Mathematical Ideas (13th Edition) - Standalone book
13th Edition
ISBN: 9780321977076
Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren
Publisher: PEARSON
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Textbook Question
Chapter 5.3, Problem 1E
In Exercises 1-10 decide whether each statement is true or false.
Given a prime number, no matter how large, there is always another prime even larger.
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Microsoft Excel snapshot for random sampling: Also note the formula used for the last
column
02
x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51))
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B
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No.
States
2
1
ALABAMA
Rand No.
0.925957526
3
2
ALASKA
0.372999976
4
3
ARIZONA
0.941323044
5
4 ARKANSAS
0.071266381
Random Sample
CALIFORNIA
NORTH CAROLINA
ARKANSAS
WASHINGTON
G7
Microsoft Excel snapshot for systematic sampling:
xfx INDEX(SD52:50551, F7)
A
B
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F
G
1
No.
States
Rand No. Random Sample
population
50
2
1 ALABAMA
0.5296685 NEW HAMPSHIRE
sample
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2 ALASKA
0.4493186 OKLAHOMA
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3 ARIZONA
0.707914 KANSAS
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4 ARKANSAS 0.4831379 NORTH DAKOTA
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5 CALIFORNIA 0.7277162 INDIANA
Random Sample
Sample Name
7
6 COLORADO 0.5865002 MISSISSIPPI
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7:ONNECTICU 0.7640596 ILLINOIS
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The spread of an infectious disease is often modeled using the following autonomous differential equation:
dI
-
- BI(N − I) − MI,
dt
where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of
transmission, and μ is the rate at which people recover from infection.
Close
a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria.
b) (5 points) For the equilbria in part a), determine whether each is stable or unstable.
c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the
dt
function by hand.) Identify the equilibria as stable or unstable in the graph.
d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.
Find the indefinite integral.
Check
Answer:
7x
4 + 1x
dx
Chapter 5 Solutions
Mathematical Ideas (13th Edition) - Standalone book
Ch. 5.1 - Decide whether each statement is true or false
1....Ch. 5.1 - Decide whether each statement is true or false. If...Ch. 5.1 - Decide whether each statement is true or false....Ch. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Decide whether each statement is true or false.
7....Ch. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Find all natural number factors of each...
Ch. 5.1 - Find all natural number factors of each number. 28Ch. 5.1 - Find all natural number factors of each number. 72Ch. 5.1 - Use divisibility tests to decide whether the given...Ch. 5.1 - Use divisibility tests to decide whether the given...Ch. 5.1 - Use divisibility tests to decide whether the given...Ch. 5.1 - Prob. 16ECh. 5.1 - (a) In constructing the Sieve of Eratosthenes for...Ch. 5.1 - (a) Continue the Sieve of Eratosthenes in Table 1...Ch. 5.1 - In your list for Exercise 18(a). consider the six...Ch. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Find the prime factorization of each composite...Ch. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Here is a divisibility test for 7.
(a) Double the...Ch. 5.1 - Here is a divisibility test for 7. (a)Double the...Ch. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Here is a divisibility test for 11. (a) Starting...Ch. 5.1 - Prob. 36ECh. 5.1 - Here is a divisibility test for 11.
(a) Starting...Ch. 5.1 - Prob. 38ECh. 5.1 - 39. Consider the divisibility test for the...Ch. 5.1 - 40. Give two factorizations of the number 75 that...Ch. 5.1 - Prob. 41ECh. 5.1 - Determine all possible digit replacements for x so...Ch. 5.1 - Determine all possible digit replacements for x so...Ch. 5.1 - Determine all possible digit replacements for x so...Ch. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Leap years occur when the year number is divisible...Ch. 5.1 - Prob. 52ECh. 5.1 - Prob. 53ECh. 5.1 - Leap years occur when the year number is divisible...Ch. 5.1 - Prob. 55ECh. 5.1 - Prob. 56ECh. 5.1 - Prob. 57ECh. 5.1 - 58. Choose any 6-digit number consisting of three...Ch. 5.1 - One of the authors has three sons who were born....Ch. 5.1 -
Ore of the authors has three sons who were born,...Ch. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.2 - In Exercises 1-6 decide whether each statement is...Ch. 5.2 - In Exercises 1-6 decide whether each statement is...Ch. 5.2 - In Exercises 1-6 decide whether each statement is...Ch. 5.2 - Prob. 4ECh. 5.2 - In Exercises 1-6 decide whether each statement is...Ch. 5.2 - Prob. 6ECh. 5.2 - Prob. 7ECh. 5.2 - Prob. 8ECh. 5.2 - Prob. 9ECh. 5.2 - Prob. 10ECh. 5.2 - Prob. 11ECh. 5.2 - Prob. 12ECh. 5.2 - Prob. 13ECh. 5.2 - Prob. 14ECh. 5.2 - 15. (a) Evaluate the Fermat number for .
