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mathematics
survey of mathematics

Questions and Answers of Survey of Mathematics

Insert either > or < in the shaded area between the paired numbers to make the statement correct.(a) -5 ■ -8(b) -5 ■ 8(c) -5 ■ -1(d) -5 ■ -1
Write the first five terms of the arithmetic sequence with the first term, a1, and common difference, d.a1 = 7, d = 6
Fill in the blanks with an appropriate word, phrase, or symbol(s).The smallest natural number that is divisible (without remainder) by each number in a set of numbers is known as the least common
Fill in the blanks with an appropriate word, phrase, or symbol(s).The number 1/3 can be represented as a(n) ___________ decimal number.
Fill in the blanks with an appropriate word, phrase, or symbol(s).When the denominator of a fraction contains no radical expressions, it is said to be _________.
From 1912 to 1971, the Milwaukee Road Railroad Company had a train stop every 15 days in Dubuque, Iowa. During this same period, the same train also stopped in Des Moines, Iowa, every 9 days. If on
Evaluate the expression. Assume x ≠ 0.(a) 32 • 33(b) (-3)2 • (-3)3
Determine whether the sequence is a Fibonacci-type sequence (each term is the sum of the two preceding terms). If it is, determine the next two terms of the sequence.2, 4, 6, 10, 16, 26, . . .
Fill in the blanks with an appropriate word, phrase, or symbol(s).The equation (5 • 6) • 7 = 2 • 3 + 2 • 4 demonstrates the _________ property of multiplication.
Write the first five terms of the arithmetic sequence with the first term, a1, and common difference, d.a1 = 9, d = 7
Fill in the blanks with an appropriate word, phrase, or symbol(s).Prime numbers of the form 2n - 1,where n is a prime number, are known as _________ prime numbers.
Fill in the blanks with an appropriate word, phrase, or symbol(s).In the decimal number 0.285714, the 2 is in the ___________ position.
Fill in the blanks with an appropriate word, phrase, or symbol(s).Consider the irrational number the square root of two.(a) We use the symbol √2 to represent the _________ value of the number.(b)
Evaluate the expression. Assume x ≠ 0.(a) 23 • 2(b) (-2)3 • (-2)
Determine whether the sequence is a Fibonacci-type sequence (each term is the sum of the two preceding terms). If it is, determine the next two terms of the sequence. 3, 5, 8, 13, 21, 34, . . .
Fill in the blanks with an appropriate word, phrase, or symbol(s).The equation 2 • (3 + 4) =2 • 3 + 2 • 4 demonstrates the _________ property of multiplication over addition.
Evaluate the expression using the order of operations:7/20 - 12/25 ÷ 9/10.
Write the first five terms of the arithmetic sequence with the first term, a1, and common difference, d.a1 = 25, d = -5
Fill in the blanks with an appropriate word, phrase, or symbol(s).A hypothesis that has not been proved or disproved is known as a(n) _________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).In the decimal number 0.285714, the 7 is in the ___________ position.
Evaluate the expression. Assume x ≠ 0.(a) 57/55(b) (-5)7/(-5)5
Fill in the blanks with an appropriate word, phrase, or symbol(s).Goldbach’s conjecture states that every even number greater than or equal to 4 can be written as the sum of two (not necessarily)
Write the first five terms of the arithmetic sequence with the first term, a1, and common difference, d.a1 = -11, d = 5
Fill in the blanks with an appropriate word, phrase, or symbol(s).The rational numbers 1/2 and 5/10 are examples of ___________ fractions.
Determine whether the number is rational or irrational.5/8
Evaluate the expression. Assume x ≠ 0.(a) 45/42 (b) (-4)5/(-4)2
Determine whether the sequence is a Fibonacci-type sequence (each term is the sum of the two preceding terms). If it is, determine the next two terms of the sequence. 2, 3, 6, 18, 108, 1944, . .
Write the first five terms of the arithmetic sequence with the first term, a1, and common difference, d.a1 = 5, d = -2
Determine whether the natural numbers are closed under the given operation.Multiplication
Determine whether the number is rational or irrational.√10
Use the sieve of Eratosthenes to find the prime numbers less than or equal to the given number.100
Evaluate the expression. Assume x ≠ 0.(a) 60(b) -60
Reduce each fraction to lowest terms.6/9
Determine whether the sequence is a Fibonacci-type sequence (each term is the sum of the two preceding terms). If it is, determine the next two terms of the sequence. -1, 1, 0, 1, 1, 2, . . .
Determine whether the natural numbers are closed under the given operation.Subtraction
Determine whether the integers are closed under the operation of multiplication. Explain your answer.
Determine whether the number is rational or irrational.π
Use the sieve of Eratosthenes to find the prime numbers less than or equal to the given number.150
Evaluate the expression. Assume x ≠ 0.(a) (-6)0(b) -(-6)0
Determine whether the sequence is a Fibonacci-type sequence (each term is the sum of the two preceding terms). If it is, determine the next two terms of the sequence. 0, π, π, 2π, 3π, 5π, .
Determine whether the natural numbers are closed under the given operation.Division
Evaluate the expression.5 + (-8)
Name the property illustrated: 3(x + 7) = 3x + 21.
