College Mathematics for Trades and Technologies (10th Edition) (What's New in Trade Math)
10th Edition
ISBN: 9780134690339
Author: Cheryl Cleaves, Margie Hobbs
Publisher: PEARSON
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Chapter 15.7, Problem 45E
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To solve: The inequality
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(^)
k
Recall that for numbers 0 ≤ k ≤ n the binomial coefficient (^) is defined as
n!
k! (n−k)!
Question 1.
(1) Prove the following identity: (22) + (1121) = (n+1).
(2) Use the identity above to prove the binomial theorem by induction. That
is, prove that for any a, b = R,
n
(a + b)" = Σ (^)
an-
n-kyk.
k=0
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Recall that Σ0 x is short hand notation for the expression x0+x1+
+xn-
(3) Fix x = R, x > 0. Prove Bernoulli's inequality: (1+x)" ≥1+nx, by using
the binomial theorem.
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Question 2. Prove that ||x| - |y|| ≤ |x − y| for any real numbers x, y.
Question 3. Assume (In) nEN is a sequence which is unbounded above. That is,
the set {xn|nЄN} is unbounded above. Prove that there are natural numbers
N] k for all k Є N.
be natural numbers (nk Є N). Prove that
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Part 1
Find the measure of
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Joy is making Christmas gifts. She has 6 1/12 feet of yarn and will need 4 1/4 to complete our project. How much yarn will she have left over compute this solution in two different ways 
Chapter 15 Solutions
College Mathematics for Trades and Technologies (10th Edition) (What's New in Trade Math)
Ch. 15.1 - Write 3x − 7 + 4x2 in descending order of x.
Ch. 15.1 - Prob. 1ECh. 15.1 - Prob. 2ECh. 15.1 - Prob. 3ECh. 15.1 - Prob. 4ECh. 15.1 - Prob. 5ECh. 15.1 - Prob. 6ECh. 15.1 - Prob. 7ECh. 15.1 - Prob. 8ECh. 15.1 - Prob. 9E
Ch. 15.1 - Prob. 10ECh. 15.1 - Prob. 11ECh. 15.1 - Prob. 12ECh. 15.1 - Prob. 13ECh. 15.1 - Prob. 14ECh. 15.1 - Prob. 15ECh. 15.1 - Prob. 16ECh. 15.1 - Write each equation in standard form and identify...Ch. 15.1 - Prob. 18ECh. 15.1 - Prob. 19ECh. 15.1 - Prob. 20ECh. 15.1 - Prob. 21ECh. 15.1 - Prob. 22ECh. 15.1 - Prob. 23ECh. 15.1 - Prob. 24ECh. 15.1 - Prob. 25ECh. 15.1 - Prob. 26ECh. 15.1 - Prob. 27ECh. 15.1 - Prob. 28ECh. 15.1 - Prob. 29ECh. 15.1 - Prob. 30ECh. 15.1 - Prob. 31ECh. 15.1 - Prob. 32ECh. 15.1 - Prob. 33ECh. 15.1 - Prob. 34ECh. 15.1 - Prob. 35ECh. 15.1 - Prob. 36ECh. 15.1 - Prob. 37ECh. 15.1 - Prob. 38ECh. 15.1 - Prob. 39ECh. 15.1 - Prob. 40ECh. 15.1 - Prob. 41ECh. 15.1 - Prob. 42ECh. 15.1 - Prob. 43ECh. 15.1 - Prob. 44ECh. 15.1 - Prob. 45ECh. 15.1 - Prob. 46ECh. 15.1 - Prob. 47ECh. 15.2 - Factor 10x2 − 15x for x.
Ch. 15.2 - Factor 3x2 + 7x − 6 for x.
Ch. 15.2 - Solve by factoring.
Ch. 15.2 - Prob. 2ECh. 15.2 - Prob. 3ECh. 15.2 - Prob. 4ECh. 15.2 - Prob. 5ECh. 15.2 - Prob. 6ECh. 15.2 - Prob. 7ECh. 15.2 - Prob. 8ECh. 15.2 - Prob. 9ECh. 15.2 - Prob. 10ECh. 15.2 - Prob. 11ECh. 15.2 - Prob. 12ECh. 15.2 - Prob. 13ECh. 15.2 - Prob. 14ECh. 15.2 - Prob. 15ECh. 15.2 - Prob. 16ECh. 15.2 - Prob. 17ECh. 15.2 - Solve the equations by factoring.