(b) In...Ch. 5.2 - 16. (a) Verify the value given in the text for the...Ch. 5.2 - Prob. 17ECh. 5.2 - Prob. 18ECh. 5.2 - 19. Why do you suppose it normally takes up to a...Ch. 5.2 - Prob. 20ECh. 5.2 - Prob. 21ECh. 5.2 - 22. Explain n your own words the proof by Euclid...Ch. 5.2 - 23. For the composite number , find
Ch. 5.2 - Prob. 24ECh. 5.2 - Prob. 25ECh. 5.2 - Prob. 26ECh. 5.2 - Prob. 27ECh. 5.2 - Prob. 28ECh. 5.2 - Explain why large prime numbers are important in...Ch. 5.2 - 30. Describe the difference between Mersenne...Ch. 5.3 - In Exercises 1-10 decide whether each statement is...Ch. 5.3 - Prob. 2ECh. 5.3 - In Exercises 1-10 decide whether each statement is...Ch. 5.3 - In Exercises 1-10 decide whether each statement is...Ch. 5.3 - Prob. 5ECh. 5.3 - In Exercises 1-10 decide whether each statement is...Ch. 5.3 - In Exercises 1-10 decide whether each statement is...Ch. 5.3 - Prob. 8ECh. 5.3 - Prob. 9ECh. 5.3 - Prob. 10ECh. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Prob. 14ECh. 5.3 - It has been proved that the reciprocals of all the...Ch. 5.3 - Prob. 16ECh. 5.3 - Prob. 17ECh. 5.3 - Prob. 18ECh. 5.3 - Prob. 19ECh. 5.3 - Prob. 20ECh. 5.3 - 21. There are four abundant numbers between 1 and...Ch. 5.3 - Prob. 22ECh. 5.3 - Prob. 23ECh. 5.3 - Prob. 24ECh. 5.3 - 25. The proper divisors of 1184 are 1.2. 4. 8, 16,...Ch. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.3 - Prob. 30ECh. 5.3 - Prob. 31ECh. 5.3 - Prob. 32ECh. 5.3 - Prob. 33ECh. 5.3 - Prob. 34ECh. 5.3 - Prob. 35ECh. 5.3 - Prob. 36ECh. 5.3 - Prob. 37ECh. 5.3 - Prob. 38ECh. 5.3 - The first four perfect numbers were identified in...Ch. 5.3 - Prob. 40ECh. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.3 - Prob. 43ECh. 5.3 - Prob. 44ECh. 5.3 - Prob. 45ECh. 5.3 - Prob. 46ECh. 5.3 - 47. Explain why the primorial formula does not...Ch. 5.3 - Prob. 48ECh. 5.3 - 49. Choose the correct completion: The primorial...Ch. 5.3 - Prob. 50ECh. 5.3 - Prob. 51ECh. 5.3 - Prob. 52ECh. 5.3 - Prob. 53ECh. 5.3 - Prob. 54ECh. 5.3 - Prob. 55ECh. 5.3 - Prob. 56ECh. 5.3 - Prob. 57ECh. 5.3 - Prob. 58ECh. 5.3 - Prob. 59ECh. 5.3 - Prob. 60ECh. 5.3 - Prob. 61ECh. 5.3 - Prob. 62ECh. 5.3 - Prob. 63ECh. 5.3 - Prob. 64ECh. 5.3 - Prob. 65ECh. 5.3 - Prob. 66ECh. 5.3 - Prob. 67ECh. 5.3 - Prob. 68ECh. 5.4 - Decide whether each statement is true or false. No...Ch. 5.4 - Decide whether each statement is true or false.
2....Ch. 5.4 - Decide whether each statement is true or false. If...Ch. 5.4 - Decide whether each statement is true or false.
4....Ch. 5.4 - Decide whether each statement is true or false....Ch. 5.4 - Decide whether each statement is true or false....Ch. 5.4 - Decide whether each statement is true or false....Ch. 5.4 - Decide whether each statement is true or false....Ch. 5.4 - Decide whether each statement is true or false.
