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Q:
Find the radius of convergence of the series .
A) 14
B) 16
C) 1
D) 8
E) 7
Q:
Write the first five terms of the power series .
A) B) C) D) E)
Q:
Test the series for convergence or divergence using any appropriate test.A) divergesB) converges
Q:
Test the series for convergence or divergence using any appropriate test.A) divergesB) converges
Q:
Determine the convergence or divergence of the series. A) inconclusive
B) diverges
C) converges
Q:
Determine the convergence or divergence of the series. A) diverges
B) converges
C) inconclusive
Q:
Determine the convergence or divergence of the following series. A) convergesB) diverges
Q:
Approximate the sum of the convergent series using three terms. Estimate the maximum error of your approximation. Round your answers to four decimal places.
A) The approximate value is 2.1854. The maximum error of your approximation is 0.0588.
B) The approximate value is 1.1620. The maximum error of your approximation is 0.0556.
C) The approximate value is 2.1676. The maximum error of your approximation is 0.0721.
D) The approximate value is 3.1591. The maximum error of your approximation is 1.0527.
E) The approximate value is 1.1644. The maximum error of your approximation is 0.0573.
Q:
Use the Ratio Test to determine the convergence or divergence of the series .A) The series converges.B) The series diverges.
Q:
Use the Ratio Test to determine the convergence or divergence of the series. A) converges
B) diverges
C) Ratio Test is inconclusive
Q:
Use the Ratio Test to determine the convergence or divergence of the series. A) Ratio Test is inconclusive
B) diverges
C) converges
Q:
Determine the convergence or divergence of the following p-series. A) The series converges.B) The series diverges.
Q:
Determine the convergence or divergence of the p-series .A) The series diverges.B) The series converges.
Q:
Determine whether the series is a p-series.A) is not aseries.B) is aseries.
Q:
A factory is polluting a river such that at every mile down river from the factory an environmental expert finds 15% less pollutant than at the preceding mile. If the pollutant's concentration is 500 ppm (parts per million) at the factory, what is its concentration 15 miles down river?
A) 75.00 ppm
B) 225.00 ppm
C) 43.68 ppm
D) 588.24 ppm
E) 51.38 ppm
Q:
You accept a job that pays a salary of 70,000 the first year. During the next 39 years, you will receive a 6% raise each year. What would be your total compensation over the 40-year period? Round your answer to the nearest integer.
A) 10,833,338
B) 1,166,667
C) 65,800
D) 420,000
E) 4,200
Q:
The annual spending by tourists in a resort city is 300 million dollars. Approximately 50% of that revenue is again spent in the resort city, and of that amount approximately 50% is again spent in the resort city. If this pattern continues, write the geometric series that gives the total amount of spending generated by the 300 million dollars (including the initial outlay of 300 million dollars) and find the sum of the series.A) The geometric series is . The sum of the series is 600.00 million.B) The geometric series is . The sum of the series is 15,000 million.C) The geometric series is . The sum of the series is 600.00 million.D) The geometric series is . The sum of the series is 15,000 million.E) The geometric series is . The sum of the series is 150.00 million.
Q:
Bouncing Ball. A ball dropped from a height of 38 feet bounces to of its former height with each bounce. Find the total vertical distance that the ball travels.
A) 266 feet
B) 304 feet
C) 146 feet
D) 104 feet
E) 152 feet
Q:
A company produces a new product for which it estimates the annual sales to be 7000 units. Suppose that in any given year % of the units (regardless of age) will become inoperative. How many units will be in use after n years?
A) B) C) D) E)
Q:
Express the value of the given repeating decimal as a fraction. [Hint: Write as an infinite series.] A) B) C) D) E)
Q:
The repeating decimal is expressed as a geometric series . Write the decimal as the ratio of two integers.
A) B) C) D) E)
Q:
Determine the convergence or divergence of the series . Use a symbolic algebra utility to verify your result.A) The series converges.B) The series diverges.
Q:
Determine the convergence or divergence of the series . Use a symbolic algebra utility to verify your result.A) The series converges.B) The series diverges.
Q:
Determine the convergence or divergence of the following series. Use a symbolic algebra utility to verify your result. A) The series converges.B) The series diverges.
Q:
Find the sum of the convergent series. A) B) C) D) E)
Q:
Find the sum of the convergent series. A) B) C) D) 7
E) 1
Q:
Write the first five terms of the sequence of partial sums. A) B) C) D) E)
Q:
A ball is dropped from a height of 10 feet, and on each rebound it rises to its preceding height. Write an expression for the height of the nth rebound.
A) B) C) D) E)
Q:
A deposit of 800 is made each month in an account that earns 8.4% interest, compounded monthly. The balance in the account after n months is given by. Find the balance after 20 years by computing the 240th term of the sequence. Round your answer to two decimal places.
