Introductory Combinatorics
5th Edition
ISBN: 9780134689616
Author: Brualdi, Richard A.
Publisher: Pearson,
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Chapter 5, Problem 24E
To determine
The different routes that are in which walk exactly 45 blocks.
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The acidity or alkalinity of a solution is measured using pH. A pH less than 7 is acidic; a pH greater than 7 is alkaline. The accompanying data represent the pH in samples of bottled water and tap
water. Complete parts (a) and (b).
Click the icon to view the data table.
(a) Determine the mean, median, and mode pH for each type of water. Comment on the differences between the two water types.
Select the correct choice below and fill in any answer boxes in your choice.
A. For tap water, the mean pH is
(Round to three decimal places as needed.)
B. The mean does not exist.
Data table
Тар
7.64 7.45
7.45 7.10
7.46 7.50
7.68
7.69
7.56
7.46
7.52
7.46
5.15 5.09 5.31
5.20
4.78
5.23
Bottled
5.52 5.31 5.13
5.31
5.21
5.24
-
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Chapter 5-Section 1 Homework X
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A computer repair shop has two work centers. The first center examines the computer to see what is wrong, and the second center repairs the computer. Let x₁ and x2 be
random variables representing the lengths of time in minutes to examine a computer (✗₁) and to repair a computer (x2). Assume x and x, are independent random variables.
Long-term history has shown the following times.
01
Examine computer, x₁₁ = 29.6 minutes; σ₁ = 8.1 minutes
Repair computer, X2: μ₂ = 92.5 minutes; σ2 = 14.5 minutes
(a) Let W = x₁ + x2 be a random variable representing the total time to examine and repair the computer. Compute the mean, variance, and standard deviation of W.
(Round your answers…
Answer this two questions:
2 . We roll seven 20-sided dice, numbered 1 to 20. Show that it is always possible to find two disjoint nonempty subsets of the dice such that the sums of the shown faces of the dice in each of the subsets coincide(only one of the faces is considered to be shown) .
4. We are given a deck of 60 cards, 40 are identical black cards, 10 are identical red cards, and 10 are identical greenc ards. How may ways are there to deal the 60 cards to three distinct players so that everyone gets exactly 20 cards?
Chapter 5 Solutions
Introductory Combinatorics
Ch. 5 - Prob. 1ECh. 5 - Fill in the rows of Pascal’s triangle...Ch. 5 - Consider the sum of the binomial coefficients...Ch. 5 - Expand (x + y)5 and (x + y)6 using the binomial...Ch. 5 - Expand (2x − y)7 using the binomial theorem.
Ch. 5 - What is the coefficient of x5y13 in the expansion...Ch. 5 - Use the binomial theorem to prove that
Generalize...Ch. 5 - Use the binomial theorem to prove that
Ch. 5 - Evaluate the sum
Ch. 5 - Use combinatorial reasoning to prove the identity...
Ch. 5 - Use combinatorial reasoning to prove the identity...Ch. 5 - Let n be a positive integer. Prove that
(Hint:...Ch. 5 - Find one binomial coefficient equal to the...Ch. 5 - Prob. 14ECh. 5 - Prove, that for every integer n > 1,
Ch. 5 - By integrating the binomial expansion, prove that,...Ch. 5 - Prob. 17ECh. 5 - Evaluate the sum
Ch. 5 - Sum the series by observing that
and using the...Ch. 5 - Find integers a, b, and c such that
for all m....Ch. 5 - Prob. 21ECh. 5 - Prob. 22ECh. 5 - Prob. 23ECh. 5 - Prob. 24ECh. 5 - Use a combinatorial argument to prove the...Ch. 5 - Let n and k be integers with 1 ≤ k ≤ n. Prove...Ch. 5 - Let n and k be positive integers. Give a...Ch. 5 - Let n and k be positive integers. Give a...Ch. 5 - Find and prove a formula for
where the summation...Ch. 5 - Prove that the only antichain of S = {1, 2, 3, 4}...Ch. 5 - Prove that there are only two antichains of S =...Ch. 5 - Let S be a set of n elements. Prove that, if n is...Ch. 5 - Construct a partition of the subsets of {1, 2, 3,...Ch. 5 - In a partition of the subsets of {1,2, …, n} into...Ch. 5 - A talk show host has just bought 10 new jokes....Ch. 5 - Prove the identity of Exercise 25 using the...Ch. 5 - Use the multinomial theorem to show that, for...Ch. 5 - Use the multinomial theorem to expand (x1 + x2 +...Ch. 5 - Determine the coefficient of in the expansion...Ch. 5 - What is the coefficient of in the expansion of
Ch. 5 - Prob. 41ECh. 5 - Prob. 42ECh. 5 - Prove by induction on n that, for n a positive...Ch. 5 - Prove that
where the summation extends over all...Ch. 5 - Prove that
where the summation extends over all...Ch. 5 - Use Newton’s binomial theorem to approximate .
Ch. 5 - Use Newton’s binomial theorem to approximate...Ch. 5 - Use Theorem 5.6.1 to show that, if m and n are...Ch. 5 - Use Theorem 5.6.1 to show that, if m and n are...Ch. 5 - Prob. 50ECh. 5 - Let R and S be two partial orders on the same set...
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- The acidity or alkalinity of a solution is measured using pH. A pH less than 7 is acidic; a pH greater than 7 is alkaline. The accompanying data represent the pH in samples of bottled water and tap water. Complete parts (a) and (b). Click the icon to view the data table. (a) Determine the mean, median, and mode pH for each type of water. Comment on the differences between the two water types. Select the correct choice below and fill in any answer boxes in your choice. A. For tap water, the mean pH is (Round to three decimal places as needed.) B. The mean does not exist. Data table Тар Bottled 7.64 7.45 7.46 7.50 7.68 7.45 7.10 7.56 7.46 7.52 5.15 5.09 5.31 5.20 4.78 5.52 5.31 5.13 5.31 5.21 7.69 7.46 5.23 5.24 Print Done - ☑arrow_forwardThe median for the given set of six ordered data values is 29.5. 9 12 23 41 49 What is the missing value? The missing value is ☐.arrow_forwardFind the population mean or sample mean as indicated. Sample: 22, 18, 9, 6, 15 □ Select the correct choice below and fill in the answer box to complete your choice. O A. x= B. μεarrow_forward
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