تكلم مع الذكاء الاصطناعي
Deck 7: Further Integration Techniques and Applications of the Integral
ملء الشاشة (f)
سؤال
Evaluate the integral. 
سؤال
Evaluate the integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate the integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Luckily, sales of your Star Wars T-shirts are now 47 T-shirts per week and increasing continuously at a rate of 6% per week. You are now charging $15 per T-shirt and are decreasing the price by 30 
per week. How much revenue will you generate during the next six weeks?
A)$4,640.72
B)$4,683.09
C)$4,810.20
D)$4,767.83
E)$4,725.46
per week. How much revenue will you generate during the next six weeks?A)$4,640.72
B)$4,683.09
C)$4,810.20
D)$4,767.83
E)$4,725.46
سؤال
Evaluate the integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate the integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate the integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate the integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate the integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate the integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
A rocket rising from the ground has a velocity of 
after t seconds. How far does it rise in the first 3 minutes and 10 seconds?
A)
B)
C)
D)
E)
after t seconds. How far does it rise in the first 3 minutes and 10 seconds?A)
B)
C)
D)
E)
سؤال
Evaluate the integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate the integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the area of the region between 
for 
in 
.
A)
B)
C)
D)
E)
for in .A)
B)
C)
D)
E)
سؤال
Evaluate the integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate the integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate the integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate the integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate the integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the area of the region between 
for 
in 
.
A)
B)
C)
D)
E)
for in .A)
B)
C)
D)
E)
سؤال
Match between columns
سؤال
Find the area of the indicated region. Enclosed by 
and 
.
A)
B)
C)
D)
E)
and .A)
B)
C)
D)
E)
سؤال
Find the area of the region enclosed by 
and the line 
.
A)
B)
C)
D)
E)
and the line .A)
B)
C)
D)
E)
سؤال
For the differential equation, find the particular solution if y (5)= 27. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the area of the region enclosed by 
and the y -axis.
A)
B)
C)
D)
E)
and the y -axis.A)
B)
C)
D)
E)
سؤال
Find the area of the indicated region. Enclosed by 
and 
.
A)
B)
C)
D)
E)
and .A)
B)
C)
D)
E)
سؤال
Find the area of the region between 
for 
in 
.
A)
B)
C)
D)
E)
for in .A)
B)
C)
D)
E)
سؤال
Find the area of the region enclosed by 
and 
.
A)
B)
C)
D)
E)
and .A)
B)
C)
D)
E)
سؤال
Find the average of the function 
over 0, 8 .
A)Average = 180
B)Average = 157
C)Average = 160
D)Average = 1440
E)Average = 179
over 0, 8 .A)Average = 180
B)Average = 157
C)Average = 160
D)Average = 1440
E)Average = 179
سؤال
Find the area of the indicated region. Enclosed by 
, 
, 
and 
.(Round answer to four significant digits.)Use technology to solve.
A)
B)
C)
D)
E)
, , and .(Round answer to four significant digits.)Use technology to solve.A)
B)
C)
D)
E)
سؤال
Find the average of the function 
over 0, 8 .
A)Average =
B)Average =
C)Average =
D)Average =
E)Average =
over 0, 8 .A)Average =
B)Average =
C)Average =
D)Average =
E)Average =
سؤال
Annual U.S. imports from China in the years 2001-2002 could be approximated by 
billion dollars per year, where 
represents time in years since the start of 1995. During the same period, annual U.S. exports to China could be approximated by 
billion dollars per year. Compute the area between the graphs of 
and 
over the interval 
.(Round your answer to the nearest $10 billion.)
A)$210 billion
B)$90 billion
C)$30 billion
D)$150 billion
E)$120 billion
billion dollars per year, where represents time in years since the start of 1995. During the same period, annual U.S. exports to China could be approximated by billion dollars per year. Compute the area between the graphs of and over the interval .(Round your answer to the nearest $10 billion.)A)$210 billion
B)$90 billion
C)$30 billion
D)$150 billion
E)$120 billion
سؤال
Suppose your annual income is 
dollars per year, where t represents the number of years since you began your job, while your annual expenses are 
dollars per year. Find the area between the graphs of 
and 
for 
.
A)Area = $197,100
B)Area = $67,200
C)Area = $129,900
D)Area = $65,400
E)Area = $62,700
dollars per year, where t represents the number of years since you began your job, while your annual expenses are dollars per year. Find the area between the graphs of and for .A)Area = $197,100
B)Area = $67,200
C)Area = $129,900
D)Area = $65,400
E)Area = $62,700
سؤال
Find the general solution of the differential equation. 
Solve for 
as a function of 
.
A)
B)
C)
D)
E)
Solve for as a function of .A)
B)
C)
D)
E)
سؤال
Find the area of the region between 
and 
for 
in 
.
A)
B)
C)
D)
E)
and for in .A)
B)
C)
D)
E)
سؤال
Find the average of the function 
over 0, 2 .
A)Average = 9
B)Average = 18
C)Average = 5
D)Average = 72
E)Average = 76
over 0, 2 .A)Average = 9
B)Average = 18
C)Average = 5
D)Average = 72
E)Average = 76
سؤال
Find the area of the indicated region. Enclosed by 
and 
and 
.
A)
B)
C)
D)
E)
and and .A)
B)
C)
D)
E)
سؤال
Find the area of the indicated region. Enclosed by 
and 
. (Round answer to four significant digits.)First use technology to determine approximately where the graphs cross.
and . (Round answer to four significant digits.)First use technology to determine approximately where the graphs cross. سؤال
Find the area of the region enclosed by 
and 
.