A) $696,946.54
B) $1,018,546.54
C) $24,073.84
D) $343,954.07
E) $1,125.60
Q:
Consider the sequence (An) whose nth term is given by An where P is the principal, An is the amount of compound interest after n months, and r is the annual percentage rate. Write the first four terms of the sequence for P = 9,500 and r = 0.04. Round your answer to two decimal places.
A) 9531.67, 9573.51, 9620.26, 9627.30
B) 9532.67, 9573.51, 9620.26, 9660.34
C) 9531.67, 9563.44, 9595.32, 9627.30
D) 9532.67, 9573.51, 9595.32, 9627.30
E) 9532.67, 9563.44, 9595.32, 9660.34
Q:
Give an example of a sequence that converges to .
A) B) C) D) E)
Q:
Find the next three terms of the geometric sequence. A) B) C) D) E)
Q:
What are the next three terms in the arithmetic sequence ?
A) B) C) D) E)
Q:
Write an expression for the nth term of the sequence .
A) B) C) D) E)
Q:
Write an expression for the nth term of the sequence. A) B) C) D) E)
Q:
Write an expression for the nth term of the sequence 2, 8, 26, 80, ....
A) B) C) D) E)
Q:
Determine the convergence or divergence of the sequence . If the sequence converges, use a symbolic algebra utility to find its limit.
A) 7
B) 1
C) 2
D) E) The sequence diverges.
Q:
Find the limit of the following sequence. A) -1B) 1C) D) 2E) The sequence diverges.
Q:
Find the limit of the following sequence. A) B) 1
C) 2
D) E) The sequence diverges.
Q:
Find the limit of the following sequence. A) B) C) D) E) The sequence diverges.
Q:
Find the limit of the sequence .
A) B) C) D) E) The sequence diverges.
Q:
Find the mean and median of .A) mean: 36.00 median: 36.00B) mean: 36.00 median: 0.11C) mean: 6.00 median: 0.50D) mean: 9.00 median: 9.00E) mean: 0.50 median: 0.50
Q:
The daily demand for a certain product (in hundreds of pounds) is a random variable with the probability density function over the interval . Find the probability that is within one standard deviation of the mean. Express your answer as a percent.
A) 96.37
B) 49.27
C) 62.61
D) 13.34
E) 72.72
Q:
The arrival time t of a bus at a bus stop is uniformly distributed between A.M. and A.M. What is the probability that you will miss the bus if you arrive at the bus stop at A.M.? Round your answer to two decimal places.
A) 0.25
B) 0.67
C) 0.36
D) 0.33
E) 0.57
Q:
Letbe a random variable that is normally distributed with the given mean and standard deviation . Find the probability using a symbolic integration utility.
A) 0.5889
B) 0.6687
C) 0.7970
D) 0.6302
E) 0.5292
Q:
Letbe a random variable that is normally distributed with the given mean and standard deviation . Find the probability using a symbolic integration utility. Round your answer to four decimal places.
A) 0.1908
B) 0.3085
C) 0.2525
D) 0.1695
E) 0.0763
Q:
Find the mean, variance, and standard deviation of the normal density function over . Do not use integration.A)expected valuemean: 4 variance: 36 standard deviation: 6B)expected valuemean: 36 variance: 4 standard deviation: 6C)expected valuemean: 36 variance: 6 standard deviation: 4D)expected valuemean: 6 variance: 4 standard deviation: 36E)expected valuemean: 4 variance: 6 standard deviation: 36
Q:
If is an exponential random variable with the probability density function find A) B) C) D) E) 1
Q:
Find the mean, variance, and standard deviation of the uniform distribution over the interval [0, 8] without using integration.A)expected valuemean: 4.000 variance: 5.333 standard deviation: 2.309B)expected valuemean: 5.333 variance: 4.000 standard deviation: 2.309C)expected valuemean: 5.333 variance: 2.309 standard deviation: 4.000D)expected valuemean: 2.309 variance: 4.000 standard deviation: 5.333E)expected valuemean: 4.000 variance: 2.309 standard deviation: 5.333
Q:
Find the median of the exponential probability density function over the interval .
A) 1.213
B) 0.693
C) 0.396
D) 1.061
E) 0.875
Q:
For the given probability density function, find A) 12.000
B) 6.400
C) 9.000
D) 5.400
E) 28.800
Q:
Sketch the graph of the following probability density function and locate the mean on the graph. A)mean : 1.600B) mean : 2.012C) mean : 0.555D) mean : 1.848E) mean : 0.714
Q:
Sketch the graph of the following probability density function and locate the mean on the graph. A) mean : 1.5B) mean : 2.0C) mean : 4.0D) mean : 3.0E) mean : 4.0
Q:
A meteorologist predicts that the amount of rainfall (in inches) expected for a certain coastal community during a hurricane has the probability density function. Find and interpret the probability.
A) 90% probability of receiving up to 13 inches of rain
B) 96% probability of receiving up to 13 inches of rain
C) 98% probability of receiving up to 13 inches of rain
D) 4% probability of receiving up to 13 inches of rain
E) 10% probability of receiving up to 13 inches of rain
Q:
The time t (in hours) required for a new employee to successfully learn to operate a machine in a manufacturing process is described by the probability density function over the interval . Find the probability that a new employee will learn to operate the machine in more than 2 hours but less than 5 hours.
