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Math Math in Our World

The number congruent to 27 in the modular system 5.

The number congruent to 27 in the modular system 5.

Solution Summary: The author explains that the number congruent to 27 in the modular system 5 is 2.

Math in Our World

Math in Our World

3rd Edition

ISBN: 9780073519678

Author: David Sobecki Professor, Allan G. Bluman

Publisher: McGraw-Hill Education

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Question

Chapter 15.3, Problem 1TTO

(a)

To determine

To find: The number congruent to 27 in the modular system 5.

(b)

To determine

To find: The number congruent to 13 in the modular system 3.

(c)

To determine

To find: The number congruent to 50 in the modular system 8.

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Chapter 15.2, Problem 121E

Chapter 15.3, Problem 2TTO

Chapter 15 Solutions

Math in Our World

Ch. 15.1 - Use Table 15-1 to find the result of each...Ch. 15.1 - Which properties does the following system...Ch. 15.1 - Prob. 3TTO Ch. 15.1 - Prob. 4TTO Ch. 15.1 - Prob. 1E Ch. 15.1 - Prob. 2E Ch. 15.1 - Prob. 3E Ch. 15.1 - Prob. 4E Ch. 15.1 - Prob. 5E Ch. 15.1 - Prob. 6E

Ch. 15.1 - Prob. 7E Ch. 15.1 - Prob. 8E Ch. 15.1 - Prob. 9E Ch. 15.1 - Prob. 10E Ch. 15.1 - Prob. 11E Ch. 15.1 - Prob. 12E Ch. 15.1 - For Exercises 724, use the elements C, D, E, and...Ch. 15.1 - For Exercises 724, use the elements C, D, E, and...Ch. 15.1 - For Exercises 724, use the elements C, D, E, and...Ch. 15.1 - For Exercises 724, use the elements C, D, E, and...Ch. 15.1 - For Exercises 724, use the elements C, D, E, and...Ch. 15.1 - For Exercises 724, use the elements C, D, E, and...Ch. 15.1 - Prob. 19E Ch. 15.1 - Prob. 20E Ch. 15.1 - For Exercises 724, use the elements C, D, E, and...Ch. 15.1 - Prob. 22E Ch. 15.1 - Prob. 23E Ch. 15.1 - Prob. 24E Ch. 15.1 - Prob. 25E Ch. 15.1 - Prob. 26E Ch. 15.1 - Prob. 27E Ch. 15.1 - Prob. 28E Ch. 15.1 - Prob. 29E Ch. 15.1 - For Exercises 2540, use the elements and the...Ch. 15.1 - Prob. 31E Ch. 15.1 - Prob. 32E Ch. 15.1 - For Exercises 2540, use the elements and the...Ch. 15.1 - For Exercises 2540, use the elements and the...Ch. 15.1 - For Exercises 2540, use the elements and the...Ch. 15.1 - Prob. 36E Ch. 15.1 - Prob. 37E Ch. 15.1 - Prob. 38E Ch. 15.1 - For Exercises 2540, use the elements and the...Ch. 15.1 - Prob. 40E Ch. 15.1 - Prob. 41E Ch. 15.1 - Prob. 42E Ch. 15.1 - Prob. 43E Ch. 15.1 - Prob. 44E Ch. 15.1 - Prob. 45E Ch. 15.1 - Prob. 46E Ch. 15.1 - Prob. 47E Ch. 