9....Ch. 5.4 - Decide whether each statement is true or false....Ch. 5.4 - Use the prime factors method to find the greatest...Ch. 5.4 - Use the prime factors method to find the greatest...Ch. 5.4 - Use the prime factors method to find the greatest...Ch. 5.4 - Use the prime factors method to find the greatest...Ch. 5.4 - Use the prime factors method to find the greatest...Ch. 5.4 - Use the prime factors method to find the greatest...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the Euclidean algorithm to find the greatest...Ch. 5.4 - Use the Euclidean algorithm to find the greatest...Ch. 5.4 - Use the Euclidean algorithm to find the greatest...Ch. 5.4 - Use the Euclidean algorithm to find the greatest...Ch. 5.4 - Use the Euclidean algorithm to find the greatest...Ch. 5.4 - Use the Euclidean algorithm to find the greatest...Ch. 5.4 - Use the prime factors method to find the least...Ch. 5.4 - Use the prime factors method to find the least...Ch. 5.4 - Use the prime factors method to find the least...Ch. 5.4 - Use the prime factors method to find the least...Ch. 5.4 - Use the prime factors method to find the least...Ch. 5.4 - Use the prime factors method to find the least...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the method of dividing by prime factors to...Ch. 5.4 - Use the formula given in the text on page 203and...Ch. 5.4 - Use the formula given in the text on page 203 and...Ch. 5.4 - Use the formula given in the text on page 203 and...Ch. 5.4 - Use the formula given in the text on page 203 and...Ch. 5.4 - Use the formula given in the text on page 203 and...Ch. 5.4 - Use the formula given in the text on page 203 and...Ch. 5.4 - Explain in your own words how to find the greatest...Ch. 5.4 - 48, Explain in your own words how to find the...Ch. 5.4 - If p. q, and r and different primes, and a. b, and...Ch. 5.4 - Find (a) the greatest common factor and (b) the...Ch. 5.4 - Prob. 51ECh. 5.4 - Prob. 52ECh. 5.4 - Prob. 53ECh. 5.4 - It is possible to extend the Euclidean algorithm...Ch. 5.4 - Prob. 55ECh. 5.4 - Suppose that the least common multiple of p and q...Ch. 5.4 - Prob. 57ECh. 5.4 - Prob. 58ECh. 5.4 - Prob. 59ECh. 5.4 - Refer to Examples 9 and 10 to solve each problem....Ch. 5.4 - Refer to Examples 9 and 10 to solve each...Ch. 5.4 - Refer to Examples 9 and 10 to solve each...Ch. 5.4 - Prob. 63ECh. 5.4 - Refer to Examples 9 and 10 to solve each problem....Ch. 5.5 - Answer each question concerning the Fibonacci...Ch. 5.5 - Prob. 2ECh. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - Prob. 5ECh. 5.5 - Prob. 6ECh. 5.5 - Prob. 7ECh. 5.5 - Prob. 8ECh. 5.5 - Prob. 9ECh. 5.5 - Prob. 10ECh. 5.5 - Prob. 11ECh. 5.5 - Prob. 12ECh. 5.5 - Prob. 13ECh. 5.5 - Prob. 14ECh. 5.5 - Prob. 15ECh. 5.5 - It has been shown that if m divides n, then Fm is...Ch. 5.5 - Prob. 17ECh. 5.5 - Prob. 18ECh. 5.5 - Prob. 19ECh. 5.5 - Prob. 20ECh. 5.5 - Prob. 21ECh. 5.5 - Prob. 22ECh. 5.5 - Prob. 23ECh. 5.5 - Prob. 24ECh. 5.5 - Prob. 25ECh. 5.5 - Prob. 26ECh. 5.5 - Prob. 27ECh. 5.5 - Recall (lie Pythagorean theorem from geometry: If...Ch. 5.5 - Recall (lie Pythagorean theorem from geometry: If...Ch. 5.5 - Prob. 30ECh. 5.5 - Prob. 31ECh. 5.5 - Prob. 32ECh. 5.5 - Prob. 33ECh. 5.5 - Prob. 34ECh. 5.5 - Prob. 35ECh. 5.5 - Prob. 36ECh. 5 - In Exercises 1-6, decide whether each statement is...Ch. 5 - In Exercises 1-6, decide whether each statement is...Ch. 5 - Prob. 3TCh. 5 - In Exercises 1-6, decide whether each statement is...Ch. 5 - Prob. 5TCh. 5 - Prob. 6TCh. 5 - Use divisibility tests to determine whether the...Ch. 5 - Prob. 8TCh. 5 - Prob. 9TCh. 5 - Prob. 10TCh. 5 - Prob. 11TCh. 5 - Prob. 12TCh. 5 - Give a pair of twin primes between 60 and 80.Ch. 5 - Prob. 14TCh. 5 - Prob. 15TCh. 5 - Prob. 16TCh. 5 - Prob. 17TCh. 5 - Prob. 18TCh. 5 - Prob. 19TCh. 5 - Prob. 20TCh. 5 - 21. Choose any term after the first in the...Ch. 5 - 22. Which one of the following is the exact value...
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