Solve the exponential equation. Give the answer correct to 3 decimal places.
15,000=500e03x
0.729
1.215
2.286
1.134
Assumed:
Calculate the annual percentage yield for each investment.
a.A savings account paying an annual rate of 4 percent compounded quarterly.
b.A checking account paying an annual rate of 1.5 percent compounded daily.
- (1+0.04/4)^4 = 1.040604i.e. 4.0604%
- (1+0.015/365)^365 = 1.015112i.e. 1.5112%
What interest will be earned if $4900 is invested for 5 years at an annual rate of 12% compounded monthly?
5149.95
5521.44
7840.00
8901.81
What is the annual percentage yield (or effective annual rate) for a nominal rate of 7.3% compounded quarterly?
5149.95
5521.44
7840.00
8901.81
7.5023%
If the total cost function for a product is
C(x)=e 0.1x+500
, where x is the number of items produced, what is the total cost of producing 70 units?
312.37
1596.63
71.35
302.01
How much more interest will be earned if $9000 is invested for 6 years at an annual rate of 9% compounded continuously, instead of at 9% compounded quarterly?
31.09
61.08
92.16
1491.96
Inflation. If inflation causes the cost of automobiles to increase by 4.5% each year, what should a car cost today if it cost $19,000 4 years ago?
22,747.13
22,420.00
19,855.00
22,657.85
Solve the exponential equation. Give answers correct to 3 decimal places.
0.18=(5-x)
This is not an exponential equation -probably a typo. None of the following answers solve this equation as it stands.
1.065
0.042
23.810
-0.042
-0.312
What interest will be earned if $4900 is invested for 3 years at an annual rate of 12% compounded monthly?
3127.95
5521.44
7010.77will be the total value (interest + investment).
8901.81
Find the future value if $4000 is invested for 8 years at an annual rate of 12% compounded quarterly.
15,360.00
10,161.41
5067.08
10,300.33
What is the annual percentage yield (or effective annual rate) for a nominal rate of 10% compounded continuously?
11.04
10.52
20.00
10.77
For the following problems, determine how many years it will take for the two accounts to reach the same amount.
a.A 1000 dollar investment at a rate of 3% compounded monthly and an 1100 dollar investment at a rate of 3.02% compounded annually.
1000 * (1+0.03/12)^(12*x) = 1100*1.0302^xx = 454.7 years
b.A 2000 dollar investment at a rate of 4% compounded continuously and a 3000 dollar investment at a rate of 5% compounded monthly.
2000 * e^(0.04x) = 3000 * (1 + 0.05/12)^(12x)x = -40.9 years
they will never be equal; the gap will just widen
IIII
A bag contains 10 red, 12 green, and 8 yellow marbles. Assuming that all marbles are equally likely to be picked from the bag, what is the probability that the second marble is yellow, given that the first marble was yellow?
7/(10+12+7) = 7/29 = 0.24138…
A new restaurant in town is offering a limited menu from which you can choose one meat, one vegetable, one bread choice, and one dessert. If there are 4 meat selections, 7 vegetable selections, 2 bread selections, and 3 desserts, how many different meals can be created?
24
16
168
184
Four women and three men sign up to work weekends at a small restaurant. Four of them will be scheduled to work this weekend. Find the probability that the group selected contains men and women.
.971
.008
.865
.783
What is the cardinality of the Cartesian product A X B when A = {5, 7} and B= {1, 2, 3, 4, 5}
7
8
9
10
What is the Cartesian product A X B when A= {R, S} and B= {1, 2, 3}
{(R, 1), (R, 2), (R, 3), (S, 1), (S, 2), (S, 3)}
{(1,1), (2.2), (3, 3), (S, S), (S, R), (R, 3)}
{(R, S), (S, R), (1, 2), (3, 3), (3, 2), (S, 3)}
{(3, 2), (1, 3), (3, 1), (S, 1), (S, 2), (S, 3)}
Consider the following sets.
U = {1, 2, 3, 4, 5, 6, 7, 8}
A= {2, 4, 6, 8}
B= {1, 2, 3, 5, 7}
Which of the following statements is true?
Which statements?
How many three letter words can be formed allowing repetition of letters?
3*26
26^3
26*25*24
3^26
Given a set of numbers S={5, 10, 11, 15, 17, 18}, what is the probability of randomly selecting a number from the set that is a multiple of 5?
50%
25%
200%
20%
Consider the following sets.
U = {1, 2, 3, 4, 5, 6, 7, 8}
A= {2, 4, 6, 8}
B= {1, 2, 3, 5, 7}
A u B is the set
U = 0
A= 1,2,3,4,5,6,7,8
B= 4,5,6
= U = {1, 2, 3, 4, 5, 6, 7, 8}
Don't really understand what you are asking.
