# A Survey of Mathematics with Applications (10th Edition)

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Theory ; Number Theory is the study of numbers and... more

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Integer ; A number can be represented as a product... more

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0 ; The fact that a is divisible by b means that b... more

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Prime ; Natural numbers are classified as prime ... more

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Composite ; Natural numbers are classified as ... more

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Divisor ; If a natural number a is completely ... more

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Multiple ; If a natural number a is completely ... more

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Mersenne ; Marin Mersenne conjectured that the ... more

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Conjecture ; A hypothesis is formed on the basis ... more

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Prime ; Goldbach conjectured that the sum of two (... more

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; List all the natural numbers up to100. ; Cancel... more

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; List all the natural numbers up to 150. ; ... more

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The number 35 can be expressed as.7 is a factor of... more

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False; 2 divides 16. ; As , it cannot divide a ... more

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False; 81 is a multiple of 9. ; A multiple of a ... more

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False; ; The expression means that 36 divides 9.... more

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Write the number 54 as a product of its factors, ... more

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A multiple of a number is the product of that ... more

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False; 4 is a divisor of 32. ; As , the division ... more

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False; 7 is a factor of 49. ; As , it cannot be a ... more

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The expression means that 7 divides 42A natural ... more

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A natural number can be expressed as a product of ... more

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Based on the divisibility rule for 6, it can be ... more

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False; If a number is not divisible by 5, then it ... more

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The divisibility rule for 6 states that the ... more

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Based on the divisibility rule for 6, it can be ... more

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Divisible by 3 and 5. ; A number should be even if... more

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Divisible by 2, 4, 5, 8, and 10. ; A number should... more

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Divisible by 2, 3, 4, 6, 8 and 9. ; A number ... more

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Divisible by 2, 3, 4, 5, 6, 9, and 10. ; The ... more

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Divisible by 2, 3, 4, 5, 6, 8 and 10. ; A number ... more

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None ; A number should be even to be divisible by ... more

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60 ; A number divisible by each of the numbers 2, ... more

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180 ; A number divisible by each of the number 3, ... more

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; Perform prime factorization by division.Divide ... more

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; Perform prime factorization by division.Divide ... more

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; Perform prime factorization by division.Divide ... more

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; Perform prime factorization by division.Divide ... more

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; Perform prime factorization by division.Divide ... more

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; Perform prime factorization by division.Divide ... more

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; Perform prime factorization by division.Divide ... more

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; Perform prime factorization by division.Divide ... more

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; Perform prime factorization by division.Divide ... more

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; Perform prime factorization by division.Divide ... more

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48 ; The number of days when both jobs coincide is... more

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; List all the divisors of 120 as a set . ; As ... more

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78 ; In order to keep Toy B and Toy K in separate ... more

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35 ; In order to keep vehicle C of color R and ... more

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72 ; In order to keep cards B and cards F in ... more

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30 ; In order to keep C trees and P trees in ... more

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42,000 ; The number of miles to be driven before ... more

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30 ; The number of days after which person S and ... more

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225 ; The number of days after which both the jobs... more

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No, the pair will include a number divisible by 2... more

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17; 1929; 31 ; A prime number has only two factors... more

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3; 7; 31; 127; 8191 ; A Mersenne prime number is 1... more

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5; 17; 257Prime numbers ; The numbers of the form... more

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Entire Proof Answer:The Goldbach Conjecture states... more

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If a number is divisible by 2 and 7, the number is... more

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If a number is divisible by 2 and 11, the number ... more

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3 ; Begin by dividing and then ignore the quotient... more

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12 ; Begin by dividing and then ignore the ... more

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35 ; Begin by dividing and then ignore the ... more

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26 ; Begin by dividing and then ignore the ... more

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30 ; Begin by dividing and then ignore the ... more

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70 ; Begin by dividing and then ignore the ... more

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28 is a perfect number. ; A number is called ... more

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Not a perfect number ; A number is called perfect ... more

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Not a perfect number ; A number is called perfect ... more

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496 is a perfect number. ; A number is called ... more

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Not necessary. ; It is not necessary for the ... more

