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mathematics
survey of mathematics

Questions and Answers of Survey of Mathematics

Evaluate the expression using the order of operations.-2(5 • 32 - 43 ÷ 8)2
Evaluate the expression. Assume x ≠ 0.(a) 43 • 4-2(b) 2-2 • 2-2
Determine whether the irrational numbers are closed under the given operation.Multiplication
(a) Select any three consecutive terms of a Fibonacci sequence. Subtract the product of the terms on each side of the middle term from the square of the middle term. What is the difference? (b)
Write an expression for the general or nth term, an, of the arithmetic sequence.3, 9, 15, 21, 27, . . .
Determine whether the statement is true or false. Modify each false statement to make it a true statement.8 is a divisor of 56.
Evaluate the expression. Assume x ≠ 0.(a) (-5)-2(-5)-2(b) (-1)-5 (-1)-5
Determine whether the irrational numbers are closed under the given operation.Addition
One of the most famous number patterns involves Pascal€™s triangle. The Fibonacci sequence can be found by using Pascal€™s triangle. Can you explain how that can be done? A hint
Write an expression for the general or nth term, an, of the arithmetic sequence.20, 14, 8, 2, -4, . . .
Evaluate the expression.-√36
Determine whether the statement is true or false. Modify each false statement to make it a true statement.If a number is not divisible by 5, then it is not divisible by 10.
Determine whether the irrational numbers are closed under the given operation.Division
Express the number in scientific notation.201,000
(a) A sequence related to the Fibonacci sequence is the Lucas sequence. The Lucas sequence is formed in a manner similar to the Fibonacci sequence. The first two numbers of the Lucas sequence are 1
Write an expression for the general or nth term, an, of the arithmetic sequence.-7, -2, 3, 8, . . .
Determine whether the statement is true or false. Modify each false statement to make it a true statement.If a number is not divisible by 10, then it is not divisible by 5.
Evaluate the expression.-√81
Determine whether the irrational numbers are closed under the given operation.Subtraction
Express the number in scientific notation.907,000,000
Determine the sum of the terms of the arithmetic sequence. The number of terms, n, is given.1, 2, 3, 4, . . . , 50; n = 50
Express the number in scientific notation.0.00275
Determine whether the statement is true or false. Modify each false statement to make it a true statement.If a number is divisible by 3 and 5, then the number is divisible by 15.
Evaluate the expression.-√225
Determine whether the real numbers are closed under the given operation.Multiplication
Express the number in scientific notation.0.000034
Determine the sum of the terms of the arithmetic sequence. The number of terms, n, is given.1, 3, 5, 7, . . ., 99; n = 50
Classify the number as a member of one or more of the following sets: the rational numbers, the integers, the natural numbers, the irrational numbers.0
Determine whether the number is divisible by each of the following numbers: 2, 3, 4, 5, 6, 8, 9, and 10.1155
Determine whether the real numbers are closed under the given operation.Subtraction
Express the number in scientific notation.0.56
Classify the number as a member of one or more of the following sets: the rational numbers, the integers, the natural numbers, the irrational numbers.-5
Determine the sum of the terms of the arithmetic sequence. The number of terms, n, is given.5, 9, 13, 17,p, 101; n = 25
Determine whether the number is divisible by each of the following numbers: 2, 3, 4, 5, 6, 8, 9, and 10.23,800
Determine whether the real numbers are closed under the given operation.Division
Express the number in scientific notation.19,000
The eleventh Fibonacci number is 89. Examine the first six digits in the decimal expression of its reciprocal, 1/89 .What do you find?
Determine the sum of the terms of the arithmetic sequence. The number of terms, n, is given.100, 90, 80, 70, . . ., -60; n = 17
Classify the number as a member of one or more of the following sets: the rational numbers, the integers, the natural numbers, the irrational numbers.√13
Determine whether the number is divisible by each of the following numbers: 2, 3, 4, 5, 6, 8, 9, and 10.72,216
Does (5 + x) + 6 = (x + 5) + 6 illustrate the commutative property or the associative property? Explain your answer
Express the number in scientific notation.1,260,000,000
Find the ratio of the second to the first term of the Fibonacci sequence. Then find the ratio of the third to the second term of the sequence and determine whether this ratio was an increase or
Determine the sum of the terms of the arithmetic sequence. The number of terms, n, is given.-4, -11, -18, -25, . . . , -193; n = 28
Classify the number as a member of one or more of the following sets: the rational numbers, the integers, the natural numbers, the irrational numbers.2√7
Determine whether the number is divisible by each of the following numbers: 2, 3, 4, 5, 6, 8, 9, and 10.170,820
Does (x +5) + 6 = x + (5 + 6) illustrate the commutative property or the associative property? Explain your answer.
Express the number in scientific notation.0.000186