A)
B)
C)
D)
E)
and .A)
B)
C)
D)
E)
سؤال
Find the area of the indicated region. Enclosed by 
and 
. (Round answer to four significant digits.)First use technology to determine approximately where the graphs cross.
A)
B)
C)
D)
E)
and . (Round answer to four significant digits.)First use technology to determine approximately where the graphs cross.A)
B)
C)
D)
E)
سؤال
Your monthly salary has been increasing steadily for the past year, and your average monthly salary over the past year was 
dollars. Would you have earned more money if you had been paid 
dollars per month?
A)No. You would have earned less money.
B)Yes. You would have earned more money.
C)No. You would have earned exactly the same amount of money.
D)More information is needed to answer the question.
dollars. Would you have earned more money if you had been paid dollars per month?A)No. You would have earned less money.
B)Yes. You would have earned more money.
C)No. You would have earned exactly the same amount of money.
D)More information is needed to answer the question.
سؤال
Calculate the producers surplus at the unit price 
for the following supply equation. 
A)$288.50
B)$291.50
C)$283.50
D)$282.50
E)$285.50
for the following supply equation. A)$288.50
B)$291.50
C)$283.50
D)$282.50
E)$285.50
سؤال
Find the total value of the given income stream and also find its present value (at the beginning of the given interval)using the given interest rate. 
A)TV = $250,000, PV =$1,512,966.53
B)TV = $10,000, PV = $1,331,148.35
C)TV = $250,000, PV = $85,097.47
D)TV = $0, PV = $9,360.72
E)TV = $0, PV = $85,097.47
A)TV = $250,000, PV =$1,512,966.53
B)TV = $10,000, PV = $1,331,148.35
C)TV = $250,000, PV = $85,097.47
D)TV = $0, PV = $9,360.72
E)TV = $0, PV = $85,097.47
سؤال
Some values of a function and its 3-unit moving average are given. Supply the missing information: 
average undefined undefined 6 ? 11 ? ?
A)x 1 2 3 4 5 6 7 r ( x )2 2 15 8 10 8 12 average undefined undefined 6 8 11 9 9
B)x 1 2 3 4 5 6 7 r ( x )2 2 14 8 11 8 8 average undefined undefined 6 8 11 9 9
C)x 1 2 3 4 5 6 7 r ( x )2 2 14 8 11 8 8 average undefined undefined 6 8 11 12 12
average undefined undefined 6 ? 11 ? ?A)x 1 2 3 4 5 6 7 r ( x )2 2 15 8 10 8 12 average undefined undefined 6 8 11 9 9
B)x 1 2 3 4 5 6 7 r ( x )2 2 14 8 11 8 8 average undefined undefined 6 8 11 9 9
C)x 1 2 3 4 5 6 7 r ( x )2 2 14 8 11 8 8 average undefined undefined 6 8 11 12 12
سؤال
Find the formula for the a -unit moving average of a general linear function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The rate of U.S. per capita sales of bottled water for the period 1993-2003 could be approximated by 
where 
is the time in years since 1990. Compute the average annual sales of bottled water over the period 1998-2002, to the nearest gallon per year.
A)18 gallons per year
B)17 gallons per year
C)19 gallons per year
D)16 gallons per year
E)20 gallons per year
where is the time in years since 1990. Compute the average annual sales of bottled water over the period 1998-2002, to the nearest gallon per year.A)18 gallons per year
B)17 gallons per year
C)19 gallons per year
D)16 gallons per year
E)20 gallons per year
سؤال
Find the total value or the given income stream and also find its future value (at the end of the given interval)using the given interest rate. 
A)TV = $2,234,000.03, FV = $1,411,333.34
B)TV = $4,468,000.07, FV = $657,058.77
C)TV =$2,234,000.03, FV =$4,729,378.11
D)TV = $4,234,000.03, FV = $314,911.04
E)TV = $67,020.00, FV = $13,161,504,599,350.49
A)TV = $2,234,000.03, FV = $1,411,333.34
B)TV = $4,468,000.07, FV = $657,058.77
C)TV =$2,234,000.03, FV =$4,729,378.11
D)TV = $4,234,000.03, FV = $314,911.04
E)TV = $67,020.00, FV = $13,161,504,599,350.49
سؤال
Calculate the 5-unit moving average of the given function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the formula for the 
-unit moving average of a general exponential function. 
A)
B)
C)
D)
E)
-unit moving average of a general exponential function. A)
B)
C)
D)
E)
سؤال
سؤال
Find the total value of the given income stream and also find its future value (at the end of the given interval)using the given interest rate. 
A)TV = $2,200,000, FV = $3,667,532.75
B)TV = $5,800,000, FV = $4,356,486.55
C)TV = $1,400,000, FV = $2,518,281.83
D)TV = $2,200,000, FV = $5,467,532.75
E)TV = $2,000,000, FV = $-2,296,343.85
A)TV = $2,200,000, FV = $3,667,532.75
B)TV = $5,800,000, FV = $4,356,486.55
C)TV = $1,400,000, FV = $2,518,281.83
D)TV = $2,200,000, FV = $5,467,532.75
E)TV = $2,000,000, FV = $-2,296,343.85
سؤال
سؤال
Calculate the producers surplus at the unit price 
for the supply following equation. 