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In a set of three consecutive number, at least one... more

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The sum of the same digit added thrice will always... more

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Yes, 18 divides 54036, that is, . ; Let 54000 and ... more

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Entire Proof Answer:Use the expression.Substitute ... more

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Entire Proof Answer: Express the integers from 8 ... more

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GIMPSstand for Great Internet Mersenne Prime ... more

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Deficient number is a positive integer such that ... more

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Whole ; The whole numbers are the set of counting ... more

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Add ; Find the additive inverse of to subtract ... more

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is smallest among all as it is the farthest to ... more

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is smallest among all as it is the farthest to ... more

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is smallest among all as it is the farthest to ... more

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is smallest among all as it is the farthest to ... more

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2 ; Apply the identity . ; Simplify the expression... more

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; Apply the identity and simplify. ; more

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; Apply the identity in the given expression. ; ... more

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; Apply the identity to simplify. ; more

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; Apply the identity in the given expression and... more

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3 ; Apply the identity in the given expression ... more

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2 ; Apply the additive inverse identity to and ... more

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3 ; Apply the identity in the given expression ... more

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; Apply the identity in the given expression. ; ... more

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; Apply the identity in the given expression. ; ... more

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; Apply the identity in the given expression. ; ... more

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13 ; Apply the identity and remove the ... more

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; Apply the identity and remove the parenthesis ... more

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; Apply the identity in the given expression. ; ... more

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; Apply the identity in the given expression. ; ... more

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11 ; Apply the identity in the given expression ... more

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; The product will be a negative number as and ... more

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; The product will be a negative number as and ... more

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81 ; The product will be a positive number as ... more

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; The product will be a negative number as and ... more

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96 ; The product of will be a positive number as... more

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120 ; The product of will be a positive number as... more

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; The product of will be a positive number as 5 ... more

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; The product will be a positive number as and... more

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8 ; The division will be a positive number as ... more

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; The division will be a negative number as and... more

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; The division will be a negative number as 15 ... more

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; The division will be a negative number as and... more

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; The division will be a negative number as 56 ... more

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; The division will be a negative number as and... more

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; The division will be a negative number as and... more

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; The division will be a negative number as 186 ... more

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; Find the product of 8 and 2. It will be a ... more

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; Divide 25 by 5. The quotient will be a positive... more

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; Perform all the operations within the ... more

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12 ; Perform all the operations within the ... more

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; Simplify within the parentheses. ; Simplify the... more

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2 ; Simplify within the parentheses. ; Simplify ... more

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; Simplify within the parentheses. ; Perform ... more

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60 ; Simplify within the parentheses. ; Perform ... more

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1 ; Simplify within the parentheses. ; Simplify ... more

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2 ; Simplify within the parentheses. ; Simplify ... more

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1100 feet under the water ; Take the initial depth... more

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17,010 points ; Subtract 237 from 17042 as DJIA ... more

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14,777 feet ; Subtract from 14,495, which gives ... more

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; Subtract from 134 to calculate the difference ... more

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27 ; Subtract 10 from 23 and add 8 to determine ... more

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Whole numbers contain .Integers contain .Every ... more

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FalseEvery whole number is an integer. ; Whole ... more

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FalseThe difference of any two negative integers ... more

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The sum of any two negative integers is always a ... more

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The product of two positive integers is positive ... more

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FalseThe difference of a positive integer and a ... more

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The quotient of two numbers with opposite signs is... more

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FalseThe quotient of any two negative integers is ... more

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FalseThe sum of a positive integer and a negative ... more

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FalseThe product of a positive integer and a ... more

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The quotient of a nonzero number divided by is ... more

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Two numbers together make up a positive number as ... more

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; Simplify the given expression by grouping the ... more

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; Add 0 to 1 and subtract 2 from it. ; Add 3 and ... more

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Around 800 A.D, the evolution of Hindu-Arabic ... more

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Integers ; Rational numbers are the numbers which... more

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Numerator. ; When numbers are written in the form ... more

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Denominator ; When numbers are written in the form... more

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Mixed ; Rational numbers, greater than 1 or less ... more

