Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
15th Edition
ISBN: 9781323047620
Author: Barnett, Ziegler, Byleen
Publisher: Pearson Education
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Chapter 9.1, Problem 1MP
Show that
is the general solution of the differential equation
On the same set of axes, graph the particular solutions obtained by letting C = –2, –1, 0, 1, and 2.
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For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months (Bureau of Labor Statistics, January 2010). Suppose the following data are for a particular region in upstate New York. The values in the first column show the number of
months unemployed and the values in the second column show the corresponding number of unemployed persons.
Months
Unemployed
Number
Unemployed
1
1029
2
1686
3
2269
4
2675
5
3487
6
4652
7
4145
8
3587
9
2325
10
1120
Let x be a random variable indicating the number of months a person is unemployed.
a. Use the data to develop an empirical discrete probability distribution for x (to 4 decimals).
(x)
f(x)
1
2
3
4
5
6
7
8
9
10
b. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
blank
c. What is the probability that a…
West Virginia has one of the highest divorce rates in the nation, with an annual rate of approximately 5 divorces per 1000 people (Centers for Disease Control and Prevention website, January 12, 2012). The Marital Counseling Center, Inc. (MCC) thinks that the high divorce rate in the state may require them to hire additional staff.
Working with a consultant, the management of MCC has developed the following probability distribution for x = the number of new clients for marriage counseling for the next year.
Excel File: data05-19.xls
x
10
f(x)
.05
20
30
.10
.10
40
.20
50
60
.35
.20
a. Is this probability distribution valid?
- Select your answer-
Explain.
f(x)
Σf(x)
Select your answer
Select your answer
b. What is the probability MCC will obtain more than 30 new clients (to 2 decimals)?
c. What is the probability MCC will obtain fewer than 20 new clients (to 2 decimals)?
d. Compute the expected value and variance of x.
Expected value
Variance
clients per year
squared clients per year
For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months (Bureau of Labor Statistics, January 2010). Suppose the following data are for a particular region in upstate New York. The values in the first column show the number of
months unemployed and the values in the second column show the corresponding number of unemployed persons.
Months
Unemployed
Number
Unemployed
1
1029
2
1686
3
2269
4
2675
5
3487
6
4652
7
4145
8
3587
9
2325
10
1120
Let x be a random variable indicating the number of months a person is unemployed.
a. Use the data to develop an empirical discrete probability distribution for x (to 4 decimals).
(x)
f(x)
1
2
3
4
5
6
7
8
9
10
b. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
c. What is the probability that a person…
Chapter 9 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
Ch. 9.1 - Show that y=Cx+1 is the general solution of the...Ch. 9.1 - Prob. 2MPCh. 9.1 - Prob. 3MPCh. 9.1 - Prob. 4MPCh. 9.1 - Prob. 5MPCh. 9.1 - Prob. 1EDCh. 9.1 - Prob. 2EDCh. 9.1 - Prob. 1ECh. 9.1 - Prob. 2ECh. 9.1 - Prob. 3E