A)$9.00
B)$18.00
C)$13.00
D)$16.00
E)$10.00
for the supply following equation. A)$9.00
B)$18.00
C)$13.00
D)$16.00
E)$10.00
سؤال
Calculate the 5-unit moving average of the given function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Calculate the 6-unit moving average of the given function. 
سؤال
Calculate the 5-unit moving average of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the average of the function 
over 0, 8 .
over 0, 8 . سؤال
Complete the table with the values of the 3-unit moving average of the given function: 
average undefined undefined ?
A)x 1 2 3 4 5 6 7 r ( x )1 2 15 4 11 18 13 average undefined undefined 7 10 11 14 6
B)x 1 2 3 4 5 6 7 r ( x )1 2 15 4 11 18 13 average undefined undefined 14 6 7 10 11
C)x 1 2 3 4 5 6 7 r ( x )1 2 15 4 11 18 13 average undefined undefined 6 7 10 11 14
average undefined undefined ?A)x 1 2 3 4 5 6 7 r ( x )1 2 15 4 11 18 13 average undefined undefined 7 10 11 14 6
B)x 1 2 3 4 5 6 7 r ( x )1 2 15 4 11 18 13 average undefined undefined 14 6 7 10 11
C)x 1 2 3 4 5 6 7 r ( x )1 2 15 4 11 18 13 average undefined undefined 6 7 10 11 14
سؤال
Find the total value of the given income stream and also find its future value (at the end of the given interval)using the given interest rate. 
A)TV = $50,000, FV = $258,135.27
B)TV = $100,000, FV = $470,353.13
C)TV = $200,000, FV = $8,221.19
D)TV = $100,000, FV = $303,686.47
E)TV = $100,000, FV = $137,019.80
A)TV = $50,000, FV = $258,135.27
B)TV = $100,000, FV = $470,353.13
C)TV = $200,000, FV = $8,221.19
D)TV = $100,000, FV = $303,686.47
E)TV = $100,000, FV = $137,019.80
سؤال
Calculate the 9-unit moving average of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
سؤال
The annual net sales (revenue)earned by the Finnish cell phone company Nokia from January 1999 to January 2003 can be approximated by 
billion euros per year 
where 
is time in years ( 
represents January 2000 ). Estimate, to the nearest billion, Nokia s total revenue from January 1999 through December 2002.
A)
B)
C)
D)
E)
billion euros per year where is time in years ( represents January 2000 ). Estimate, to the nearest billion, Nokia s total revenue from January 1999 through December 2002.A)
B)
C)
D)
E)
سؤال
A fast-food outlet finds that the demand equation for its new side dish, Sweetdough Tidbit , is given by 
where p is the price (in cents)per serving and q is the number of servings that can be sold per hour at this price. At the same time, the franchise is prepared to sell 
servings per hour at a price of p cents. Find the consumers surplus at the equilibrium price level.
A)$6.04
B)$6.02
C)$6.10
D)$6.00
E)$6.06
where p is the price (in cents)per serving and q is the number of servings that can be sold per hour at this price. At the same time, the franchise is prepared to sell servings per hour at a price of p cents. Find the consumers surplus at the equilibrium price level.A)$6.04
B)$6.02
C)$6.10
D)$6.00
E)$6.06
سؤال
سؤال
سؤال
Find the total value of the given income stream and also find its present value (at the beginning of the given interval)using the given interest rate. 
A)TV = $0, PV = $248,477.55
B)TV = $45,317.31, PV = $59,866.79
C)TV = $55,350.69, PV = $46,430.67
D)TV = $454,682.69, PV = $1,392.92
E)TV = $2,214.03, PV = $46,430.67
A)TV = $0, PV = $248,477.55
B)TV = $45,317.31, PV = $59,866.79
C)TV = $55,350.69, PV = $46,430.67
D)TV = $454,682.69, PV = $1,392.92
E)TV = $2,214.03, PV = $46,430.67
سؤال
Find the total value of the given income stream and also find its present value (at the beginning of the given interval)using the given interest rate. 
Please enter your answer in the form TV = , PV = . Give the answer to the nearest cent if necessary. TV = $__________ PV = $__________
Please enter your answer in the form TV = , PV = . Give the answer to the nearest cent if necessary. TV = $__________ PV = $__________ سؤال
Find the total value of the given income stream and also find its future value (at the end of the given interval)using the given interest rate. 
Please enter your answer in the form TV = , FV = . Round FV to the nearest cent. TV = $__________ FV = $__________
Please enter your answer in the form TV = , FV = . Round FV to the nearest cent. TV = $__________ FV = $__________ سؤال
The annual revenue earned by Target for fiscal years 1998 through 2005 can be approximated by 
billion dollars per year 
where 
is time in years ( 
represents the beginning of fiscal year 2000). Suppose that, from fiscal year 1998 on, Target invested its revenue in an investment that depreciated continuously at a rate of 7% per year. What, to the nearest $10 billion, would the total value of Target s revenue have been by the end of fiscal year 2003?
A)
B)
C)
D)
E)
billion dollars per year where is time in years ( represents the beginning of fiscal year 2000). Suppose that, from fiscal year 1998 on, Target invested its revenue in an investment that depreciated continuously at a rate of 7% per year. What, to the nearest $10 billion, would the total value of Target s revenue have been by the end of fiscal year 2003?A)
B)
C)
D)
E)
سؤال
سؤال
سؤال
The annual net sales (revenue)earned by the Finnish cell phone company Nokia from January 1999 to January 2004 can be approximated by 
billion euros per year 
where 
is time in years ( 
represents January 2000 ). Suppose that, from January 1999 on, Nokia invested its revenue in an investment yielding 7% compounded continuously. What, to the nearest 10 billion, would the total value of Nokia s revenues have been at the end of 2003?