Ch. 15.2 - Prob. 19ECh. 15.2 - Prob. 20ECh. 15.2 - Prob. 21ECh. 15.2 - Prob. 22ECh. 15.2 - Prob. 23ECh. 15.2 - Prob. 24ECh. 15.2 - Prob. 25ECh. 15.2 - Prob. 26ECh. 15.2 - Prob. 27ECh. 15.2 - Prob. 28ECh. 15.2 - Prob. 29ECh. 15.2 - Prob. 30ECh. 15.2 - Prob. 31ECh. 15.2 - Prob. 32ECh. 15.2 - Prob. 33ECh. 15.2 - Prob. 34ECh. 15.2 - Prob. 35ECh. 15.2 - Prob. 36ECh. 15.2 - Prob. 37ECh. 15.2 - Prob. 38ECh. 15.2 - Prob. 39ECh. 15.2 - Prob. 40ECh. 15.2 - Prob. 41ECh. 15.2 - Prob. 42ECh. 15.3 - Expand .
Ch. 15.3 - Prob. 1ECh. 15.3 - Prob. 2ECh. 15.3 - Prob. 3ECh. 15.3 - Prob. 4ECh. 15.3 - Prob. 5ECh. 15.3 - Prob. 6ECh. 15.3 - Prob. 7ECh. 15.3 - Prob. 8ECh. 15.3 - Prob. 9ECh. 15.3 - Prob. 10ECh. 15.3 - Prob. 11ECh. 15.3 - Prob. 12ECh. 15.3 - Prob. 13ECh. 15.3 - Prob. 14ECh. 15.3 - Prob. 15ECh. 15.3 - Prob. 16ECh. 15.3 - Prob. 17ECh. 15.3 - Prob. 18ECh. 15.3 - Prob. 19ECh. 15.3 - Prob. 20ECh. 15.3 - Prob. 21ECh. 15.3 - Prob. 22ECh. 15.3 - Prob. 23ECh. 15.3 - Prob. 24ECh. 15.3 - Prob. 25ECh. 15.3 - Prob. 26ECh. 15.3 - Prob. 27ECh. 15.3 - Prob. 28ECh. 15.3 - Prob. 29ECh. 15.3 - Prob. 30ECh. 15.3 - Prob. 31ECh. 15.3 - Prob. 32ECh. 15.3 - Prob. 33ECh. 15.3 - Prob. 34ECh. 15.3 - Prob. 35ECh. 15.3 - Prob. 36ECh. 15.4 - Prob. 1LCCh. 15.4 - Prob. 1ECh. 15.4 - Prob. 2ECh. 15.4 - Prob. 3ECh. 15.4 - Prob. 4ECh. 15.4 - Prob. 5ECh. 15.4 - Prob. 6ECh. 15.4 - Prob. 7ECh. 15.4 - Prob. 8ECh. 15.4 - Prob. 9ECh. 15.4 - Prob. 10ECh. 15.4 - Prob. 11ECh. 15.4 - Prob. 12ECh. 15.4 - Prob. 13ECh. 15.4 - Prob. 14ECh. 15.4 - Prob. 15ECh. 15.4 - Prob. 16ECh. 15.4 - Prob. 17ECh. 15.4 - Prob. 18ECh. 15.4 - Prob. 19ECh. 15.4 - Prob. 20ECh. 15.4 - Prob. 21ECh. 15.4 - Prob. 22ECh. 15.4 - Prob. 23ECh. 15.4 - Prob. 24ECh. 15.4 - Prob. 25ECh. 15.4 - Prob. 26ECh. 15.4 - Prob. 27ECh. 15.4 - Prob. 28ECh. 15.4 - Prob. 29ECh. 15.4 - Prob. 30ECh. 15.4 - Prob. 31ECh. 15.4 - Prob. 32ECh. 15.5 - Prob. 1LCCh. 15.5 - Prob. 2LCCh. 15.5 - Prob. 3LCCh. 15.5 - Prob. 1ECh. 15.5 - Prob. 2ECh. 15.5 - Prob. 3ECh. 15.5 - Prob. 4ECh. 15.5 - Prob. 5ECh. 15.5 - Prob. 6ECh. 15.5 - Prob. 7ECh. 15.5 - Prob. 8ECh. 15.5 - Prob. 9ECh. 15.5 - Prob. 10ECh. 15.5 - Prob. 11ECh. 15.5 - Prob. 12ECh. 15.5 - Prob. 13ECh. 15.5 - Prob. 14ECh. 15.5 - Prob. 15ECh. 15.5 - Prob. 16ECh. 15.5 - Prob. 17ECh. 15.5 - Prob. 18ECh. 15.5 - Prob. 19ECh. 15.5 - Prob. 20ECh. 15.5 - Prob. 21ECh. 15.5 - Prob. 22ECh. 15.5 - Prob. 23ECh. 15.5 - Prob. 24ECh. 15.5 - Prob. 25ECh. 15.5 - Prob. 26ECh. 15.5 - Prob. 27ECh. 15.5 - Prob. 28ECh. 15.5 - Prob. 29ECh. 15.5 - Prob. 30ECh. 15.5 - Find the domain and range of the functions or...Ch. 15.5 - Prob. 32ECh. 15.5 - Prob. 33ECh. 15.5 - Find the domain and range of the functions or...Ch. 15.5 - Prob. 35ECh. 15.5 - Find the domain and range of the functions or...Ch. 15.6 - Prob. 1LCCh. 15.6 - Prob. 1ECh. 15.6 - Prob. 2ECh. 15.6 - Prob. 3ECh. 15.6 - Prob. 4ECh. 15.6 - Prob. 5ECh. 15.6 - Prob. 6ECh. 15.6 - Prob. 7ECh. 15.6 - Prob. 8ECh. 15.6 - Prob. 9ECh. 15.6 - Prob. 10ECh. 15.6 - Prob. 11ECh. 15.6 - Prob. 12ECh. 15.6 - Prob. 13ECh. 15.6 - Prob. 14ECh. 15.6 - Prob. 15ECh. 15.6 - Prob. 16ECh. 15.6 - Prob. 17ECh. 15.6 - Prob. 18ECh. 15.7 - Prob. 1LCCh. 15.7 - Prob. 1ECh. 15.7 - Prob. 2ECh. 15.7 - Prob. 3ECh. 15.7 - Prob. 4ECh. 15.7 - Prob. 5ECh. 15.7 - Prob. 6ECh. 15.7 - Prob. 7ECh. 15.7 - Prob. 8ECh. 15.7 - Prob. 9ECh. 15.7 - Prob. 10ECh. 15.7 - Prob. 11ECh. 15.7 - Prob. 12ECh. 15.7 - Prob. 13ECh. 15.7 - Prob. 14ECh. 15.7 - Prob. 15ECh. 15.7 - Prob. 16ECh. 15.7 - Prob. 17ECh. 15.7 - Prob. 18ECh. 15.7 - Prob. 19ECh. 15.7 - Prob. 20ECh. 15.7 - Prob. 21ECh. 15.7 - Prob. 22ECh. 15.7 - Prob. 23ECh. 15.7 - Prob. 24ECh. 15.7 - Prob. 25ECh. 15.7 - Prob. 26ECh. 15.7 - Prob. 27ECh. 15.7 - Prob. 28ECh. 15.7 - Prob. 29ECh. 15.7 - Prob. 30ECh. 15.7 - Prob. 31ECh. 15.7 - Prob. 32ECh. 15.7 - Prob. 33ECh. 15.7 - Prob. 34ECh. 15.7 - Find the solution set for each inequality. Graph...Ch. 15.7 - Prob. 36ECh. 15.7 - Prob. 37ECh. 15.7 - Prob. 38ECh. 15.7 - Prob. 39ECh. 15.7 - Prob. 40ECh. 15.7 - Prob. 41ECh. 15.7 - Prob. 42ECh. 15.7 - Prob. 43ECh. 15.7 - Prob. 44ECh. 15.7 - Prob. 45ECh. 15.7 - Prob. 46ECh. 15.7 - Prob. 47ECh. 15.7 - Prob. 48ECh. 15.7 - Prob. 49ECh. 15.7 - Prob. 50ECh. 15.7 - Prob. 51ECh. 15.7 - Prob. 52ECh. 15.7 - Prob. 53ECh. 15.7 - Prob. 54ECh. 15.7 - Prob. 55ECh. 15.7 - Prob. 56ECh. 15.7 - Prob. 57ECh. 15.7 - Prob. 58ECh. 15.7 - Prob. 59ECh. 15.7 - Prob. 60ECh. 15.7 - Prob. 61ECh. 15.7 - Prob. 62ECh. 15.7 - Prob. 63ECh. 15.7 - Prob. 64ECh. 15.7 - Prob. 65ECh. 15.7 - Prob. 66ECh. 15.7 - Prob. 67ECh. 15.7 - Prob. 68ECh. 15.7 - Prob. 69ECh. 15.7 - Prob. 70ECh. 15 - Prob. 1RECh. 15 - Prob. 2RECh. 15 - Prob. 3RECh. 15 - Prob. 4RECh. 15 - Prob. 5RECh. 15 - Prob. 6RECh. 15 - Prob. 7RECh. 15 - Prob. 8RECh. 15 - Prob. 9RECh. 15 - Prob. 10RECh. 15 - Prob. 11RECh. 15 - Prob. 12RECh. 15 - Prob. 13RECh. 15 - Prob. 14RECh. 15 - Prob. 15RECh. 15 - Prob. 16RECh. 15 - Prob. 17RECh. 15 - Prob. 18RECh. 15 - Prob. 19RECh. 15 - Prob. 20RECh. 15 - Solve the equations by the square-root method....Ch. 15 - Prob. 22RECh. 15 - Prob. 23RECh. 15 - Prob. 24RECh. 15 - Prob. 25RECh. 15 - Prob. 26RECh. 15 - Prob. 27RECh. 15 - Prob. 28RECh. 15 - Prob. 29RECh. 15 - Prob. 30RECh. 15 - Prob. 31RECh. 15 - Prob. 32RECh. 15 - Prob. 33RECh. 15 - Prob. 34RECh. 15 - Prob. 35RECh. 15 - Prob. 36RECh. 15 - Prob. 37RECh. 15 - Prob. 38RECh. 15 - Prob. 39RECh. 15 - Prob. 40RECh. 15 - Prob. 41RECh. 15 - Prob. 42RECh. 15 - Prob. 43RECh. 15 - Prob. 44RECh. 15 - Prob. 45RECh. 15 - Prob. 46RECh. 15 - Prob. 47RECh. 15 - Prob. 48RECh. 15 - Prob. 49RECh. 15 - Prob. 50RECh. 15 - Prob. 51RECh. 15 - Prob. 52RECh. 15 - Prob. 53RECh. 15 - Prob. 54RECh. 15 - Prob. 55RECh. 15 - Prob. 56RECh. 15 - Prob. 57RECh. 15 - Prob. 58RECh. 15 - Prob. 59RECh. 15 - Prob. 60RECh. 15 - Prob. 61RECh. 15 - Prob. 62RECh. 15 - Prob. 63RECh. 15 - Prob. 64RECh. 15 - Prob. 65RECh. 15 - Prob. 66RECh. 15 - Prob. 67RECh. 15 - Prob. 68RECh. 15 - Prob. 69RECh. 15 - Prob. 70RECh. 15 - Prob. 71RECh. 15 - Prob. 72RECh. 15 - Prob. 73RECh. 15 - Prob. 74RECh. 15 - Prob. 75RECh. 15 - Prob. 76RECh. 15 - Prob. 77RECh. 15 - Prob. 78RECh. 15 - Prob. 79RECh. 15 - Prob. 80RECh. 15 - Prob. 81RECh. 15 - Prob. 82RECh. 15 - Prob. 83RECh. 15 - Prob. 84RECh. 15 - Prob. 85RECh. 15 - Prob. 86RECh. 15 - Prob. 87RECh. 15 - Prob. 88RECh. 15 - Prob. 89RECh. 15 - Prob. 90RECh. 15 - Prob. 91RECh. 15 - Prob. 92RECh. 15 - Prob. 93RECh. 15 - Prob. 94RECh. 15 - Prob. 95RECh. 15 - Prob. 96RECh. 