and the account earns interest at the rate of 10% per year compounded continuously. Please round the answer to the nearest cent dollar.
$__________
$__________
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38
It is known that the quantity demanded of a certain make of portable hair dryer is x hundred units/week and the corresponding wholesale unit price is dollars. Determine the consumers' surplus if the wholesale market price is set at $10/unit. Round your answer to the nearest dollar.
$__________
dollars. Determine the consumers' surplus if the wholesale market price is set at $10/unit. Round your answer to the nearest dollar.$__________
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39
A firm purchased a 11-year franchise for a computer outlet store that is expected to generate income at the rate of dollars per year. If the prevailing interest rate is 9% per year compounded continuously, find the present value of the franchise. Please round the answer to the nearest dollar.
$__________
dollars per year. If the prevailing interest rate is 9% per year compounded continuously, find the present value of the franchise. Please round the answer to the nearest dollar.$__________
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40
Find the area of the shaded region.
A) A = 23.6 sq units.
B) A = 19.9 sq units.
C) A = 18.1 sq units.
D) A = 21.3 sq units.
A) A = 23.6 sq units.
B) A = 19.9 sq units.
C) A = 18.1 sq units.
D) A = 21.3 sq units.
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41
Sketch the region completely enclosed by the graphs of the given functions f and g.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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42
Find the area of the region enclosed by these graphs and the vertical lines and .
A)
B)
C) 12
D)
E)
and . A)
B)
C) 12
D)
E)
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43
Sketch the graph and find the area of the region bounded by the graph of the function f and lines y = 0, x = a and x = b.
A)
B)
C)
D)
A)
B)
C)
D)
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44
Sketch the graph and find the area of the region bounded below by the graph of the given function and above by the x-axis from x = a to x = b.
A)
B)
C)
D)
A)
B)
C)
D)
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45
Sketch the region completely enclosed by the graphs of the given functions f and g.
A)
B)
C)
D)
A)
B)
C)
D)
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46
Sketch the graph and find the area of the region completely enclosed by the graphs of the given functions f and g.
A)
B)
C)
D)
A)
B)
C)
D)
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47
Sketch the graphs of the functions f and g and find the area of the region enclosed by these graphs and the vertical lines x = a and x = b.
A)
B)
C)
D)
A)
B)
C)
D)
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48
Sketch the graphs of the functions f and g and find the area of the region enclosed by these graphs and the vertical lines x = a and x = b.
A)
B)
C)
D)
A)
B)
C)
D)
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49
Find the area of the shaded region.
A) A = 10 sq units.
B) A = 13 sq units.
C) A = 9 sq units.
D) A = 12 sq units.
A) A = 10 sq units.
B) A = 13 sq units.
C) A = 9 sq units.
D) A = 12 sq units.
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50
Sketch the graph of the region bounded by the graph of the function f and lines y = 0, x = a and x = b.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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51
Sketch the region completely enclosed by the graphs of the given functions f and g.
A)
B)
C)
D)
A)
B)
C)
D)
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52
Find the area of the shaded region.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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53
Find the area of the region bounded below by the graph of the function and above by the -axis from to .
A)
B)
C)
D)
E)
-axis from to . A)
B)
C)
D)
E)
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54
Find the area of the shaded region.
A) A = 4 ln 2 sq units.
B) A = 5 ln 2 sq units.
C) A = ln 4 sq units.
D) A = 2 ln 2 sq units.
A) A = 4 ln 2 sq units.
B) A = 5 ln 2 sq units.
C) A = ln 4 sq units.
D) A = 2 ln 2 sq units.
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55
Sketch the graph and find the area of the region bounded by the graph of the function f and lines y = 0, x = a and x = b.
A)
B)
C)
D)
A)
B)
C)
D)
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56
Sketch the graphs of the functions f and g and find the area of the region enclosed by these graphs and the vertical lines x = a and x = b.
A)
B)
C)
D)
A)
B)
C)
D)
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57
Find the area of the region bounded by the graph of the function and the lines , , and .
A)
B)
C)
D)
E)
and the lines , , and . A)
B)
C)
D)
E)
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58
Sketch the graphs of the functions f and g and find the area of the region enclosed by these graphs and the vertical lines x = a and x = b.
A)
B)
C)
D)
A)
B)
C)
D)
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59
Sketch the graph and find the area of the region bounded by the graph of the function f and lines y = 0, x = a and x = b.
A)
B)
C)
D)
A)
B)
C)
D)
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60
Sketch the graph and find the area of the region bounded below by the graph of the given function and above by the x-axis from x = a to x = b.
A)
B)
C)
D)
A)
B)
C)
D)
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61
Evaluate the given definite integral.
A)
B)
C)
D)
A)
B)
C)
D)
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62
Evaluate the given definite integral.
A)
B)
C)
D)
A)
B)
C)
D)
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63
Because of the increasingly important role played by coal as a viable alternative energy source, the production of coal has been growing at the rate of billion metric tons/year t years from 1970 (which corresponds to t = 0). Had it not been for the energy crisis, the rate of production of coal since 1970 might have been only billion metric tons/year t years from 1970. Determine how much additional coal was produced between 1970 and the end of the century as an alternate energy source. Round your answer to one decimal place.
__________ billion metric tons
billion metric tons/year t years from 1970 (which corresponds to t = 0). Had it not been for the energy crisis, the rate of production of coal since 1970 might have been only billion metric tons/year t years from 1970. Determine how much additional coal was produced between 1970 and the end of the century as an alternate energy source. Round your answer to one decimal place.__________ billion metric tons
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64
Evaluate the given definite integral.