A)
B)
C)
D)
E)
billion euros per year where is time in years ( represents January 2000 ). Suppose that, from January 1999 on, Nokia invested its revenue in an investment yielding 7% compounded continuously. What, to the nearest 10 billion, would the total value of Nokia s revenues have been at the end of 2003?A)
B)
C)
D)
E)
سؤال
سؤال
Find the total value of the given income stream and also find its future value (at the end of the given interval)using the given interest rate. 
Please enter your answer in the form TV = , FV = . Round FV to the nearest cent. TV = $__________ FV = $__________
Please enter your answer in the form TV = , FV = . Round FV to the nearest cent. TV = $__________ FV = $__________ سؤال
Calculate the producers surplus at the unit price 
for the following supply equation. 
$ __________
for the following supply equation. $ __________ سؤال
Find the total value of the given income stream and also find its present value (at the beginning of the given interval)using the given interest rate. 
A)TV = $130,000, PV = $449,142.92
B)TV = $550,000, PV = $7,886,675.30
C)TV = $1,050,000, PV = $809,958.97
D)TV = $1,055,000, PV = $809,958.97
E)TV = $400,125,000, PV = $997,897.20
A)TV = $130,000, PV = $449,142.92
B)TV = $550,000, PV = $7,886,675.30
C)TV = $1,050,000, PV = $809,958.97
D)TV = $1,055,000, PV = $809,958.97
E)TV = $400,125,000, PV = $997,897.20
سؤال
The annual net sales (revenue)earned by Nintendo Co., Ltd., in the fiscal years ending March 31, 1995 to March 31, 2003, can be approximated by 
billion yen per year 
where 
is time in years ( 
represents March 31, 2000). Suppose that, from April 1994 on, Nintendo invested its revenue in an investment yielding 3% compounded continuously. What, to the nearest 
billion, would the total value of Nintendo s revenue have been by the end of March 2003?
A)
B)
C)
D)
E)
billion yen per year where is time in years ( represents March 31, 2000). Suppose that, from April 1994 on, Nintendo invested its revenue in an investment yielding 3% compounded continuously. What, to the nearest billion, would the total value of Nintendo s revenue have been by the end of March 2003?A)
B)
C)
D)
E)
سؤال
Find the total value or the given income stream and also find its future value (at the end of the given interval)using the given interest rate. 
Please enter your answer in the form TV = , FV = . Give the answers to the nearest cent. TV = $__________ FV = $__________
Please enter your answer in the form TV = , FV = . Give the answers to the nearest cent. TV = $__________ FV = $__________ سؤال
The annual revenue earned by Wal-Mart in the fiscal years ending January 31, 1994 to January 31, 2003 can be approximated by 
billion dollars per year 
where 
is time in years 
represents January 31, 2000). Suppose that, from January 1999 on, Wal-Mart invested its revenue in an investment that depreciated continuously at a rate of 4% per year. What, to the nearest $10 billion, would the total value of Wal-Mart s revenues have been by the end of January 2003?
A)
B)
C)
D)
E)
billion dollars per year where is time in years represents January 31, 2000). Suppose that, from January 1999 on, Wal-Mart invested its revenue in an investment that depreciated continuously at a rate of 4% per year. What, to the nearest $10 billion, would the total value of Wal-Mart s revenues have been by the end of January 2003?A)
B)
C)
D)
E)
سؤال
Find the total value of the given income stream and also find its present value (at the beginning of the given interval)using the given interest rate. 
Please enter your answer in the form TV = , PV = . Give the answer to the nearest cent if necessary. TV = $__________ PV = $__________
Please enter your answer in the form TV = , PV = . Give the answer to the nearest cent if necessary. TV = $__________ PV = $__________
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ملء الشاشة (f)
Deck 7: Further Integration Techniques and Applications of the Integral
1
Evaluate the integral.
2
Evaluate the integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
3
Evaluate the integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
Luckily, sales of your Star Wars T-shirts are now 47 T-shirts per week and increasing continuously at a rate of 6% per week. You are now charging $15 per T-shirt and are decreasing the price by 30 per week. How much revenue will you generate during the next six weeks?
A)$4,640.72
B)$4,683.09
C)$4,810.20
D)$4,767.83
E)$4,725.46
per week. How much revenue will you generate during the next six weeks?A)$4,640.72
B)$4,683.09
C)$4,810.20
D)$4,767.83
E)$4,725.46
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5
Evaluate the integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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6
Evaluate the integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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7
Evaluate the integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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8
Evaluate the integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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9
Evaluate the integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
Evaluate the integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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11
A rocket rising from the ground has a velocity of after t seconds. How far does it rise in the first 3 minutes and 10 seconds?
A)
B)
C)
D)
E)
after t seconds. How far does it rise in the first 3 minutes and 10 seconds?A)
B)
C)
D)
E)
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12
Evaluate the integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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13
Evaluate the integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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14
Find the area of the region between for in .
A)
B)
C)
D)
E)
for in .A)
B)
C)
D)
E)
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15
Evaluate the integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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16
Evaluate the integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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17
Evaluate the integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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18
Evaluate the integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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19
Evaluate the integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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20
Find the area of the region between for in .
A)
B)
C)
D)
E)
for in .A)
B)
C)
D)
E)
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21
Match between columns
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22
Find the area of the indicated region. Enclosed by and .