15 - Prob. 97RECh. 15 - Prob. 98RECh. 15 - Prob. 99RECh. 15 - Prob. 100RECh. 15 - Prob. 101RECh. 15 - Prob. 102RECh. 15 - Prob. 103RECh. 15 - Prob. 104RECh. 15 - Prob. 105RECh. 15 - Prob. 106RECh. 15 - Prob. 107RECh. 15 - Prob. 108RECh. 15 - Prob. 109RECh. 15 - Prob. 110RECh. 15 - Prob. 111RECh. 15 - Prob. 112RECh. 15 - Prob. 113RECh. 15 - Prob. 114RECh. 15 - Prob. 115RECh. 15 - Prob. 116RECh. 15 - Prob. 117RECh. 15 - Prob. 118RECh. 15 - Prob. 119RECh. 15 - Prob. 120RECh. 15 - Prob. 121RECh. 15 - Prob. 122RECh. 15 - Prob. 123RECh. 15 - Prob. 124RECh. 15 - Prob. 125RECh. 15 - Prob. 126RECh. 15 - Prob. 127RECh. 15 - Prob. 128RECh. 15 - Prob. 129RECh. 15 - Prob. 130RECh. 15 - Prob. 131RECh. 15 - Prob. 132RECh. 15 - Prob. 133RECh. 15 - Prob. 134RECh. 15 - Prob. 135RECh. 15 - Prob. 136RECh. 15 - Prob. 137RECh. 15 - Prob. 138RECh. 15 - Prob. 139RECh. 15 - Prob. 140RECh. 15 - Prob. 141RECh. 15 - Prob. 142RECh. 15 - Prob. 143RECh. 15 - Prob. 144RECh. 15 - Prob. 145RECh. 15 - Prob. 146RECh. 15 - Prob. 147RECh. 15 - Prob. 148RECh. 15 - Prob. 149RECh. 15 - Prob. 150RECh. 15 - Prob. 151RECh. 15 - Prob. 152RECh. 15 - Prob. 153RECh. 15 - Prob. 154RECh. 15 - Prob. 155RECh. 15 - Prob. 156RECh. 15 - Prob. 157RECh. 15 - Prob. 158RECh. 15 - Prob. 159RECh. 15 - Prob. 160RECh. 15 - Prob. 161RECh. 15 - Prob. 162RECh. 15 - Prob. 163RECh. 15 - Prob. 164RECh. 15 - Prob. 165RECh. 15 - Prob. 166RECh. 15 - Prob. 167RECh. 15 - Prob. 168RECh. 15 - Prob. 169RECh. 15 - Prob. 170RECh. 15 - Prob. 171RECh. 15 - Prob. 172RECh. 15 - Prob. 173RECh. 15 - Prob. 174RECh. 15 - Prob. 175RECh. 15 - Prob. 176RECh. 15 - Prob. 177RECh. 15 - Prob. 178RECh. 15 - Prob. 179RECh. 15 - Prob. 180RECh. 15 - Prob. 181RECh. 15 - Prob. 182RECh. 15 - Solve each inequality and graph the solution on a...Ch. 15 - Prob. 184RECh. 15 - Solve each inequality and graph the solution on a...Ch. 15 - Prob. 186RECh. 15 - Prob. 187RECh. 15 - Prob. 188RECh. 15 - Prob. 189RECh. 15 - Prob. 190RECh. 15 - Prob. 191RECh. 15 - Prob. 192RECh. 15 - Prob. 193RECh. 15 - Prob. 194RECh. 15 - Prob. 195RECh. 15 - Prob. 196RECh. 15 - Prob. 197RECh. 15 - Prob. 198RECh. 15 - Prob. 199RECh. 