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Improper ; Improper fraction is a fraction where ... more

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Terminating ; Terminating decimals are those ... more

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Repeating ; Repeating decimal numbers are those ... more

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tenths ; If a number has a decimal point, then the... more

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ten-thousandths ; If a number has a decimal point... more

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Equivalent ; A fraction, when reduced to its ... more

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; Write the prime factors of 6 and 9. ; The ... more

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; Write the prime factors of 20 and 25. ; The ... more

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; Write the prime factors of 28 and 63. ; The ... more

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; Write the prime factors of 36 and 56. ; The ... more

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; Write the prime factors of 95 and 125. ; The ... more

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; Write the prime factors of 13 and 221. ; The ... more

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; Multiply the denominator of the given mixed ... more

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; Multiply the denominator of the given mixed ... more

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; Ignore the negative sign of the given mixed ... more

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; Ignore the negative sign of the given mixed ... more

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; Neglect the negative sign of the given mixed ... more

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; Multiply the denominator term of the given ... more

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; The arrow is on the right by fraction of ... more

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; The arrow is to the right of the integer on ... more

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; The arrow is to the right of the integer on ... more

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; The arrow is to the right of the integer on ... more

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; Divide the numerator, which is , by the ... more

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; Divide the numerator, which is 39, by the ... more

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; Divide the numerator, which is 73, by the ... more

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; Divide the numerator, which is 157,by the ... more

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; Divide the numerator, which is 878, by the ... more

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; Divide the numerator, which is 1028, by the ... more

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; Divide 4 by 5 and determine the quotient and ... more

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; Divide 5 by 8 and determine the quotient and ... more

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; Divide 2 by 3 and determine the quotient and ... more

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; Divide by 6 and determine the quotient and the... more

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; Divide 3 by 8, and determine the quotient and ... more

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; Divide the numerator,23, by the denominator,7.... more

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; Divide 13 by 6, and determine the quotient and ... more

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; Divide 115 by 15, and determine the quotient ... more

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; Observe the last digit after the decimal.Since ... more

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; Observe the last digit after the decimal.Since ... more

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; Observe the last digit after the decimal.Since ... more

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; Observe the last digit after the decimal.Since ... more

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; Observe the last digit number.Since the last ... more

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; Observe the last digit after the decimal.Since ... more

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; Observe the last digit after the decimal.Since ... more

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; Observe the last digit after the decimal.Since ... more

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; Equate the given repeating decimal with a ... more

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; Equate the given repeating decimal with a ... more

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1 ; Equate the given repeating decimal with a ... more

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; Equate the given repeating decimal with a ... more

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; Equate the given repeating decimal with a ... more

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; Equate the given repeating decimal with a ... more

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; Equate the given repeating decimal with a ... more

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; Equate the given repeating decimal with a ... more

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; Apply the rule for multiplication of fractions... more

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; Apply the rule for multiplication of fractions... more

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; Apply the rule for multiplication of fractions... more

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; Apply the rule for division of fractions, . ; ... more

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; Apply the rule for division of fractions, . ; ... more

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1 ; Apply the rule for division of fractions, . ; ... more

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; Apply the rule for multiplication of fractions... more

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; Apply the rule for division of fractions, . ; ... more

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; Apply the rule of multiplication of fractions... more

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; Apply the rule of multiplication for fractions... more

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; The least common multiple of 5 and 3 is 15.... more

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; The least common multiple of 6 and 4 is 12.... more

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; The least common multiple of 11 and 22 is 22.... more

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; The least common multiple of 9 and 6 is 18.... more

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; The least common multiple of 14 and 21 is 42.... more

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; The least common multiple of 15 and 35 is 105.... more

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; The least common multiple of 12, 48, and 72 is ... more

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; The least common multiple of 5 and 15 is 15.... more

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; The least common multiple of 30 and 40 is 120.... more

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; The least common multiple of 25 and 100 is 100.... more

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; Apply the rule . ; Simplify the obtained ... more

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; Apply the rule . ; Simplify the obtained ... more

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; Apply the rule . ; Simplify the obtained ... more

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; Apply the rule . ; Simplify the obtained ... more