A)
B)
C)
D)
E)
and .A)
B)
C)
D)
E)
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23
Find the area of the region enclosed by and the line .
A)
B)
C)
D)
E)
and the line .A)
B)
C)
D)
E)
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24
For the differential equation, find the particular solution if y (5)= 27.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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25
Find the area of the region enclosed by and the y -axis.
A)
B)
C)
D)
E)
and the y -axis.A)
B)
C)
D)
E)
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26
Find the area of the indicated region. Enclosed by and .
A)
B)
C)
D)
E)
and .A)
B)
C)
D)
E)
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27
Find the area of the region between for in .
A)
B)
C)
D)
E)
for in .A)
B)
C)
D)
E)
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28
Find the area of the region enclosed by and .
A)
B)
C)
D)
E)
and .A)
B)
C)
D)
E)
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29
Find the average of the function over 0, 8 .
A)Average = 180
B)Average = 157
C)Average = 160
D)Average = 1440
E)Average = 179
over 0, 8 .A)Average = 180
B)Average = 157
C)Average = 160
D)Average = 1440
E)Average = 179
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30
Find the area of the indicated region. Enclosed by , , and .(Round answer to four significant digits.)Use technology to solve.
A)
B)
C)
D)
E)
, , and .(Round answer to four significant digits.)Use technology to solve.A)
B)
C)
D)
E)
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31
Find the average of the function over 0, 8 .
A)Average =
B)Average =
C)Average =
D)Average =
E)Average =
over 0, 8 .A)Average =
B)Average =
C)Average =
D)Average =
E)Average =
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32
Annual U.S. imports from China in the years 2001-2002 could be approximated by billion dollars per year, where represents time in years since the start of 1995. During the same period, annual U.S. exports to China could be approximated by billion dollars per year. Compute the area between the graphs of and over the interval .(Round your answer to the nearest $10 billion.)
A)$210 billion
B)$90 billion
C)$30 billion
D)$150 billion
E)$120 billion
billion dollars per year, where represents time in years since the start of 1995. During the same period, annual U.S. exports to China could be approximated by billion dollars per year. Compute the area between the graphs of and over the interval .(Round your answer to the nearest $10 billion.)A)$210 billion
B)$90 billion
C)$30 billion
D)$150 billion
E)$120 billion
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33
Suppose your annual income is dollars per year, where t represents the number of years since you began your job, while your annual expenses are dollars per year. Find the area between the graphs of and for .
A)Area = $197,100
B)Area = $67,200
C)Area = $129,900
D)Area = $65,400
E)Area = $62,700
dollars per year, where t represents the number of years since you began your job, while your annual expenses are dollars per year. Find the area between the graphs of and for .A)Area = $197,100
B)Area = $67,200
C)Area = $129,900
D)Area = $65,400
E)Area = $62,700
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34
Find the general solution of the differential equation. Solve for as a function of .
A)
B)
C)
D)
E)
Solve for as a function of .A)
B)
C)
D)
E)
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35
Find the area of the region between and for in .
A)
B)
C)
D)
E)
and for in .A)
B)
C)
D)
E)
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36
Find the average of the function over 0, 2 .
A)Average = 9
B)Average = 18
C)Average = 5
D)Average = 72
E)Average = 76
over 0, 2 .A)Average = 9
B)Average = 18
C)Average = 5
D)Average = 72
E)Average = 76
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37
Find the area of the indicated region. Enclosed by and and .
A)
B)
C)
D)
E)
and and .A)
B)
C)
D)
E)
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38
Find the area of the indicated region. Enclosed by and . (Round answer to four significant digits.)First use technology to determine approximately where the graphs cross.
and . (Round answer to four significant digits.)First use technology to determine approximately where the graphs cross. فتح الحزمة
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39
Find the area of the region enclosed by and .
A)
B)
C)
D)
E)
and .A)
B)
C)
D)
E)
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40
Find the area of the indicated region. Enclosed by and . (Round answer to four significant digits.)First use technology to determine approximately where the graphs cross.
A)
B)
C)
D)
E)
and . (Round answer to four significant digits.)First use technology to determine approximately where the graphs cross.A)
B)
C)
D)
E)
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41
Your monthly salary has been increasing steadily for the past year, and your average monthly salary over the past year was dollars. Would you have earned more money if you had been paid dollars per month?
A)No. You would have earned less money.
B)Yes. You would have earned more money.
C)No. You would have earned exactly the same amount of money.
D)More information is needed to answer the question.
dollars. Would you have earned more money if you had been paid dollars per month?A)No. You would have earned less money.
B)Yes. You would have earned more money.
C)No. You would have earned exactly the same amount of money.
D)More information is needed to answer the question.
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42
Calculate the producers surplus at the unit price for the following supply equation.
A)$288.50
B)$291.50
C)$283.50
D)$282.50
E)$285.50
for the following supply equation. A)$288.50
B)$291.50
C)$283.50
D)$282.50
E)$285.50
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43
Find the total value of the given income stream and also find its present value (at the beginning of the given interval)using the given interest rate.
A)TV = $250,000, PV =$1,512,966.53
B)TV = $10,000, PV = $1,331,148.35
C)TV = $250,000, PV = $85,097.47
D)TV = $0, PV = $9,360.72
E)TV = $0, PV = $85,097.47
A)TV = $250,000, PV =$1,512,966.53
B)TV = $10,000, PV = $1,331,148.35
C)TV = $250,000, PV = $85,097.47
D)TV = $0, PV = $9,360.72
E)TV = $0, PV = $85,097.47
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44
Some values of a function and its 3-unit moving average are given. Supply the missing information: average undefined undefined 6 ? 11 ? ?