For the given sets, answer the following questions
A={1, 2, 3, 4}
B={1, 2, 5, 7}
C={3, 4, 5, 7}
B n C {5,7}
A {1, 2, 3, 4}
A n C {3}
A n A {1, 2, 3, 4}
A u B {1,2,3,4,5,7}
Calculate the following expressions
a. P(4, 2) 12
b. P(8, 7) 40320
c. C(9, 7) 36
d. C(8, 0) 1
A and B are finite subsets of the universal set U with n(U)=10, n(A)=7, n(AnB)=2 and
N(AuB)=9
Find the cardinality of each of the specified sets.
B 4
B 4
A n B 2
VII
A bag contains 10 red, 12 green, and 8 yellow marbles. Assuming that all marbles are equally likely to be picked from the bag, what is the probability that the second marble is yellow, given that the first marble was yellow?
7/(10+12+7) = 7/29 = 0.24138…
Find a steady state distribution vector for the Markov chain with transition
P=[ 0.250.75 ]
[ 0.20.8 ]
[0.5 0.5]T
What does a probability tree have that a regular decision tree does not?
A starting point
More branches
More choices
Annotated probability
Given a Markov chain with a transition matrix
P= [ 0.2 0.8]
0.40.6
Find p2
[0.36 0.64
0.32 0.68]
The probability that a person with a positive test result will actually have the disease is referred to as
PVP
PVN
Sensitivity
Specificity
Predictive-value negative (PVN) is
The probability that a person with a negative test result will not have the disease
The probability that a person with a positive test result will actually have the disease
The probability that a test result will be positive when the test is administered tto a person with the disease
The probability that a test result will be negative when the test is administered to a person without the disease
P(A/B)=.85 and P(B) = .12
Find P (A n B)
0.343
0.102
0.574
0.054
The statement P(A| B) reads
The probability that event A occurs after event B
The probability that event A occurs before event B
The probability that event A occurs given event B
The probability that event A occurs during event B
Given the following information, compute the PVP using Bayes’ Theorem. Prevalence = 20% Sensitivity = 50% Specificity = 75%
25%
33.3%
45%
60.4%
Specificity is
The probability that a person with a negative test result will not have the disease
The probability that a person with a positive test result will actually have the disease
The probability that a test result will be positive when the test is administered tto a person with the disease
The probability that a test result will be negative when the test is administered to a person without the disease
Given the transition matrix
P=[0.20.8]
[0.40.6]
What is the probability of moving from state S1 to state S2?
0.8
0.2
0.4
0.6
Are the following two events independent or dependent? Two dice are rolled. E= the first dice shows a 3 F= the second dice shows a 5
Independent
Dependent
Given the following information, calculate the Predictive value positive and the predictive value negative
Prevalence =5%
Sensitivity =85%
Specificity =74%
PVP = 14.68%
PVN = 98.94%
VIIII
Suppose a normal distribution has
U = 1.5 and Q= 0.3
Find the z-score and the associated area under the standard normal curve for the following values of x.
2.3 z=2.66670.996170
1.7 z=0.66670.747518
2 z=1.66670.952213
1.9 z=1.33330.908800
2.1 z=2.00000.977250
Which of the following is also referred to as the average
Mean
Standard deviation
Median
Mode
Determine the probability that a randomly selected data value will fall within 1.67 standard deviations of the mean
45.25
90.5
85.5
30.25
How do you calculate the deviation from the mean
Add the mean to each number
Subtract the mean from each number
Multiply the mean by each number
Divide each number by the mean
Calculate the z-score for x = 20 given a normal distribution with
U = 25 and o= 4
-2.5
1.5
.75
-1.25
All of the following are properties of a normal distribution except
The graph of the distribution is a bell shaped curve
The mean, median and mode are different
The graph is symmetric about a vertical line that passes through the population mean
The area below the graph of the distribution and above the horizontal axis is equal to 1.
Calculate the standard deviation of the following set of scores: 45, 52, 45, 40
45
45.5
5.77
4.93
23.04
Which of the following is true
The graph of a probability distribution is a histogram
A histogram is a pie chart
The number of times a value occurs is referred to as a probability distribution
The collection of probabilities is a frequency distribution
What is the correct interval of values within one standard deviation of the mean if the mean of a certain set of data is 50 and the standard deviation is 10
45,50
50,60
40,60
40,50
A die is rolled 30 times. What is the expected value that a 5 will appear
2
3
4
5
A campus club sells 500 raffle tickets at a price of $2 each. The raffle offers one $100 dollar prize, two $50 prizes, and five $25 prizes. What is the expected value of a raffle ticket? (number 12 in section 8.4 of text
-2+100/500+2*50/500+5*25/500 = -1.35$