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mathematics
survey of mathematics

Questions and Answers of Survey of Mathematics

Fill in the blank with an appropriate word, phrase, or symbol(s).The set of all 2 x 3 matrices under the operation of matrix addition forms a commutative ________.
Fill in the blank with an appropriate word, phrase, or symbol(s).Multiplication of matrices is possible only when the number of _______ of the first matrix is the same as the number of _________ of
Fill in the blank with an appropriate word, phrase, or symbol(s).When multiplying a matrix by a real number, the real number is called a(n) _______.
Fill in the blank with an appropriate word, phrase, or symbol(s).To add or subtract two matrices, the matrices must have the same __________ .
Fill in the blank with an appropriate word, phrase, or symbol(s).The number of rows in a 4 x 3 matrix is ___________.
Fill in the blank with an appropriate word, phrase, or symbol(s).The number of columns in a 3 x 2 matrix is ___________ .
Fill in the blank with an appropriate word, phrase, or symbol(s).A matrix that contains the same number of rows and columns is called a(n) __________ matrix.
Fill in the blank with an appropriate word, phrase, or symbol(s).A rectangular array of real numbers, symbols, or expressions is called a(n) __________ .
The wheel shown is to be rolled. Before the wheel is rolled, it is resting on number 0. The wheel will be rolled at a uniform rate of one complete roll every 4 minutes. In exactly 1 year (not a leap
Read the Recreational Mathematics. Using the same coding circle and a code key of the letter e, decipher the following message.16 19 20 1 17
During a certain leap year, Josephine’s birthday is on Tuesday, May 18. What is the minimum number of years in which Josephine’s birthday will fall on a(a) Friday? (b) Saturday?
During a certain year, Clarence’s birth-day is on Monday, April 18.(a) If next year is not a leap year, on what day of the week will Clarence’s birthday fall next year?(b) If next year is a leap
Determine the smallest positive number divisible by 5 to which 2 is congruent in modulo 6.
Solve for x where k is any counting number.4k - 2 ≡ x (mod 4)
Solve for x where k is any counting number.7k + 1 ≡ x (mod 7)
Solve for x where k is any counting number.8k ≡ x (mod 8)
With what number or numbers, if any, can you replace the question marks to make the statement true? The question mark must be a positive number less than the modulus. (Use the fact that a/b = c (mod
With what number or numbers, if any, can you replace the question marks to make the statement true? The question mark must be a positive number less than the modulus. (Use the fact that a/b = c (mod
With what number or numbers, if any, can you replace the question marks to make the statement true? The question mark must be a positive number less than the modulus. (Use the fact that a/b = c (mod
With what number or numbers, if any, can you replace the question marks to make the statement true? The question mark must be a positive number less than the modulus. (Use the fact that a/b = c (mod
(a) Construct a modulo 7 multiplication table.(b) Is the system closed under the operation of multiplication?(c) Is there an identity element in the set? If so, what is it?(d) Does every element in
(a) Construct a modulo 4 multiplication table.(b) Is the system closed under the operation of multiplication?(c) Is there an identity element in the set? If so, what is it?(d) Does every element in
(a) Construct a modulo 8 addition table. (b) Is the system closed? Explain.(c) Is there an identity element in the set? If so, what is it?(d) Does every element in the set have an inverse? If
(a) Construct a modulo 3 addition table.(b) Is the system closed? Explain.(c) Is there an identity element in the set? If so, what is it?(d) Does every element in the set have an inverse? If so, list
A nurse’s work pattern at Community Hospital consists of working the 7 A.M. – 3 P.M. shift for 3 weeks and then the 3 P.M. –11 P.M. shift for 2 weeks.(a) If it is the third week of the pattern,
A waiter at a restaurant works both daytime and evening shifts. He works daytime for 5 consecutive days, then evenings for 3 consecutive days, then daytime for 4 consecutive days, then evenings for 2
A man has an Achilles’ tendon injury and is receiving physical therapy. He must have physical therapy twice a day for 5 days, physical therapy once a day for 3 days, and then 2 days off; then he
A manager of a theater has both Saturday and Sunday off every 7 weeks. It is week 2 of the 7 weeks.(a) Determine the number of weeks before he will have both Saturday and Sunday off.(b) Will he have