A)x 1 2 3 4 5 6 7 r ( x )2 2 15 8 10 8 12 average undefined undefined 6 8 11 9 9
B)x 1 2 3 4 5 6 7 r ( x )2 2 14 8 11 8 8 average undefined undefined 6 8 11 9 9
C)x 1 2 3 4 5 6 7 r ( x )2 2 14 8 11 8 8 average undefined undefined 6 8 11 12 12
average undefined undefined 6 ? 11 ? ?A)x 1 2 3 4 5 6 7 r ( x )2 2 15 8 10 8 12 average undefined undefined 6 8 11 9 9
B)x 1 2 3 4 5 6 7 r ( x )2 2 14 8 11 8 8 average undefined undefined 6 8 11 9 9
C)x 1 2 3 4 5 6 7 r ( x )2 2 14 8 11 8 8 average undefined undefined 6 8 11 12 12
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45
Find the formula for the a -unit moving average of a general linear function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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46
The rate of U.S. per capita sales of bottled water for the period 1993-2003 could be approximated by where is the time in years since 1990. Compute the average annual sales of bottled water over the period 1998-2002, to the nearest gallon per year.
A)18 gallons per year
B)17 gallons per year
C)19 gallons per year
D)16 gallons per year
E)20 gallons per year
where is the time in years since 1990. Compute the average annual sales of bottled water over the period 1998-2002, to the nearest gallon per year.A)18 gallons per year
B)17 gallons per year
C)19 gallons per year
D)16 gallons per year
E)20 gallons per year
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47
Find the total value or the given income stream and also find its future value (at the end of the given interval)using the given interest rate.
A)TV = $2,234,000.03, FV = $1,411,333.34
B)TV = $4,468,000.07, FV = $657,058.77
C)TV =$2,234,000.03, FV =$4,729,378.11
D)TV = $4,234,000.03, FV = $314,911.04
E)TV = $67,020.00, FV = $13,161,504,599,350.49
A)TV = $2,234,000.03, FV = $1,411,333.34
B)TV = $4,468,000.07, FV = $657,058.77
C)TV =$2,234,000.03, FV =$4,729,378.11
D)TV = $4,234,000.03, FV = $314,911.04
E)TV = $67,020.00, FV = $13,161,504,599,350.49
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48
Calculate the 5-unit moving average of the given function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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49
Find the formula for the -unit moving average of a general exponential function.
A)
B)
C)
D)
E)
-unit moving average of a general exponential function. A)
B)
C)
D)
E)
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50
If you invest $8,000 at 12% interest compounded continuously, what is the average amount in your account over one year? Round your answer to the nearest cent.
A)$8,499.79
B)$8,598.43
C)$8,697.07
D)$8,302.51
E)$8,401.15
A)$8,499.79
B)$8,598.43
C)$8,697.07
D)$8,302.51
E)$8,401.15
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51
Find the total value of the given income stream and also find its future value (at the end of the given interval)using the given interest rate.
A)TV = $2,200,000, FV = $3,667,532.75
B)TV = $5,800,000, FV = $4,356,486.55
C)TV = $1,400,000, FV = $2,518,281.83
D)TV = $2,200,000, FV = $5,467,532.75
E)TV = $2,000,000, FV = $-2,296,343.85
A)TV = $2,200,000, FV = $3,667,532.75
B)TV = $5,800,000, FV = $4,356,486.55
C)TV = $1,400,000, FV = $2,518,281.83
D)TV = $2,200,000, FV = $5,467,532.75
E)TV = $2,000,000, FV = $-2,296,343.85
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52
If you invest $20,000 at 9% interest compounded continuously, what is the average amount in your account over 1 year? Please round your answer to the nearest cent.
A)$20,900
B)$10,900
C)$5,450
D)$21,800
E)$20,927.62
A)$20,900
B)$10,900
C)$5,450
D)$21,800
E)$20,927.62
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53
Calculate the producers surplus at the unit price for the supply following equation.
A)$9.00
B)$18.00
C)$13.00
D)$16.00
E)$10.00
for the supply following equation. A)$9.00
B)$18.00
C)$13.00
D)$16.00
E)$10.00
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54
Calculate the 5-unit moving average of the given function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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55
Calculate the 6-unit moving average of the given function.
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56
Calculate the 5-unit moving average of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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57
Find the average of the function over 0, 8 .
over 0, 8 . فتح الحزمة
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58
Complete the table with the values of the 3-unit moving average of the given function: average undefined undefined ?
A)x 1 2 3 4 5 6 7 r ( x )1 2 15 4 11 18 13 average undefined undefined 7 10 11 14 6
B)x 1 2 3 4 5 6 7 r ( x )1 2 15 4 11 18 13 average undefined undefined 14 6 7 10 11
C)x 1 2 3 4 5 6 7 r ( x )1 2 15 4 11 18 13 average undefined undefined 6 7 10 11 14
average undefined undefined ?A)x 1 2 3 4 5 6 7 r ( x )1 2 15 4 11 18 13 average undefined undefined 7 10 11 14 6
B)x 1 2 3 4 5 6 7 r ( x )1 2 15 4 11 18 13 average undefined undefined 14 6 7 10 11
C)x 1 2 3 4 5 6 7 r ( x )1 2 15 4 11 18 13 average undefined undefined 6 7 10 11 14
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59
Find the total value of the given income stream and also find its future value (at the end of the given interval)using the given interest rate.
