Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
14th Edition
ISBN: 9780134677972
Author: Barnett
Publisher: PEARSON
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Chapter B.3, Problem 4MP
Use the binomial theorem to find the fourth term in the expansion of
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1. (i) Give the definition of a metric on a set X.
[5 Marks]
(ii) Let X = {a, b, c} and let a function d : XxX → [0, ∞) be defined
as d(a, a) = d(b,b) = d(c, c) 0, d(a, c) = d(c, a) 1, d(a, b) = d(b, a) = 4,
d(b, c) = d(c,b) = 2. Decide whether d is a metric on X. Justify your answer.
=
(iii) Consider a metric space (R, d.), where
=
[10 Marks]
0
if x = y,
d* (x, y)
5
if xy.
In the metric space (R, d*), describe:
(a) open ball B2(0) of radius 2 centred at 0;
(b) closed ball B5(0) of radius 5 centred at 0;
(c) sphere S10 (0) of radius 10 centred at 0.
[5 Marks]
[5 Marks]
[5 Marks]
(c) sphere S10 (0) of radius 10 centred at 0.
[5 Marks]
2. Let C([a, b]) be the metric space of continuous functions on the interval
[a, b] with the metric
doo (f,g)
=
max f(x)g(x)|.
xЄ[a,b]
= 1x. Find:
Let f(x) = 1 - x² and g(x):
(i) do(f, g) in C'([0, 1]);
(ii) do(f,g) in C([−1, 1]).
[20 Marks]
[20 Marks]
1. (i) Explain the difference in application between the Mann-Whitney U test
and the Wilcoxon Signed-Rank test, i.e. in which scenarios would each test be
used?
(ii) What is the main procedure underlying these nonparametric tests?
[3 Marks]
Chapter B Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Ch. B.1 - Write the first four terms of each sequence: (a)...Ch. B.1 - Find the general term of a sequence whose first...Ch. B.1 - Write k=15k+11 Without summation notion. Do not...Ch. B.1 - Write the alternating series 113+19127+181 using...Ch. B.1 - Find the arithmetic mean of 9,3,8,4,3, and 6.Ch. B.1 - Write the first four terms for each sequence in...Ch. B.1 - Write the first four terms for each sequence in...Ch. B.1 - Write the first four terms for each sequence in...Ch. B.1 - Write the first four terms for each sequence in...Ch. B.1 - Write the first four terms for each sequence in...
Ch. B.1 - Write the first four terms for each sequence in...Ch. B.1 - Write the 10th term of the sequence in Problem 1.Ch. B.1 - Write the 15th term of the sequence in Problem 2.Ch. B.1 - Write the 99th term of the sequence in Problem 3.Ch. B.1 - Write the 200th term of the sequence in Problem 4.Ch. B.1 - In Problems 11-16, write each series in expanded...Ch. B.1 - In Problems 11-16, write each series in expanded...Ch. B.1 - In Problems 11-16, write each series in expanded...Ch. B.1 - In Problems 11-16, write each series in expanded...Ch. B.1 - In Problems 11-16, write each series in expanded...Ch. B.1 - In Problems 11-16, write each series in expanded...Ch. B.1 - Find the arithmetic mean of each list of numbers...Ch. B.1 - Find the arithmetic mean of each list of numbers...Ch. B.1 - Find the arithmetic mean of each list of numbers...Ch. B.1 - Find the arithmetic mean of each list of numbers...Ch. B.1 - Write the first five terms of each sequence in...Ch. B.1 - Write the first five terms of each sequence in...Ch. B.1 - Write the first five terms of each sequence in...Ch. B.1 - Write the first five terms of each sequence in...Ch. B.1 - Write the first five terms of each sequence in...Ch. B.1 - Write the first five terms of each sequence in...Ch. B.1 - In Problems 27-42, find the general term of a...Ch. B.1 - In Problems 27-42, find the general term of a...Ch. B.1 - In Problems 27-42, find the general term of a...Ch. B.1 - In Problems 27-42, find the general term of a...Ch. B.1 - In Problems 27-42, find the general term of a...Ch. B.1 - In Problems 27-42, find the general term of a...Ch. B.1 - In Problems 27-42, find the general term of a...Ch. B.1 - In Problems 27-42, find the general term of a...Ch. B.1 - In Problems 27-42, find the general term of a...Ch. B.1 - In Problems 27-42, find