A) 0.4498
B) 0.1264
C) 0.3714
D) 0.0981
E) 0.2733
Q:
The daily demand for gasoline (in millions of gallons) in a city is described by the probability density function over the interval . Find the probability that the daily demand for gasoline will be at least 3 million gallons.
A) 0.444
B) 0.111
C) 0.174
D) 0.340
E) 0.250
Q:
Buses arrive and depart from a college every 40 minutes. The probability density function for the waiting time t (in minutes) for a person arriving at the bus stop is on the interval . Find the probability that the person will wait no longer than 20 minutes.
A) B) C) D) E)
Q:
For the probability density function on the interval , find the probability that . Round your answer to the nearest thousandth.
A) 0.088
B) 0.245
C) 0.224
D) 0.250
E) 0.264
Q:
For the probability density function on the interval find the probability that . Round your answer to the nearest hundredth.
A) 0.15
B) 0.67
C) 0.78
D) 0.33
E) 0.12
Q:
For the probability density function on the interval , find the probability that . Round your answer to the nearest hundredth.
A) 0.07
B) 0.83
C) 0.97
D) 0.09
E) 0.06
Q:
Sketch the graph of the probability density function over the interval .A)B)C)D)E)
Q:
Find the constantsuch that the functionis a probability density function over the interval.
A) 1
B) C) D) E)
Q:
Find the value of the constant a that makes the given function a probability density function on the stated interval. A) B) C) D) E) 1
Q:
Find the constant k such that the function is a probability density function over the interval .
A) 5
B) C) D) E)
Q:
A baseball fan examined the record of a favorite baseball player's performance during his last 50 games. The numbers of games in which the player had zero, one, two, three, and four hits are recorded in the table shown below. Find the standard deviation . Round your answer to two decimal places. Number of hits01234Frequency10225121A) 1.44B) 1.12C) 1.55D) 1.25E) 1.20
Q:
If x is the net gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose over the long run. A service organization is selling $2 raffle tickets as part of a fundraising program. The first prize is a boat valued at $2920, and the second prize is a camping tent valued at $600. In addition to the first and second prizes, there are twenty-two $20 gift certificates to be awarded. The number of tickets sold is 3000. Find the expected net gain to the player for one play of the game. Round your answer to the nearest cent.A) 1178.00B) 1.47C) 0.68D) -$0.68E) -$1178.00
Q:
An insurance company needs to determine the annual premium required to break even on fire protection policies with a face value of 90,000. If x is the claim size on these policies and the analysis is restricted to the losses 30,000, 50,000, and 90,000, then the probability distribution of x is as shown in the table. What premium should customers be charged for the company to break even? Round your answer to the nearest dollar.030,00050,00090,0000.99100.00360.00090.0045A) 553B) 24C) 42,500D) 558E) 62,000
Q:
A publishing company introduces a new weekly magazine that sells for $4.69 on the newsstand. The marketing group of the company estimates that sales x (in thousands) will be approximated by the following probability function. Find the expected revenue. Round your answer to the nearest dollar.10152030400.240.290.230.100.14A) 93,565B) 94C) 456D) 19,950E) 456,091
Q:
Find the expected valuefor the following probability distribution. Round your answer to three decimal places. -5,000 -2,500 3000.0140.0620.924A) 7.225B) 904.398C) 2,724.840D) 817,935.160E) 52.200
Q:
Find the standard deviation for the following probability distribution. Round your answer to three decimal places. A) 2.600B) 1.562C) 5.954D) 2.440E) 1.612
Q:
Estimate the variance for the following probability distribution to two decimal places. A) B) C) D) E) 1.00
Q:
Find given the probability distribution.01230.0290.1810.4400.350A) 0.440B) 1.000C) 0.790D) 0.650E) 0.250
Q:
Find given the probability distribution.0123450.0470.1850.240.3250.1590.044A) 0.159B) 0.797C) 0.203D) 0.956E) 0.044
Q:
Sketch a graph of the probability distribution. 0 1 2 3 4 0 1 2 3 4 A)B)C)D)E)
Q:
Determine whether the table represents a probability distribution. A) noB) yes
Q:
A card is chosen at random from three 52-card decks of standard playing cards . What is the probability that the card will be black and a face card? A face card is a king, a queen, or a jack.
A) B) C) D) E)
Q:
Three people are asked their opinions on a political issue. They can answer "Opposed" (O) or "Undecided" (U). Find the sample space S.
A) B) C) D) E)
Q:
A coin is tossed five times. Describe the event A that at least four tails occur.
A) B) C) D) E)
Q:
Evaluate the definite integral .
A) 3
B) "3
C) D) E)
Q:
Evaluate the definite integral. A) B) C) 0
D) 4
E) undefined