Write the first five terms of the geometric sequence with the first term, a1, and common ratio, r.a1 = 3, r = 2
Classify the number as a member of one or more of the following sets: the rational numbers, the integers, the natural numbers, the irrational numbers.0.040040004
Determine whether the number is divisible by each of the following numbers: 2, 3, 4, 5, 6, 8, 9, and 10.1,882,320
Does the commutative property hold for the integers under the operation of subtraction? Give an example to support your answer.
Classify the number as a member of one or more of the following sets: the rational numbers, the integers, the natural numbers, the irrational numbers.2.718
Write the first five terms of the geometric sequence with the first term, a1, and common ratio, r.a1 = 2, r = 3
Determine whether the number is divisible by each of the following numbers: 2, 3, 4, 5, 6, 8, 9, and 10.3,941,221
Draw a line of length 5 in. Determine and mark the point on the line that will create the golden ratio. Explain how you determined your answer.
Does the commutative property hold for the rational numbers under the operation of division? Give an example to support your answer.
Express the number in decimal notation.1.6 x 103
Classify the number as a member of one or more of the following sets: the rational numbers, the integers, the natural numbers, the irrational numbers.0.1̅2̅3̅
Write the first five terms of the geometric sequence with the first term, a1, and common ratio, r.a1 = 5, r = 2
The divine proportion is (a + b)/a = a/b (see Fig. 5.13 ), which can be written 1 + (b/a) = a/b. Now let x = a/b,which gives 1 + (1/x) = x. Multiply both sides of this equation by x to get a
Determine a number that is divisible by 2, 3, 4, 5, and 6.
Give an example to show that the commutative property of addition may be true for the negative integers.
Express the number in decimal notation.5.3 x 104
Classify the number as a member of one or more of the following sets: the rational numbers, the integers, the natural numbers, the irrational numbers.0.123123123
Write the first five terms of the geometric sequence with the first term, a1, and common ratio, r.a1 = 8, r = 1/2
Give an example to show that the commutative property of multiplication may be true for the negative integers.
Express the number in decimal notation.1.32 x 10-2
Write the first five terms of the geometric sequence with the first term, a1, and common ratio, r.a1 = -3, r = -1
Give an example to show that the associative property of addition may be true for the negative integers.
Give an example to show that the associative property of multiplication may be true for the negative integers.
Express the number in decimal notation.4.04 x 10-3
Write the first five terms of the geometric sequence with the first term, a1, and common ratio, r.a1 = -6, r = -2
Express the number in decimal notation.8.62 x 10-5
Does the associative property hold for the integers under the operation of division? Give an example to support your answer.
Determine the indicated term for the geometric sequence with the first term, a1, and common ratio, r.Determine a5 when a1 = 7, r = 2.
Express the number in decimal notation.2.19 x 10-4
Does the associative property hold for the integers under the operation of subtraction? Give an example to support your answer.
Find the prime factorization of the number.315
Determine the indicated term for the geometric sequence with the first term, a1, and common ratio, r.Determine a8 when a1 = 3, r = 4.
Does the associative property hold for the real numbers under the operation of division? Give an example to support your answer.
Express the number in decimal notation.2.01 x 100
Simplify the radical.√54
Determine the indicated term for the geometric sequence with the first term, a1, and common ratio, r.Determine a7 when a1 = 64, r = 1/2.
Evaluate the expression.56/-8
Does a + (b • c) = (a + b) • (a + c)? Give an example to support your answer.
Express the number in decimal notation.4.6 x 101
Determine the indicated term for the geometric sequence with the first term, a1, and common ratio, r.Determine a8 when a1 = 1/2, r = -2.
Perform the indicated operation without the use of a calculator and express each answer in decimal notation. (2.4 x 103)(3 x 102)
State the name of the property illustrated.7(x + 5) = 7 • x + 7 • 5
Determine the indicated term for the geometric sequence with the first term, a1, and common ratio, r.Determine a7 when a1 = -5, r = 3.
Perform the indicated operation without the use of a calculator and express each answer in decimal notation. (3.8 x 102)(2 x 104)
State the name of the property illustrated.13 + 5 = 5 + 13
Determine the indicated term for the geometric sequence with the first term, a1, and common ratio, r.Determine a5 when a1 = -3, r = -3.
Evaluate the expression.186/-6
Perform the indicated operation without the use of a calculator and express each answer in decimal notation.(5.1 x 101)(3 x 10-4)
State the name of the property illustrated.(7 • 8) • 9 = 7 • (8 • 9)
Evaluate the expression.(a) 32(b) 23
Simplify the expression. Rationalize the denominator when necessary.√2 - 4√2
Perform the indicated operation without the use of a calculator and express each answer in decimal notation.(1.6 x 10-2)(4 x 10-3)

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