15.1 - For Exercises 4150, determine which properties the...Ch. 15.1 - Prob. 49E Ch. 15.1 - Prob. 50E Ch. 15.1 - Prob. 51E Ch. 15.1 - Prob. 52E Ch. 15.1 - Prob. 53E Ch. 15.1 - Prob. 54E Ch. 15.1 - Prob. 55E Ch. 15.1 - Prob. 56E Ch. 15.1 - For exercises 5160, determine whether the given...Ch. 15.1 - Prob. 58E Ch. 15.1 - For exercises 5160, determine whether the given...Ch. 15.1 - Prob. 60E Ch. 15.1 - Exercises 6166 use the mathematical system...Ch. 15.1 - Prob. 62E Ch. 15.1 - Prob. 63E Ch. 15.1 - Prob. 64E Ch. 15.1 - Prob. 65E Ch. 15.1 - Prob. 66E Ch. 15.1 - Prob. 67E Ch. 15.1 - Prob. 68E Ch. 15.1 - Prob. 69E Ch. 15.1 - Prob. 70E Ch. 15.1 - Prob. 71E Ch. 15.1 - Prob. 72E Ch. 15.1 - Prob. 73E Ch. 15.1 - Prob. 74E Ch. 15.1 - Prob. 75E Ch. 15.1 - Prob. 76E Ch. 15.1 - Prob. 77E Ch. 15.1 - Prob. 78E Ch. 15.1 - Prob. 79E Ch. 15.1 - Prob. 80E Ch. 15.1 - Prob. 81E Ch. 15.1 - Prob. 82E Ch. 15.1 - Exercises 8184 are based on the classic game of...Ch. 15.1 - Exercises 8184 are based on the classic game of...Ch. 15.1 - Suppose that a mathematical system consists of the...Ch. 15.2 - Using the 12-hour clock, find these sums. (a)3+12...Ch. 15.2 - Prob. 2TTO Ch. 15.2 - Prob. 3TTO Ch. 15.2 - Prob. 4TTO Ch. 15.2 - Prob. 1E Ch. 15.2 - Prob. 2E Ch. 15.2 - Prob. 3E Ch. 15.2 - Prob. 4E Ch. 15.2 - Prob. 5E Ch. 15.2 - Prob. 6E Ch. 15.2 - Prob. 7E Ch. 15.2 - Prob. 8E Ch. 15.2 - Prob. 9E Ch. 15.2 - Prob. 10E Ch. 15.2 - Prob. 11E Ch. 15.2 - Prob. 12E Ch. 15.2 - Prob. 13E Ch. 15.2 - Prob. 14E Ch. 15.2 - Prob. 15E Ch. 15.2 - Prob. 16E Ch. 15.2 - For Exercises 920, find the equivalent number on...Ch. 15.2 - For Exercises 920, find the equivalent number on...Ch. 15.2 - Prob. 19E Ch. 15.2 - Prob. 20E Ch. 15.2 - For Exercises 2130, perform the additions on the...Ch. 15.2 - Prob. 22E Ch. 15.2 - For Exercises 2130, perform the additions on the...Ch. 15.2 - Prob. 24E Ch. 15.2 - For Exercises 2130, perform the additions on the...Ch. 15.2 - Prob. 26E Ch. 15.2 - For Exercises 2130, perform the additions on the...Ch. 15.2 - Prob. 28E Ch. 15.2 - For Exercises 2130, perform the additions on the...Ch. 15.2 - Prob. 30E Ch. 15.2 - For Exercises 3140, perform the subtractions on...Ch. 15.2 - Prob. 32E Ch. 15.2 - For Exercises 3140, perform the subtractions on...Ch. 15.2 - Prob. 34E Ch. 15.2 - For Exercises 3140, perform the subtractions on...Ch. 15.2 - Prob. 36E Ch. 15.2 - For Exercises 3140, perform the subtractions on...Ch. 15.2 - Prob. 38E Ch. 15.2 - For Exercises 3140, perform the subtractions on...Ch. 15.2 - Prob. 40E Ch. 15.2 - For