A)
B)
C)
D)
A)
B)
C)
D)
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65
Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The area of the region bounded by the graphs of and and the vertical lines x = 0 and x = 6 is given by
A) True. Since f and g are continuous functions and on the interval [0, 6], then the area of the region bounded above by y = f(x) and below by y = g(x) on [0, 6] is given by
B) False. Since f and g are continuous functions and on the interval [0, 6], then the area of the region bounded above by y = g(x) and below by y = f(x) on [0, 6] is given by
and and the vertical lines x = 0 and x = 6 is given by A) True. Since f and g are continuous functions and
on the interval [0, 6], then the area of the region bounded above by y = f(x) and below by y = g(x) on [0, 6] is given byB) False. Since f and g are continuous functions and
on the interval [0, 6], then the area of the region bounded above by y = g(x) and below by y = f(x) on [0, 6] is given by فتح الحزمة
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66
In an endeavor to curb population growth in a certain country, the government has decided to launch an extensive propaganda campaign. Without curbs, the government expects the rate of population growth to have been thousand people per year years from now, over the next years. However, successful implementation of the proposed campaign is expected to result in a population growth rate of thousand people per year years from now, over the next years. Assuming that the campaign is mounted, how many fewer people will there be in that country years from now then there would have been if no curbs had been imposed?
Please round your answer to the nearest whole number.
__________ thousand people
thousand people per year years from now, over the next years. However, successful implementation of the proposed campaign is expected to result in a population growth rate of thousand people per year years from now, over the next years. Assuming that the campaign is mounted, how many fewer people will there be in that country years from now then there would have been if no curbs had been imposed?Please round your answer to the nearest whole number.
__________ thousand people
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67
Evaluate the given definite integral.
A)
B)
C)
D)
A)
B)
C)
D)
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68
Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
The area of the region bounded by the graphs of and and the vertical lines x = 0 and x = 4 is given by
The area of the region bounded by the graphs of
and and the vertical lines x = 0 and x = 4 is given by فتح الحزمة
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69
Find the area of the region completely enclosed by the graphs of the given functions and .
A)
B)
C)
D)
E)
and . A)
B)
C)
D)
E)
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70
Find the area of the shaded region.
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71
Find the area of the shaded region. Round your answer to one decimal place.
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72
Find the area of the shaded region.
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73
In tests conducted by Auto Test Magazine on two identical models of the Phoenix Elite - one equipped with a standard engine and the other with a turbo-charger - it was found that the acceleration of the former is given by ft/sec, t seconds after starting from rest at full throttle, whereas the acceleration of the latter is given by ft/sec. How much faster is the turbo-charged model moving than the model with the standard engine at the end of a 10-second test run at full throttle?
__________ ft/sec
ft/sec, t seconds after starting from rest at full throttle, whereas the acceleration of the latter is given by ft/sec. How much faster is the turbo-charged model moving than the model with the standard engine at the end of a 10-second test run at full throttle?__________ ft/sec
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74
In tests conducted by Auto Test Magazine on two identical models of the Phoenix Elite - one equipped with a standard engine and the other with a turbo-charger - it was found that the acceleration of the former is given by ft/sec, t sec after starting from rest at full throttle, whereas the acceleration of the latter is given by ft/sec. How much faster is the turbo-charged model moving than the model with the standard engine at the end of a 10-second test run at full throttle?
A) 65 ft/sec
B) 58 ft/sec
C) 75 ft/sec
D) 70 ft/sec
ft/sec, t sec after starting from rest at full throttle, whereas the acceleration of the latter is given by ft/sec. How much faster is the turbo-charged model moving than the model with the standard engine at the end of a 10-second test run at full throttle?A) 65 ft/sec
B) 58 ft/sec
C) 75 ft/sec
D) 70 ft/sec
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75
Find the area of the shaded region.
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76
Evaluate the given definite integral.
A)
B)
C)
D)
A)
B)
C)
D)
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77
In an endeavor to curb population growth in a certain country, the government has decided to launch an extensive propaganda campaign. Without curbs, the government expects the rate of population growth to have been thousand people per year years from now, over the next years. However, successful implementation of the proposed campaign is expected to result in a population growth rate of thousand people per year years from now, over the next years. Assuming that the campaign is mounted, how many fewer people will there be in that country years from now then there would have been if no curbs had been imposed? Please round your answer to the nearest integer number of thousands.
A) thousand people
B) thousand people
C) thousand people
D) thousand people
E) thousand people
thousand people per year years from now, over the next years. However, successful implementation of the proposed campaign is expected to result in a population growth rate of thousand people per year years from now, over the next years. Assuming that the campaign is mounted, how many fewer people will there be in that country years from now then there would have been if no curbs had been imposed? Please round your answer to the nearest integer number of thousands.A)
thousand peopleB)
thousand peopleC)
thousand peopleD)
thousand peopleE)
thousand people فتح الحزمة
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78
Because of the increasingly important role played by coal as a viable alternative energy source, the production of coal has been growing at the rate of billion metric tons/year t years from 1990 (which corresponds to t = 0). Had it not been for the energy crisis, the rate of production of coal since 1990 might have been only billion metric tons/year t years from 1990. Determine how much additional coal was produced between 1990 and the end of the century as an alternate energy source.
A) 13.6 billion metric tons
B) 0.6 billion metric tons
C) 4.7 billion metric tons
D) 7.9 billion metric tons
billion metric tons/year t years from 1990 (which corresponds to t = 0). Had it not been for the energy crisis, the rate of production of coal since 1990 might have been only billion metric tons/year t years from 1990. Determine how much additional coal was produced between 1990 and the end of the century as an alternate energy source.A) 13.6 billion metric tons
B) 0.6 billion metric tons
C) 4.7 billion metric tons
D) 7.9 billion metric tons
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79
Evaluate the definite integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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80
Evaluate the given definite integral.
A)
B)
C)
D)
A)
B)
C)
D)
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