the general term of a...Ch. B.1 - In Problems 27-42, find the general term of a...Ch. B.1 - In Problems 27-42, find the general term of a...Ch. B.1 - In Problems 27-42, find the general term of a...Ch. B.1 - In Problems 27-42, find the general term of a...Ch. B.1 - In Problems 27-42, find the general term of a...Ch. B.1 - In Problems 27-42, find the general term of a...Ch. B.1 - Write each series in Problems 43-50 in expanded...Ch. B.1 - Write each series in Problems 43-50 in expanded...Ch. B.1 - Write each series in Problems 43-50 in expanded...Ch. B.1 - Write each series in Problems 43-50 in expanded...Ch. B.1 - Write each series in Problems 43-50 in expanded...Ch. B.1 - Write each series in Problems 43-50 in expanded...Ch. B.1 - Write each series in Problems 43-50 in expanded...Ch. B.1 - Write each series in Problems 43-50 in expanded...Ch. B.1 - Write each series in Problems 51-54 using...Ch. B.1 - Write each series in Problems 51-54 using...Ch. B.1 - Write each series in Problems 51-54 using...Ch. B.1 - Write each series in Problems 51-54 using...Ch. B.1 - Write each series in Problems 55-58 using...Ch. B.1 - Write each series in Problems 55-58 using...Ch. B.1 - Write each series in Problems 55-58 using...Ch. B.1 - Write each series in Problems 55-58 using...Ch. B.1 - In Problems 59-62, discuss the validity of each...Ch. B.1 - In Problems 59-62, discuss the validity of each...Ch. B.1 - In Problems 59-62, discuss the validity of each...Ch. B.1 - In Problems 59-62, discuss the validity of each...Ch. B.1 - Some sequences are defined by a recursive formula-...Ch. B.1 - Some sequences are defined by a recursive formula-...Ch. B.1 - Some sequences are defined by a recursive formula-...Ch. B.1 - Some sequences are defined by a recursive formula-...Ch. B.1 - If A is a positive real number, the terms pf the...Ch. B.1 - If A is a positive real number, the terms pf the...Ch. B.1 - The sequence defined recursively by...Ch. B.1 - The sequence defined by bn=551+52n is related to...Ch. B.2 - Which of the following can be the first four terms...Ch. B.2 - (A) If the 1st and 15th terms of an arithmetic...Ch. B.2 - Find the sum of the first 40 terms in the...Ch. B.2 - Find the sum of all the odd numbers between 24 and...Ch. B.2 - Find the sum of the first eight terms of the...Ch. B.2 - Repeat Example 6 with a loan of 6,000 over 5...Ch. B.2 - Repeat Example 7 with a tax rebate of 2,000.Ch. B.2 - In Problems 1 and 2, determine whether the...Ch. B.2 - In Problems 1 and 2, determine whether the...Ch. B.2 - In Problems 3-8, determine whether the finite...Ch. B.2 - In Problems 3-8, determine whether the finite...Ch. B.2 - In Problems 3-8, determine whether the finite...Ch. B.2 - In Problems 3-8, determine whether the finite...Ch. B.2 - In Problems 3-8, determine whether the finite...Ch. B.2 - In Problems 3-8, determine whether the finite...Ch. B.2 - Let a1,a2,a3,an, be an arithmetic sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an arithmetic sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an arithmetic sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an arithmetic sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an arithmetic sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an arithmetic sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an geometric sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an geometric sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an geometric sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an geometric sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an geometric sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an geometric sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an geometric sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an geometric sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an geometric sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an geometric sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an geometric sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an geometric sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an geometric sequence. In...Ch. B.2 - Let a1,a2,a3,an, be an geometric sequence. In...Ch. B.2 - Find the sum of the odd integers between 12 and 68Ch. B.2 - Find the sum of all the even integers between 23...Ch. B.2 - Find the sum of each infinite geometric sequence...Ch. B.2 - Repeat Problem 31 for: (a) 16,4,1, (b) 1,3,9,Ch. B.2 - Find f1+f2+f3++f50 if fx=2x3.Ch. B.2 - Find g1+g2+g3++g100 if gx=183t.Ch. B.2 - Find f1+f2++f10 if fx=12x.Ch. B.2 - Find g1+g2++g10 if gx=2x.Ch. B.2 - Show that the sum of the first n odd positive...Ch. B.2 - Show that the sum of the first n even positive...Ch. B.2 - If r=1, neither the first form nor the second form...Ch. B.2 - If all of the terms of an infinite geometric...Ch. B.2 - Dose there exist a finite arithmetic series with...Ch. B.2 - Dose there exist a finite arithmetic series with...Ch. B.2 - Does there exist an infinite geometric series with...Ch. B.2 - Dose there exist an infinite geometric series with...Ch. B.2 - Loan repayment. If you borrow $4,800 and repay the...Ch. B.2 - Loan repayment. If you borrow $5,400 and repay the...Ch. B.2 - Economy stimulation. The government, through a...Ch. B.2 - Economy stimulation. Due to reduced taxes, a...Ch. B.2 - Compound interest. If $1,000 is invested at 5...Ch. B.2 - Compound interest. If $P is invested at 100r...Ch. B.3 - Evaluate. (A)4!(B)7!6!(C)8!5!Ch. B.3 - Find A5C2B6C0Ch. B.3 - Use the binomial theorem to expand x+25.Ch. B.3 - Use the binomial theorem to find the fourth term...Ch. B.3 - In Problems 1-20, evaluate each expression. 6!Ch. B.3 - In Problems 1-20, evaluate each expression. 7!Ch. B.3 - In Problems 1-20, evaluate each expression. 10!9!Ch. B.3 - In Problems 1-20, evaluate each expression. 20!19!Ch. B.3 - In Problems 1-20, evaluate each expression. 12!9!Ch. B.3 - In Problems 1-20, evaluate each expression. 10!6!Ch. B.3 - In Problems 1-20, evaluate each expression. 5!2!3!Ch. B.3 - In Problems 1-20, evaluate each expression. 7!3!4!Ch. B.3 - In Problems 1-20, evaluate each expression....Ch. B.3 - In Problems 1-20, evaluate each expression....Ch. B.3 - In Problems 1-20, evaluate each expression....Ch. B.3 - In Problems 1-20, evaluate each expression....Ch. B.3 - In Problems 1-20, evaluate each expression. 5C3Ch. B.3 - In Problems 1-20, evaluate each expression. 7C3Ch. B.3 - In Problems 1-20, evaluate each expression. 6C5Ch. B.3 - In Problems 1-20, evaluate each expression. 7C4Ch. B.3 - In Problems 1-20, evaluate each expression. 5C0Ch. B.3 - In Problems 1-20, evaluate each expression. 5C5Ch. B.3 - In Problems 1-20, evaluate each expression. 18C15Ch. B.3 - In Problems 1-20, evaluate each expression. 18C3Ch. B.3 - Expand each expression in Problems 21-26 using the...Ch. B.3 - Expand each expression in Problems 21-26 using the...Ch. B.3 - Expand each expression in Problems 21-26 using the...Ch. B.3 - Expand each expression in Problems 21-26 using the...Ch. B.3 - Expand each expression in Problems 21-26 using the...Ch. B.3 - Expand each expression in Problems 21-26 using the...Ch. B.3 - Find the indicated term in each expansion in...Ch. B.3 - Find the indicated term in each expansion in...Ch. B.3 - Find the indicated term in each expansion in...Ch. B.3 - Find the indicated term in each expansion in...Ch. B.3 - Find the indicated term in each expansion in...Ch. B.3 - Find the indicated term in each expansion in...Ch. B.3 - Show that nC0=nCnforn0.Ch. B.3 - Show that nCr=nCnrfornr0.Ch. B.3 - The triangle shown here is called Pascal’s...Ch. B.3 - Explain why the sum of the entries in each row of...Ch. B.3 - Explain why the alternating sum of the entries in...Ch. B.3 - Show that nCr=nr+1rnCr1fornr1.Ch. B.3 - Show that nCr1+nCr=n+1Crfornr1.
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