Evaluate.45/42
Determine the indicated term for the arithmetic sequence with the first term, a1, and common difference, d.Determine a9 when a1 = 4, d = 5.
Determine whether the number is rational or irrational.3.575775777. . .
Determine whether the statement is true or false. Modify each false statement to make it a true statement.7 is a factor of 35.
Evaluate the expression. Assume x ≠ 0.(a) (6x)0(b) 6x0
Reduce each fraction to lowest terms.28/63
Determine whether the sequence is a Fibonacci-type sequence (each term is the sum of the two preceding terms). If it is, determine the next two terms of the sequence. 5, 10, 15, 25, 40, 65, . . .
Determine whether the integers are closed under the given operation.Multiplication
Evaluate the expression.-10 + 3
Evaluate.43 • 42
Determine the indicated term for the arithmetic sequence with the first term, a1, and common difference, d.Determine a10 when a1 = -, d = -3.
Determine whether the statement is true or false. Modify each false statement to make it a true statement.16 divides 2.
Evaluate the expression.8 • (-8)
Evaluate the expression. Assume x ≠ 0.(a) -6x0(b) (-6x)0
Reduce each fraction to lowest terms.36/56
Determine whether the sequence is a Fibonacci-type sequence (each term is the sum of the two preceding terms). If it is, determine the next two terms of the sequence. 1/4, 1/4, 1/2, 3/4, 2, . .
Determine whether the integers are closed under the given operation.Addition
Evaluate the expression.- 5 + (-5)
Evaluate.3-4
Determine the indicated term for the arithmetic sequence with the first term, a1, and common difference, d.Determine a11 when a1 = 20, d = 5.
Determine whether the number is rational or irrational.22/7
Determine whether the statement is true or false. Modify each false statement to make it a true statement.9 is a multiple of 81.
Evaluate the expression. Assume x ≠ 0.(a)3-3(b)7-2
Reduce each fraction to lowest terms.95/125
Determine whether the integers are closed under the given operation.Division
Evaluate the expression.6 + (-11) + 0
Write out the first 15 terms of the Fibonacci sequence.
Perform the operation by first converting the numerator and denominator to scientific notation. Write the answer in scientific notation.7,200,00/0.000009
Determine whether the number is rational or irrational.3.14159
Determine whether the statement is true or false. Modify each false statement to make it a true statement.36|9.
Evaluate the expression.-35/-7
Evaluate the expression. Assume x ≠ 0.(a) 5-1(b) 2-4
Reduce each fraction to lowest terms.13/221
Determine whether the integers are closed under the given operation.Subtraction
Evaluate the expression.2 + 5 + (-4)
(a) perform the indicated operation without the use of a calculator and express each answer in scientific notation.28,000/0.004
(a) perform the indicated operation without the use of a calculator and express each answer in scientific notation.5,600,000/80,000
Perform the indicated operation without the use of a calculator and express each answer in scientific notation.(50,000) (0.00011)
Perform the indicated operation without the use of a calculator and express each answer in scientific notation.(0.003) (0.00015)
Perform the indicated operation without the use of a calculator and express each answer in decimal notation.(5.2 x 10-7)/(4 x 10-9)
Perform the indicated operation without the use of a calculator and express each answer in decimal notation.(8.4 x 10-6)/(4 x 10-3)
Perform the indicated operation without the use of a calculator and express each answer in decimal notation. (2.7 x 103)/(9 x 10-2)
Perform the indicated operation without the use of a calculator and express each answer in decimal notation. (7.5 x 106)/(3 x 10-2)
Express the number in scientific notation.0.003
Express the number in scientific notation.0.00467
Evaluate the expression. Assume x ≠ 0.(a) (23)2(b) (32)3
Determine whether the rational numbers are closed under the given operation.Subtraction.
For any four consecutive Fibonacci numbers, the difference of the squares of the middle two numbers equals the product of the smallest and largest numbers. Select four consecutive Fibonacci numbers
Write an expression for the general or nth term, an, of the arithmetic sequence.2, 4, 6, 8, . . .
Determine whether the statement is true or false. Modify each false statement to make it a true statement.49 is a factor of 7.
Evaluate the expression using the order of operations.(64 ÷ 4 • 2) - (25 - 7 • 4)
Evaluate the expression. Assume x ≠ 0.(a) [(1/2)2]3(b) [(-1/2)2]3
Determine whether the rational numbers are closed under the given operation.Division
Twice any Fibonacci number minus the next Fibonacci number equals the second number preceding the original number. Select a number in the Fibonacci sequence and show that this pattern holds for the
(a) Select any two one-digit (nonzero) numbers and add them to obtain a third number. Continue adding the two previous terms to get a Fibonacci-type sequence.(b) Form ratios of successive terms to
Write an expression for the general or nth term, an, of the arithmetic sequence.1, 3, 5, 7, . . .
Determine whether the statement is true or false. Modify each false statement to make it a true statement.7|42

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