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; Since multiplication is performed before ... more

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; Since division is performed before addition,... more

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; Since division is performed before subtraction,... more

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; Since multiplication is performed before ... more

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; Since the division is performed before ... more

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; Since division is performed before ... more

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; Since multiplication is performed before ... more

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; Since multiplication is performed before ... more

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; Since parenthesis is performed before any order... more

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; Since parenthesis is performed before any order... more

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, in. ; Subtract height of Person D at the time ... more

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, ; Form an expression to get fraction of Thistle ... more

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, inches ; Form an expression to get the vertical ... more

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, , , ; Multiply cup of Ingredient SP by to get ... more

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; ; Subtract available length of pipe from total ... more

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; ; Add all the fractions given for the capacity ... more

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; Subtract all the fractions of given budget from... more

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cup. ; Multiply total number of students with ... more

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; in. ; Add all the given dimensions of the stand ... more

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; in. ; Equate the given dimension of the width ... more

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; Convert feet to inches.Use the fact that . ; ... more

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; Convert and into fractions. ; ; Calculate ... more

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; Convert and into fractions. ; ; Calculate ... more

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; Convert and into fractions. ; ; Calculate ... more

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; Convert and into fractions. ; ; Calculate ... more

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; Calculate the average of the given fractions to... more

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; Calculate the average of the given fractions to... more

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; Calculate the average of the given fractions to... more

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; Calculate the average of the given fractions to... more

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Ancient Greeks played a major role in the world of... more

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Irrational ; The definition states that irrational... more

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Radical ; Take an irrational number .In , the ... more

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Radicand ; In a radical expression, the symbol is... more

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Coefficient ; The number that is multiplied by ... more

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Itself ; The principal square root of a number is ... more

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Perfect ; Any number that is obtained by squaring ... more

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Rationalized ; The denominator of the fraction ... more

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Use the product rule of radicals, , to simplify ... more

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An irrational number cannot be represented as a ... more

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Write the expression as a product of two radicals.... more

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is used to represent the ratio of a circle’s ... more

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The given decimal number is non-repeating and non-... more

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The given decimal number is non-repeating and non-... more

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An irrational number cannot be represented as a ... more

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An irrational number is non-repeating and non-... more

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Use the Quotient rule of radical, to simplify the... more

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Use the Quotient rule of radical, for simplifying... more

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0 ; Use the product rule for radicals, to ... more

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1 ; Use the product rule for radicals, to ... more

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5 ; Use the product rule for radicals, and ... more

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6 ; Use the product rule for radical, , to ... more

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; Use the product rule for radical, , to simplify... more

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; Use the product rule to simplify the given ... more

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; Use the product rule to simplify the given ... more

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; Use the product rule to simplify the given ... more

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; Factor the radical where one of the factors ... more

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; Factor the radical where one of the factors ... more

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; Factor the radical where one of the factors ... more

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; Factor the radical where one of the factors ... more

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; Factor the radical where one of the factors ... more

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; Factor the radical where one of the factors ... more

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; Factor the radical where one of the factors ... more

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; Factor the radical as one of the factors should... more

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; Take out the common radicand and simplify the ... more

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; Take out the common radicand and simplify the ... more

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; Factor each radical where one of the factors ... more

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; Simplify the two terms to make the radicand ... more

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; Factor each radical as one of the factors ... more

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; Factor each radical as one of the factors ... more

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; Factor each radical as one of the factors ... more

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; Factor each radical as one of the factors ... more

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6 ; Use the product rule for radicals, to ... more

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9 ; Use the product rule for radicals, to ... more

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; Use the product rule for radicals, and ... more

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; Use the product rule for radicals, and ... more

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2 ; Use the Quotient rule for radical, and ... more

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5 ; Use the Quotient rule for radical, and ... more

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3 ; Use the Quotient rule for radical, and ... more

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; Use the Quotient rule for radical, and ... more

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; Multiply the numerator and denominator by to ... more

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; Multiply the numerator and denominator by to ... more

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; Multiply the numerator and denominator by to ... more

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; Multiply the numerator and denominator by to ... more