A pilot is scheduled to fly for 5 consecutive days and rest for 3 consecutive days. If today is the second day of her rest shift, determine whether she will be flying or resting.(a) 60 days from
Jahlil is a golf pro who works at two different golf courses. His schedule is to work at Longboat Key golf course for 4 days, then work at The Meadows golf course for 3 days, and then rest for 2
Wisconsin gubernatorial elections (elections for governor) have been held every four years starting in 1970. Each of these years is congruent to 2 in modulo 4. (a) List the first five Wisconsin
In the United States, presidential elections have been held every four years starting in 1788. Each of these years is congruent to 0 in modulo 4.(a) List the first five presidential election years
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.? - 3 ≡ 4 (mod 8)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.? - 8 ≡ 9 (mod 12)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.3 • ? ≡ 3 (mod 12)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.4 • ? ≡ 4 (mod 10)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.3 • ? ≡ 5 (mod 6)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.2 • ? ≡ 1 (mod 6)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.4 • ? ≡ 3 (mod 7)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.5 • ? ≡ 7 (mod 9)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.3 - ? ≡ 7 (mod 9)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.4 - ? ≡ 5 (mod 6)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.4 + ? ≡ 3 (mod 6)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.6 + ? ≡ 2 (mod 7)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.? + 3 ≡ 2 (mod 5)
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.? + 5 ≡ 3 (mod 6)
Find the modulo class to which each number belongs for the indicated modulo system.-39, mod 7
Find the modulo class to which each number belongs for the indicated modulo system.-27, mod 8
Find the modulo class to which each number belongs for the indicated modulo system.-7, mod 4
Find the modulo class to which each number belongs for the indicated modulo system.-1, mod 7
Find the modulo class to which each number belongs for the indicated modulo system.75, mod 8
Find the modulo class to which each number belongs for the indicated modulo system.41, mod 9
Find the modulo class to which each number belongs for the indicated modulo system.43, mod 6
Find the modulo class to which each number belongs for the indicated modulo system.60, mod 7
Find the modulo class to which each number belongs for the indicated modulo system.38, mod 9
Find the modulo class to which each number belongs for the indicated modulo system.17, mod 2
Determine what number the sum, difference, or product is congruent to in modulo 5.(4 - 9) • 7
Determine what number the sum, difference, or product is congruent to in modulo 5.(15 • 4) - 8
Determine what number the sum, difference, or product is congruent to in modulo 5.2 - 4
Determine what number the sum, difference, or product is congruent to in modulo 5.4 - 8
Determine what number the sum, difference, or product is congruent to in modulo 5.8 • 7
Determine what number the sum, difference, or product is congruent to in modulo 5.8 • 9
Determine what number the sum, difference, or product is congruent to in modulo 5.12 - 5
Determine what number the sum, difference, or product is congruent to in modulo 5.9 - 3
Determine what number the sum, difference, or product is congruent to in modulo 5.2 + 3
Determine what number the sum, difference, or product is congruent to in modulo 5.4 + 4
Consider the 12 months to be a modulo 12 system with January being month 0. If it is currently October, determine the month it will be in the specified number of months.5 years, 9 months.
Consider the 12 months to be a modulo 12 system with January being month 0. If it is currently October, determine the month it will be in the specified number of months.105 months.
Consider the 12 months to be a modulo 12 system with January being month 0. If it is currently October, determine the month it will be in the specified number of months.7 years.
Consider the 12 months to be a modulo 12 system with January being month 0. If it is currently October, determine the month it will be in the specified number of months.83 months.
Consider the 12 months to be a modulo 12 system with January being month 0. If it is currently October, determine the month it will be in the specified number of months.4 years, 8 months.
Consider the 12 months to be a modulo 12 system with January being month 0. If it is currently October, determine the month it will be in the specified number of months.2 years, 10 months.