Exercises 4150, perform the multiplications on...Ch. 15.2 - Prob. 42E Ch. 15.2 - For Exercises 4150, perform the multiplications on...Ch. 15.2 - Prob. 44E Ch. 15.2 - For Exercises 4150, perform the multiplications on...Ch. 15.2 - Prob. 46E Ch. 15.2 - For Exercises 4150, perform the multiplications on...Ch. 15.2 - Prob. 48E Ch. 15.2 - For Exercises 4150, perform the multiplications on...Ch. 15.2 - Prob. 50E Ch. 15.2 - In Exercises 5162, perform the indicated operation...Ch. 15.2 - Prob. 52E Ch. 15.2 - In Exercises 5162, perform the indicated operation...Ch. 15.2 - Prob. 54E Ch. 15.2 - In Exercises 5162, perform the indicated operation...Ch. 15.2 - Prob. 56E Ch. 15.2 - Prob. 57E Ch. 15.2 - Prob. 58E Ch. 15.2 - Prob. 59E Ch. 15.2 - Prob. 60E Ch. 15.2 - In Exercises 5162, perform the indicated operation...Ch. 15.2 - Prob. 62E Ch. 15.2 - For Exercises 6370, find the additive inverse for...Ch. 15.2 - Prob. 64E Ch. 15.2 - Prob. 65E Ch. 15.2 - Prob. 66E Ch. 15.2 - Prob. 67E Ch. 15.2 - For Exercises 6370, find the additive inverse for...Ch. 15.2 - Prob. 69E Ch. 15.2 - For Exercises 6370, find the additive inverse for...Ch. 15.2 - For Exercises 7176, find the multiplicative...Ch. 15.2 - Prob. 72E Ch. 15.2 - For Exercises 7176, find the multiplicative...Ch. 15.2 - Prob. 74E Ch. 15.2 - Prob. 75E Ch. 15.2 - Prob. 76E Ch. 15.2 - Prob. 77E Ch. 15.2 - Prob. 78E Ch. 15.2 - Prob. 79E Ch. 15.2 - Prob. 80E Ch. 15.2 - Prob. 81E Ch. 15.2 - Prob. 82E Ch. 15.2 - Prob. 83E Ch. 15.2 - Prob. 84E Ch. 15.2 - Prob. 85E Ch. 15.2 - Prob. 86E Ch. 15.2 - Prob. 87E Ch. 15.2 - Prob. 88E Ch. 15.2 - For Exercises 8190, find the value of y using the...Ch. 15.2 - Prob. 90E Ch. 15.2 - Prob. 91E Ch. 15.2 - Prob. 92E Ch. 15.2 - Prob. 93E Ch. 15.2 - Prob. 94E Ch. 15.2 - Prob. 95E Ch. 15.2 - Prob. 96E Ch. 15.2 - Prob. 97E Ch. 15.2 - Prob. 98E Ch. 15.2 - Prob. 99E Ch. 15.2 - Prob. 100E Ch. 15.2 - Prob. 101E Ch. 15.2 - Prob. 102E Ch. 15.2 - Prob. 103E Ch. 15.2 - Prob. 104E Ch. 15.2 - Prob. 105E Ch. 15.2 - Prob. 106E Ch. 15.2 - Prob. 107E Ch. 15.2 - Prob. 108E Ch. 15.2 - Prob. 109E Ch. 15.2 - Prob. 110E Ch. 15.2 - Prob. 111E Ch. 15.2 - Prob. 112E Ch. 15.2 - Prob. 113E Ch. 15.2 - Prob. 114E Ch. 15.2 - Prob. 115E Ch. 15.2 - Prob. 116E Ch. 15.2 - Prob. 117E Ch. 15.2 - Prob. 118E Ch. 15.2 - Prob. 119E Ch. 15.2 - Prob. 120E Ch. 15.2 - Prob. 121E Ch. 15.3 - Prob. 1TTO Ch. 15.3 - Prob. 2TTO Ch. 15.3 - Prob. 3TTO Ch. 15.3 - Prob. 4TTO Ch. 15.3 - Prob. 5TTO Ch. 15.3 - Find all natural number solutions to 4x 24 mod 8.Ch. 15.3 - Prob. 1E Ch. 15.3 - Prob. 2E Ch. 15.3 - Prob. 3E Ch. 15.3 - Prob. 4E Ch. 15.3 - Prob. 5E Ch. 15.3 - Prob. 6E Ch. 15.3 - Prob. 7E Ch. 15.3 - Prob. 8E Ch. 15.3 - Prob. 9E Ch. 15.3 - Prob. 10E Ch. 15.3 - For Exercises 516, find the values of each number...Ch. 15.3 - For Exercises 516, find the values of each number...Ch. 15.3 - Prob. 13E Ch. 15.3 - Prob. 14E Ch. 15.3 - Prob. 15E Ch. 15.3 - Prob. 16E Ch. 15.3 - Prob. 17E Ch. 15.3 - Prob. 18E Ch. 15.3 - Prob. 19E Ch. 15.3 - Prob. 20E Ch. 15.3 - Prob. 21E Ch. 15.3 - For Exercises 1746, perform the following...Ch. 15.3 - Prob. 23E Ch. 15.3 - Prob. 24E Ch. 15.3 - Prob. 25E Ch. 15.3 - Prob. 26E Ch. 15.3 - Prob. 27E Ch. 15.3 - Prob. 28E Ch. 15.3 - Prob. 29E Ch. 15.3 - Prob. 30E Ch. 15.3 - Prob. 31E Ch. 15.3 - Prob. 32E Ch. 15.3 - Prob. 33E Ch. 15.3 - Prob. 34E Ch. 15.3 - For Exercises 1746, perform the following...Ch. 15.3 - Prob. 36E Ch. 15.3 - Prob. 37E Ch. 15.3 - For Exercises 1746, perform the following...Ch. 15.3 - Prob. 39E Ch. 15.3 - Prob. 40E Ch. 15.3 - Prob. 41E Ch. 15.3 - Prob. 42E Ch. 15.3 - Prob. 43E Ch. 15.3 - Prob. 44E Ch. 15.3 - Prob. 45E Ch. 15.3 - Prob. 46E Ch. 15.3 - Prob. 47E Ch. 15.3 - Prob. 48E Ch. 15.3 - Prob. 49E Ch. 15.3 - Prob. 50E Ch. 15.3 - Prob. 51E Ch. 15.3 - Prob. 52E Ch. 15.3 - Prob. 53E Ch. 15.3 - For Exercises 4754, find all natural number...Ch. 15.3 - Prob. 55E Ch. 15.3 - Prob. 56E Ch. 15.3 - Prob. 57E Ch. 15.3 - Prob. 58E Ch. 15.3 - Prob. 59E Ch. 15.3 - Prob. 60E Ch. 15.3 - Prob. 61E Ch. 15.3 - Prob. 62E Ch. 15.3 - Prob. 63E Ch. 15.3 - Prob. 64E Ch. 15.3 - Prob. 65E Ch. 15.3 - Prob. 66E Ch. 15.3 - Prob. 67E Ch. 15.3 - Prob. 68E Ch. 15.3 - Prob. 69E Ch. 15.3 - Prob. 70E Ch. 15.3 - Prob. 71E Ch. 15.3 - Prob. 72E Ch. 15.3 - Prob. 73E Ch. 15.3 - Prob. 74E Ch. 15.3 - Prob. 75E Ch. 15.3 - Prob. 76E Ch. 15.3 - Prob. 77E Ch. 15.3 - Prob. 78E Ch. 15.3 - Prob. 79E Ch. 15.3 - Prob. 80E Ch. 15.3 - Prob. 81E Ch. 15.3 - Write a congruence that solves each conversion...Ch. 15.3 - Prob. 83E Ch. 15.3 - Prob. 85E Ch. 15.3 - Prob. 86E Ch. 15.3 - Prob. 87E Ch. 15.3 - Prob. 88E Ch. 15.3 - Prob. 89E Ch. 15.3 - Consider the congruence x2 4 mod 5. (a)Check that...Ch. 15.3 - Prob. 91E Ch. 15.3 - For each congruence, find all possible values for...Ch. 15 - For Exercises 111, use the elements A, B, C and...Ch. 15 - Prob. 2RE Ch. 15 - For Exercises 111, use the elements A, B, C and...Ch. 15 - Prob. 4RE Ch. 15 - Prob. 5RE Ch. 15 - Prob. 6RE Ch. 15 - Prob. 7RE Ch. 15 - Prob. 8RE Ch. 15 - Prob. 9RE Ch. 15 - Prob. 10RE Ch. 15 - Prob. 11RE Ch. 15 - Prob. 12RE Ch. 15 - For