A)TV = $50,000, FV = $258,135.27
B)TV = $100,000, FV = $470,353.13
C)TV = $200,000, FV = $8,221.19
D)TV = $100,000, FV = $303,686.47
E)TV = $100,000, FV = $137,019.80
A)TV = $50,000, FV = $258,135.27
B)TV = $100,000, FV = $470,353.13
C)TV = $200,000, FV = $8,221.19
D)TV = $100,000, FV = $303,686.47
E)TV = $100,000, FV = $137,019.80
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60
Calculate the 9-unit moving average of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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61
You are saving for your retirement by investing $900 per month in an annuity with a guaranteed interest rate of 6% per year. With a continuous stream of investment and continuous compounding, how much will you have accumulated in the annuity by the time you retire in 50 years?
A)$540,000.00
B)$3,795,396.65
C)$3,435,396.65
D)$188,961.67
E)$17,176.98
A)$540,000.00
B)$3,795,396.65
C)$3,435,396.65
D)$188,961.67
E)$17,176.98
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62
The annual net sales (revenue)earned by the Finnish cell phone company Nokia from January 1999 to January 2003 can be approximated by billion euros per year where is time in years ( represents January 2000 ). Estimate, to the nearest billion, Nokia s total revenue from January 1999 through December 2002.
A)
B)
C)
D)
E)
billion euros per year where is time in years ( represents January 2000 ). Estimate, to the nearest billion, Nokia s total revenue from January 1999 through December 2002.A)
B)
C)
D)
E)
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63
A fast-food outlet finds that the demand equation for its new side dish, Sweetdough Tidbit , is given by where p is the price (in cents)per serving and q is the number of servings that can be sold per hour at this price. At the same time, the franchise is prepared to sell servings per hour at a price of p cents. Find the consumers surplus at the equilibrium price level.
A)$6.04
B)$6.02
C)$6.10
D)$6.00
E)$6.06
where p is the price (in cents)per serving and q is the number of servings that can be sold per hour at this price. At the same time, the franchise is prepared to sell servings per hour at a price of p cents. Find the consumers surplus at the equilibrium price level.A)$6.04
B)$6.02
C)$6.10
D)$6.00
E)$6.06
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64
You are saving for your retirement by investing $700 per month in an annuity with a guaranteed interest rate of 6% per year. You increase the amount you invest at the rate of 4% per year. With continuous investment and compounding, how much will you have accumulated in the annuity by the time you retire in 25 years?
A)$7,406.31
B)$4,209,782.72
C)$740,631.04
D)$38,218.71
E)$165,257.12
A)$7,406.31
B)$4,209,782.72
C)$740,631.04
D)$38,218.71
E)$165,257.12
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65
When your first child is born, you begin to save for college by depositing $500 per month in an account paying 6% interest per year. With a continuous stream of investment and continuous compounding, how much will you have accumulated in the account by the time your child enters college 18 years later?
A)$972.34
B)$294,467.96
C)$394,467.96
D)$66,040.45
E)$194,467.96
A)$972.34
B)$294,467.96
C)$394,467.96
D)$66,040.45
E)$194,467.96
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66
Find the total value of the given income stream and also find its present value (at the beginning of the given interval)using the given interest rate.
A)TV = $0, PV = $248,477.55
B)TV = $45,317.31, PV = $59,866.79
C)TV = $55,350.69, PV = $46,430.67
D)TV = $454,682.69, PV = $1,392.92
E)TV = $2,214.03, PV = $46,430.67
A)TV = $0, PV = $248,477.55
B)TV = $45,317.31, PV = $59,866.79
C)TV = $55,350.69, PV = $46,430.67
D)TV = $454,682.69, PV = $1,392.92
E)TV = $2,214.03, PV = $46,430.67
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67
Find the total value of the given income stream and also find its present value (at the beginning of the given interval)using the given interest rate. Please enter your answer in the form TV = , PV = . Give the answer to the nearest cent if necessary. TV = $__________ PV = $__________
Please enter your answer in the form TV = , PV = . Give the answer to the nearest cent if necessary. TV = $__________ PV = $__________ فتح الحزمة
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68
Find the total value of the given income stream and also find its future value (at the end of the given interval)using the given interest rate. Please enter your answer in the form TV = , FV = . Round FV to the nearest cent. TV = $__________ FV = $__________
Please enter your answer in the form TV = , FV = . Round FV to the nearest cent. TV = $__________ FV = $__________ فتح الحزمة
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69
The annual revenue earned by Target for fiscal years 1998 through 2005 can be approximated by billion dollars per year where is time in years ( represents the beginning of fiscal year 2000). Suppose that, from fiscal year 1998 on, Target invested its revenue in an investment that depreciated continuously at a rate of 7% per year. What, to the nearest $10 billion, would the total value of Target s revenue have been by the end of fiscal year 2003?
A)
B)
C)
D)
E)
billion dollars per year where is time in years ( represents the beginning of fiscal year 2000). Suppose that, from fiscal year 1998 on, Target invested its revenue in an investment that depreciated continuously at a rate of 7% per year. What, to the nearest $10 billion, would the total value of Target s revenue have been by the end of fiscal year 2003?A)
B)
C)
D)
E)
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70
The U. S. Treasury issued a 10-year bond on November 16, 1998, paying 6.47% interest. Thus, if you bought $600,000 worth of these bonds, you would receive $38,820 per year in interest for 10 years. At investor wishes to buy the rights to receive the interest on $600,000 worth of these bonds. The amount the investor is willing to pay is the present value of the interest payments, assuming a 6% rate of return. If we assume (incorrectly, but approximately)that the interest payments are made continuously, what will the investor pay?