Consider the 12 months to be a modulo 12 system with January being month 0. If it is currently October, determine the month it will be in the specified number of months.61 months.
Consider the 12 months to be a modulo 12 system with January being month 0. If it is currently October, determine the month it will be in the specified number of months.18 months.
Assume that Sunday is represented as day 0, Monday is represented as day 1, and so on. If today is Thursday (day 4), determine the day of the week it will be in the specified number of days. Assume
Assume that Sunday is represented as day 0, Monday is represented as day 1, and so on. If today is Thursday (day 4), determine the day of the week it will be in the specified number of days. Assume
Assume that Sunday is represented as day 0, Monday is represented as day 1, and so on. If today is Thursday (day 4), determine the day of the week it will be in the specified number of days. Assume
Assume that Sunday is represented as day 0, Monday is represented as day 1, and so on. If today is Thursday (day 4), determine the day of the week it will be in the specified number of days. Assume
Assume that Sunday is represented as day 0, Monday is represented as day 1, and so on. If today is Thursday (day 4), determine the day of the week it will be in the specified number of days. Assume
Assume that Sunday is represented as day 0, Monday is represented as day 1, and so on. If today is Thursday (day 4), determine the day of the week it will be in the specified number of days. Assume
Assume that Sunday is represented as day 0, Monday is represented as day 1, and so on. If today is Thursday (day 4), determine the day of the week it will be in the specified number of days. Assume
Fill in the blanks with an appropriate word, phrase, or symbol(s).If a and b have the same remainder when divided by m, we say that a is _________ to b modulo m.
Fill in the blanks with an appropriate word, phrase, or symbol(s).In a modulo m system, the number m is called the ____________ of the system.
Fill in the blanks with an appropriate word, phrase, or symbol(s).In any modulo m system, we can develop a set of modulo classes by dividing the numbers by m and placing all numbers with the same
Fill in the blanks with an appropriate word, phrase, or symbol(s).In a modulo m system, in addition to the m elements, there is also a(n) ________ operation.
Fill in the blanks with an appropriate word, phrase, or symbol(s).The elements in a modulo m system consist of the m numbers, 0 through _____________.
Do research on the 24-hour clock system (see the Did You Know?). Write a paper on its use throughout the world, including in the U.S. military and in medical facilities.
Consider the mathematical system with the single element {1} under the operation of multiplication.(a) Is this system closed? (b) Is there an identity element in the set? (c) Does 1 have an
Sup-pose that three books numbered 1, 2, and 3 are placed next to one another on a shelf. If we remove volume 3 and place it before volume 1, the new order of books is 3, 1, 2. Let’s call this
The tables shown below are examples of noncommutative, or nonabelian, groups. For each exercise, do the following.(a) Show that the system under the given operation is a group. (It would be very time
The tables shown below are examples of noncommutative, or nonabelian, groups. For each exercise, do the following.(a) Show that the system under the given operation is a group. (It would be very time
(a) Let E and O represent even numbers and odd numbers, respectively. Complete the table for the operation of multiplication.(b) Determine whether this mathematical system forms a commutative group
(a) Consider the set consisting of two elements {E, O}, where E stands for an even number and O stands for an odd number. For the operation of addition, complete the table.(b) Determine whether this
For the mathematical system given, determine which of the five properties of a commutative group do not hold. 2 3 4 3 4 5 2 4 2 4 3 3 3 3 2 5 4 3 2 4,
For the mathematical system given, determine which of the five properties of a commutative group do not hold. a b d e a d e a b b d a b e a b d d a b e d e b d a
For the mathematical system given, determine which of the five properties of a commutative group do not hold. b Д TT т TT IT Д .воч
For the mathematical system given, determine which of the five properties of a commutative group do not hold. P P ? P P
For the mathematical system given, determine which of the five properties of a commutative group do not hold. м (X) M M M
For the mathematical system given, determine which of the five properties of a commutative group do not hold. Ф Г Ф Г Д Ф Ф Г Г Г п еен
Consider the mathematical system defined by the following table.(a) Is the system closed? Explain. (b) Is there an identity element in the set? If so, what is it?(c) For each element in

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