15 - Prob. 200RECh. 15 - Prob. 201RECh. 15 - Prob. 202RECh. 15 - Prob. 203RECh. 15 - Prob. 204RECh. 15 - Prob. 205RECh. 15 - Prob. 206RECh. 15 - Prob. 207RECh. 15 - Prob. 208RECh. 15 - Solve each equation containing an absolute...Ch. 15 - Prob. 210RECh. 15 - Prob. 211RECh. 15 - Prob. 212RECh. 15 - Prob. 213RECh. 15 - Prob. 214RECh. 15 - Prob. 215RECh. 15 - Prob. 216RECh. 15 - Prob. 217RECh. 15 - Prob. 218RECh. 15 - Prob. 219RECh. 15 - Prob. 1CACh. 15 - Prob. 2CACh. 15 - Prob. 3CACh. 15 - Prob. 4CACh. 15 - Prob. 5CACh. 15 - Prob. 6CACh. 15 - Prob. 7CACh. 15 - Prob. 8CACh. 15 - Prob. 9CACh. 15 - Prob. 10CACh. 15 - Prob. 11CACh. 15 - Prob. 12CACh. 15 - Prob. 13CACh. 15 - Prob. 14CACh. 15 - Prob. 1PTCh. 15 - Prob. 2PTCh. 15 - Prob. 3PTCh. 15 - Prob. 4PTCh. 15 - Prob. 5PTCh. 15 - Prob. 6PTCh. 15 - Prob. 7PTCh. 15 - Prob. 8PTCh. 15 - Prob. 9PTCh. 15 - Prob. 10PTCh. 15 - Prob. 11PTCh. 15 - Prob. 12PTCh. 15 - Prob. 13PTCh. 15 - Prob. 14PTCh. 15 - Prob. 15PTCh. 15 - Prob. 16PTCh. 15 - Prob. 17PTCh. 15 - Prob. 18PTCh. 15 - Prob. 19PTCh. 15 - Prob. 20PTCh. 15 - Prob. 21PTCh. 15 - Prob. 22PTCh. 15 - Prob. 23PTCh. 15 - Prob. 24PTCh. 15 - Prob. 25PTCh. 15 - Prob. 26PTCh. 15 - Prob. 27PTCh. 15 - Prob. 28PTCh. 15 - Prob. 29PTCh. 15 - Prob. 30PTCh. 15 - Prob. 31PTCh. 15 - Prob. 35PTCh. 15 - Prob. 36PTCh. 15 - Prob. 37PTCh. 15 - Prob. 38PTCh. 15 - Prob. 39PTCh. 15 - Prob. 40PTCh. 15 - Prob. 41PTCh. 15 - Prob. 42PTCh. 15 - Prob. 43PTCh. 15 - Prob. 1CPTCh. 15 - Prob. 2CPTCh. 15 - Prob. 3CPTCh. 15 - Prob. 4CPTCh. 15 - Prob. 5CPTCh. 15 - Prob. 6CPTCh. 15 - Prob. 7CPTCh. 15 - Prob. 8CPTCh. 15 - Prob. 9CPTCh. 15 - Prob. 10CPTCh. 15 - Prob. 11CPTCh. 15 - Prob. 12CPTCh. 15 - Prob. 13CPTCh. 15 - Prob. 14CPTCh. 15 - Prob. 15CPTCh. 15 - Prob. 16CPTCh. 15 - Prob. 17CPTCh. 15 - Prob. 18CPTCh. 15 - Prob. 19CPTCh. 15 - Prob. 20CPTCh. 15 - Prob. 21CPTCh. 15 - Prob. 22CPTCh. 15 - Prob. 23CPTCh. 15 - Prob. 24CPTCh. 15 - Prob. 25CPTCh. 15 - Prob. 26CPTCh. 15 - Prob. 27CPTCh. 15 - Prob. 28CPTCh. 15 - Prob. 29CPTCh. 15 - Prob. 30CPTCh. 15 - Prob. 31CPTCh. 15 - Prob. 32CPTCh. 15 - Prob. 33CPT
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