Exercises 1216, determine if the given system...Ch. 15 - Prob. 14RE Ch. 15 - Prob. 15RE Ch. 15 - Prob. 16RE Ch. 15 - Prob. 17RE Ch. 15 - Prob. 18RE Ch. 15 - Prob. 19RE Ch. 15 - Prob. 20RE Ch. 15 - Prob. 21RE Ch. 15 - Prob. 22RE Ch. 15 - For Exercises 2328, perform the indicated...Ch. 15 - Prob. 24RE Ch. 15 - Prob. 25RE Ch. 15 - Prob. 26RE Ch. 15 - Prob. 27RE Ch. 15 - Prob. 28RE Ch. 15 - Prob. 29RE Ch. 15 - Prob. 30RE Ch. 15 - Prob. 31RE Ch. 15 - Prob. 32RE Ch. 15 - Prob. 33RE Ch. 15 - Prob. 34RE Ch. 15 - For Exercises 3142, find the equivalent number for...Ch. 15 - Prob. 36RE Ch. 15 - Prob. 37RE Ch. 15 - Prob. 38RE Ch. 15 - Prob. 39RE Ch. 15 - Prob. 40RE Ch. 15 - Prob. 41RE Ch. 15 - Prob. 42RE Ch. 15 - Prob. 43RE Ch. 15 - Prob. 44RE Ch. 15 - Prob. 45RE Ch. 15 - Prob. 46RE Ch. 15 - Prob. 47RE Ch. 15 - Prob. 48RE Ch. 15 - Prob. 49RE Ch. 15 - Prob. 50RE Ch. 15 - Prob. 51RE Ch. 15 - Prob. 52RE Ch. 15 - Prob. 53RE Ch. 15 - Prob. 54RE Ch. 15 - Prob. 55RE Ch. 15 - Prob. 56RE Ch. 15 - Prob. 57RE Ch. 15 - Prob. 58RE Ch. 15 - Prob. 59RE Ch. 15 - Prob. 60RE Ch. 15 - Prob. 61RE Ch. 15 - Prob. 62RE Ch. 15 - Prob. 63RE Ch. 15 - Prob. 64RE Ch. 15 - Prob. 65RE Ch. 15 - Prob. 66RE Ch. 15 - Prob. 1CT Ch. 15 - Prob. 2CT Ch. 15 - Prob. 3CT Ch. 15 - Prob. 4CT Ch. 15 - Prob. 5CT Ch. 15 - Prob. 6CT Ch. 15 - Prob. 7CT Ch. 15 - Prob. 8CT Ch. 15 - Prob. 9CT Ch. 15 - Prob. 10CT Ch. 15 - Prob. 11CT Ch. 15 - Prob. 12CT Ch. 15 - Prob. 13CT Ch. 15 - Prob. 14CT Ch. 15 - Prob. 15CT Ch. 15 - Prob. 16CT Ch. 15 - Prob. 17CT Ch. 15 - Prob. 18CT Ch. 15 - Prob. 19CT Ch. 15 - Prob. 20CT Ch. 15 - Prob. 21CT Ch. 15 - Prob. 22CT Ch. 15 - Prob. 23CT Ch. 15 - Prob. 24CT Ch. 15 - An entire baseball league is signed up for an...Ch. 15 - Prob. 26CT

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Suppose that the check digit is computed as described in Example . Prove that transposition errors of adjacent digits will not be detected unless one of the digits is the check digit. Example Using Check Digits Many companies use check digits for security purposes or for error detection. For example, an the digit may be appended to a -bit identification number to obtain the -digit invoice number of the form where the th bit, , is the check digit, computed as . If congruence modulo is used, then the check digit for an identification number . Thus the complete correct invoice number would appear as . If the invoice number were used instead and checked, an error would be detected, since .

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