Ch. 9.1 - Prob. 4ECh. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - Prob. 7ECh. 9.1 - Prob. 8ECh. 9.1 - In Problems 110, find the derivative. (If...Ch. 9.1 - Prob. 10ECh. 9.1 - Prob. 11ECh. 9.1 - In Problems 1120, show that the given function is...Ch. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - In Problems 2124, determine which of the slope...Ch. 9.1 - In Problems 2124, determine which of the slope...Ch. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - In Problems 2528, use the appropriate slope...Ch. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - In Problems 2938, show that the given function y...Ch. 9.1 - Prob. 30ECh. 9.1 - Prob. 31ECh. 9.1 - In Problems 2938, show that the given function y...Ch. 9.1 - Prob. 33ECh. 9.1 - Prob. 34ECh. 9.1 - Prob. 35ECh. 9.1 - Prob. 36ECh. 9.1 - Prob. 37ECh. 9.1 - Prob. 38ECh. 9.1 - Prob. 39ECh. 9.1 - Prob. 40ECh. 9.1 - Prob. 41ECh. 9.1 - Prob. 42ECh. 9.1 - Prob. 43ECh. 9.1 - If y is defined implicitly by the given equation,...Ch. 9.1 - Prob. 45ECh. 9.1 - Prob. 46ECh. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Prob. 49ECh. 9.1 - Prob. 50ECh. 9.1 - Prob. 51ECh. 9.1 - Prob. 52ECh. 9.1 - Prob. 53ECh. 9.1 - Prob. 54ECh. 9.1 - Prob. 55ECh. 9.1 - In Problems 55 and 56, use the general solution y...Ch. 9.1 - Prob. 57ECh. 9.1 - Prob. 58ECh. 9.1 - In Problems 59 and 60, use window dimensions Xmin...Ch. 9.1 - Prob. 60ECh. 9.1 - Prob. 61ECh. 9.1 - Prob. 62ECh. 9.1 - Prob. 63ECh. 9.1 - Prob. 64ECh. 9.1 - Prob. 65ECh. 9.1 - Prob. 66ECh. 9.1 - Rumor spreadGompertz growth model. The rate of...Ch. 9.2 - Solve: y=4x3y2.Ch. 9.2 - Prob. 2MPCh. 9.2 - Repeat Example 3 if the mothballs lose half their...Ch. 9.2 - Prob. 4MPCh. 9.2 - Prob. 5MPCh. 9.2 - Prob. 1EDCh. 9.2 - Prob. 2EDCh. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - In Problems 18, find the most general...Ch. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - In Problems 912, write a differential equation...Ch. 9.2 - In Problems 912, write a differential equation...Ch. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Prob. 16ECh. 9.2 - Prob. 17ECh. 9.2 - Prob. 18ECh. 9.2 - Prob. 19ECh. 9.2 - Prob. 20ECh. 9.2 - Prob. 21ECh. 9.2 - In Problems 2130, find the general solution for...Ch. 9.2 - Prob. 23ECh. 9.2 - Prob. 24ECh. 9.2 - Prob. 25ECh. 9.2 - In Problems 2130, find the general solution for...Ch. 9.2 - Prob. 27ECh. 9.2 - Prob. 28ECh. 9.2 - In Problems 2130, find the general solution for...Ch. 9.2 - Prob. 30ECh. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.2 - In Problems 3140, find the general solution for...Ch. 9.2 - Prob. 37ECh. 9.2 - Prob. 38ECh. 9.2 - Prob. 39ECh. 9.2 - In Problems 3140, find the general solution for...Ch. 9.2 - Prob. 41ECh. 9.2 - Prob. 42ECh. 9.2 - Prob. 43ECh. 9.2 - Prob. 44ECh. 9.2 - In Problems 4146, find the general solution for...Ch. 9.2 - Prob. 46ECh. 9.2 - Prob. 47ECh. 9.2 - Prob. 48ECh. 9.2 - Prob. 49ECh. 9.2 - Prob. 50ECh. 9.2 - Prob. 51ECh. 9.2 - Prob. 52ECh. 9.2 - Prob. 53ECh. 9.2 - Prob. 54ECh. 9.2 - Prob. 55ECh. 9.2 - Prob. 56ECh. 9.2 - Prob. 57ECh. 9.2 - Prob. 58ECh. 9.2 - Prob. 59ECh. 9.2 - Prob. 60ECh. 9.2 - Advertising. A company is using radio advertising...Ch. 9.2 - Prob. 62ECh. 9.2 - Prob. 63ECh. 9.2 - Prob. 64ECh. 9.2 - Prob. 65ECh. 9.2 - Prob. 66ECh. 9.2 - Prob. 67ECh. 9.2 - Prob. 68ECh. 9.2 - Prob. 69ECh. 9.2 - Prob. 70ECh. 9.2 - Prob. 71ECh. 9.2 - Prob. 72ECh. 9.2 - Newtons law of cooling states that the rate of...Ch. 9.2 - Prob. 74ECh. 9.2 - Population growth. A culture of bacteria is...Ch. 9.2 - Prob. 76ECh. 9.2 - Prob. 77ECh. 9.2 - Prob. 78ECh. 9.2 - Prob. 79ECh. 9.2 - Prob. 80ECh. 9.2 - Prob. 81ECh. 9.2 - Learning. The number of words per minute. N, a...Ch. 9.2 - Prob. 83ECh. 9.3 - Solve:xy+3y=4x.Ch. 9.3 - Prob. 2MPCh. 9.3 - Repeat Example 3 if the account earns 5%...Ch. 9.3 - If D = 70 + 2p(t) + 2p(t), S = 30 + 6p(t) + 3p(t)....Ch. 9.3 - Repeat Example 5 if water is released from the...Ch. 9.3 - Prob. 1EDCh. 9.3 - Prob. 2EDCh. 9.3 - Prob. 1ECh. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Prob. 12ECh. 9.3 - Prob. 13ECh. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - In Problems 2334, find the integrating factor, the...Ch. 9.3 - Prob. 25ECh. 9.3 - In Problems 2334, find the integrating factor, the...Ch. 9.3 - Prob. 27ECh. 9.3 - Prob. 28ECh. 9.3 - In Problems 2334, find the integrating factor, the...Ch. 9.3 - Prob. 30ECh. 9.3 - Prob. 31ECh. 9.3 - Prob. 32ECh. 9.3 - Prob. 33ECh. 9.3 - In Problems 2334, find the integrating factor, the...Ch. 9.3 - Prob. 35ECh. 9.3 - Prob. 36ECh. 9.3 - Prob. 37ECh. 9.3 - Prob. 38ECh. 9.3 - In Problems 3514, find the integrating factor fix...Ch. 9.3 - In Problems 3514, find the integrating factor fix...Ch. 9.3 - Prob. 41ECh. 9.3 - Prob. 42ECh. 9.3 - Prob. 43ECh. 9.3 - Prob. 44ECh. 9.3 - Prob. 45ECh. 9.3 - Prob. 46ECh. 9.3 - Prob. 47ECh. 9.3 - Prob. 48ECh. 9.3 - Prob. 49ECh. 9.3 - Prob. 50ECh. 9.3 - Prob. 51ECh. 9.3 - Prob. 52ECh. 9.3 - Prob. 53ECh. 9.3 - Prob. 54ECh. 9.3 - Prob. 55ECh. 9.3 - Prob. 56ECh. 9.3 - Prob. 57ECh. 9.3 - Prob. 58ECh. 9.3 - Prob. 59ECh. 9.3 - Prob. 60ECh. 9.3 - Prob. 61ECh. 9.3 - Prob. 62ECh. 9.3 - Prob. 63ECh. 9.3 - Prob. 64ECh. 9.3 - Prob. 65ECh. 9.3 - Prob. 66ECh. 9.3 - Supply-demand. The supply S and demand D for a...Ch. 9.3 - Prob. 68ECh. 9.3 - Pollution. A 1,000-gallon holding tank contains...Ch. 9.3 - Pollution. Rework Problem 69 if water is entering...Ch. 9.3 - Pollution. Rework Problem 69 if water is entering...Ch. 9.3 - Prob. 72ECh. 9.3 - Pollution. Refer to Problem 69. When will the tank...Ch. 9.3 - Prob. 74ECh. 9.3 - Prob. 75ECh. 9.3 - Prob. 76ECh. 9.3 - Prob. 77ECh. 9.3 - In an article in the College Mathematics Journal...Ch. 9.3 - Prob. 79ECh. 9.3 - In 1960, William K. Estes proposed the following...Ch. 9 - In Problems 1 and 2, show that the given function...Ch. 9 - In Problems 1 and 2, show that the given function...Ch. 9 - In Problems 3 and 4, determine which of the...Ch. 9 - In Problems 3 and 4, determine which of the...Ch. 9 - In Problems 5 and 6, use the appropriate slope...Ch. 9 - In Problems 5 and 6, use the appropriate slope...Ch. 9 - In Problems 7 and 8, write a differential equation...Ch. 9 - In Problems 7 and 8, write a differential equation...Ch. 9 - In Problems 9 and 10, describe in words the rate...Ch. 9 - In Problems 9 and 10, describe in words the rate...Ch. 9 - In Problems 1116, determine whether the...Ch. 9 - In Problems 1116, determine whether the...Ch. 9 - In Problems 1116, determine whether the...Ch. 9 - In Problems 1116, determine whether the...Ch. 9 - In Problems 1116, determine whether the...Ch. 9 - Prob. 16RECh. 9 - In Problems 1724, find the general solution....Ch. 9 - In Problems 1724, find the general solution....Ch. 9 - In Problems 1724, find the general solution....Ch. 9 - In Problems 1724, find the general solution....Ch. 9 - In Problems 1724, find the general solution....Ch. 9 - In Problems 1724, find the general solution....Ch. 9 - Prob. 23RECh. 9 - In Problems 1724, find the general solution....Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - Solve the following differential equation two...Ch. 9 - Give an example of an equation that can be solved...Ch. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Prob. 37RECh. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Prob. 47RECh. 9 - Rumor spread. A single individual starts a rumor...
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