A)$291,918.87
B)$2,919.19
C)$1,178,910.86
D)$270,713.02
E)$1,825,910.86
A)$291,918.87
B)$2,919.19
C)$1,178,910.86
D)$270,713.02
E)$1,825,910.86
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71
When your first child is born, you begin to save for college by depositing $700 per month in an account paying 12% interest per year. You increase the amount you save by 2% per year. With continuous investment and compounding, how much will you have accumulated in the account by the time your child enters college 18 years later?
A)$5,945,936.09
B)$6,079.76
C)$70,114.89
D)$607,975.89
E)$7,073.13
A)$5,945,936.09
B)$6,079.76
C)$70,114.89
D)$607,975.89
E)$7,073.13
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72
The annual net sales (revenue)earned by the Finnish cell phone company Nokia from January 1999 to January 2004 can be approximated by billion euros per year where is time in years ( represents January 2000 ). Suppose that, from January 1999 on, Nokia invested its revenue in an investment yielding 7% compounded continuously. What, to the nearest 10 billion, would the total value of Nokia s revenues have been at the end of 2003?
A)
B)
C)
D)
E)
billion euros per year where is time in years ( represents January 2000 ). Suppose that, from January 1999 on, Nokia invested its revenue in an investment yielding 7% compounded continuously. What, to the nearest 10 billion, would the total value of Nokia s revenues have been at the end of 2003?A)
B)
C)
D)
E)
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73
The Megabucks Corporation is issuing a 5-year bond paying 8% interest. An investor wishes to buy the rights to receive the interest on $90,000 worth of these bonds and seeks a 6% rate of return. If the investor payments are made continuously, what will the investor pay?
A)$281,983.06
B)$31,101.81
C)$311.02
D)$120,000.00
E)$1,866.11
A)$281,983.06
B)$31,101.81
C)$311.02
D)$120,000.00
E)$1,866.11
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74
Find the total value of the given income stream and also find its future value (at the end of the given interval)using the given interest rate. Please enter your answer in the form TV = , FV = . Round FV to the nearest cent. TV = $__________ FV = $__________
Please enter your answer in the form TV = , FV = . Round FV to the nearest cent. TV = $__________ FV = $__________ فتح الحزمة
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75
Calculate the producers surplus at the unit price for the following supply equation. $ __________
for the following supply equation. $ __________ فتح الحزمة
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76
Find the total value of the given income stream and also find its present value (at the beginning of the given interval)using the given interest rate.
A)TV = $130,000, PV = $449,142.92
B)TV = $550,000, PV = $7,886,675.30
C)TV = $1,050,000, PV = $809,958.97
D)TV = $1,055,000, PV = $809,958.97
E)TV = $400,125,000, PV = $997,897.20
A)TV = $130,000, PV = $449,142.92
B)TV = $550,000, PV = $7,886,675.30
C)TV = $1,050,000, PV = $809,958.97
D)TV = $1,055,000, PV = $809,958.97
E)TV = $400,125,000, PV = $997,897.20
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77
The annual net sales (revenue)earned by Nintendo Co., Ltd., in the fiscal years ending March 31, 1995 to March 31, 2003, can be approximated by billion yen per year where is time in years ( represents March 31, 2000). Suppose that, from April 1994 on, Nintendo invested its revenue in an investment yielding 3% compounded continuously. What, to the nearest billion, would the total value of Nintendo s revenue have been by the end of March 2003?
A)
B)
C)
D)
E)
billion yen per year where is time in years ( represents March 31, 2000). Suppose that, from April 1994 on, Nintendo invested its revenue in an investment yielding 3% compounded continuously. What, to the nearest billion, would the total value of Nintendo s revenue have been by the end of March 2003?A)
B)
C)
D)
E)
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78
Find the total value or the given income stream and also find its future value (at the end of the given interval)using the given interest rate. Please enter your answer in the form TV = , FV = . Give the answers to the nearest cent. TV = $__________ FV = $__________
Please enter your answer in the form TV = , FV = . Give the answers to the nearest cent. TV = $__________ FV = $__________ فتح الحزمة
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79
The annual revenue earned by Wal-Mart in the fiscal years ending January 31, 1994 to January 31, 2003 can be approximated by billion dollars per year where is time in years represents January 31, 2000). Suppose that, from January 1999 on, Wal-Mart invested its revenue in an investment that depreciated continuously at a rate of 4% per year. What, to the nearest $10 billion, would the total value of Wal-Mart s revenues have been by the end of January 2003?
A)
B)
C)
D)
E)
billion dollars per year where is time in years represents January 31, 2000). Suppose that, from January 1999 on, Wal-Mart invested its revenue in an investment that depreciated continuously at a rate of 4% per year. What, to the nearest $10 billion, would the total value of Wal-Mart s revenues have been by the end of January 2003?A)
B)
C)
D)
E)
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80
Find the total value of the given income stream and also find its present value (at the beginning of the given interval)using the given interest rate. Please enter your answer in the form TV = , PV = . Give the answer to the nearest cent if necessary. TV = $__________ PV = $__________
Please enter your answer in the form TV = , PV = . Give the answer to the nearest cent if necessary. TV = $__________ PV = $__________ فتح الحزمة
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