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; Multiply the numerator and denominator by to ... more

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; Multiply the numerator and denominator by to ... more

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; Multiply the numerator and denominator by to ... more

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; Multiply the numerator and denominator by to ... more

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Lies between 6 and . ; In the radicand 37 lies ... more

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Between inches and 8 inches. ; For the given ... more

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Between inches and 10 inches ; For the given ... more

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Between 11 inches and inches ; For the given ... more

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Between 13 inches and inches ; For the given ... more

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Between 14 inches and inches ; For the given ... more

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36 inches ; Substitute 30 for into the given ... more

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; Substitute 35 for and 980 for into the ... more

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False; may be or may not be a rational number for... more

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False; is an irrational number for any prime ... more

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True ; Let two rational numbers be and , where... more

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True ; Let two rational numbers be and , where... more

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False; The multiplication of a rational number and... more

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False; The multiplication of two irrational ... more

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Entire proof answer: Assume two irrational numbers... more

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Entire proof answer: Assume two irrational numbers... more

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, ; Assess two irrational numbers and . Use the ... more

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Entire proof answer: Assume two irrational numbers... more

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is an irrational number as the radicand is a prime... more

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is an irrational number as the radicand is a ... more

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is an irrational number. is a rational number as ... more

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Entire Proof Answer:Assume and to be 9 and 16, ... more

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Assume and to be 4 and 9, respectively.Substitute... more

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Entire Proof Answer:Assume and to be 36 and 9, ... more

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No; the sum of the additive inverse of the ... more

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Irrational numbers are numbers that neither have a... more

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In mathematics, the ratio of the circumference of ... more

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Real ; Rational numbers are the numbers which can ... more

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; is the standard symbol which is used to ... more

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Closed ; The set is closed under any given ... more

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Commutative ; The commutative property of addition... more

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Commutative ; The commutative property of ... more

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Associative ; The associative property of addition... more

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Associative ; The associative property of ... more

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Distributive ; The distributive property of ... more

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As the result of adding two natural numbers is ... more

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As the result of multiplying two natural numbers ... more

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As the result of subtracting two natural numbers ... more

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As the result of dividing two natural numbers is ... more

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As the result of multiplying two integers is ... more

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As the result of adding two integers is always an ... more

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As the result of dividing two integers is not ... more

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As the result of subtracting two integers is ... more

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As the result of adding two rational numbers is ... more

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As the result of multiplying two rational numbers ... more

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As the result of subtracting two rational numbers ... more

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As the result of dividing two rational numbers is ... more

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Upon multiplication of two irrational numbers, the... more

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On addition, irrational numbers don’t form any ... more

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On division, irrational numbers don’t form any ... more

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On subtraction, irrational numbers don’t form any ... more

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The addition of two real numbers will give another... more

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The multiplication of two real numbers will give ... more

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The subtraction of two real numbers will give ... more

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The division of nearly all values will give a real... more

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Commutative Property, as there is a change in ... more

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Associative Property, as the terms inside the ... more

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No; take two integers 3 and 5 and apply the ... more

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No; take two rational numbers 4 and 2, and apply ... more

**Verified Answer ✓**

Apply the commutative property to the numbers and... more

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Apply the commutative property to multiply the ... more

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Apply the associative property to add the numbers... more

**Verified Answer ✓**

Apply the associative property to multiply the ... more

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No; Apply the associative property to obtain the ... more

**Verified Answer ✓**

No; Apply the associative property to obtain ... more

**Verified Answer ✓**

No; Apply the associative property to obtain the ... more

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No;Take three numbers, 4, 2, and 1. ; Let the ... more

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Distributive property of multiplication over ... more

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Commutative property of addition ; The commutative... more

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Associative property of multiplication ; The ... more

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Commutative property of addition ; The commutative... more

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Associative property of addition ; The associative... more

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Associative property of multiplication ; The ... more

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Commutative property of multiplication ; The ... more

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Associative property of addition ; The associative... more

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Distributive property ; The distributive property ... more

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Distributive property ; The distributive property ... more

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Commutative property of addition ; The commutative... more

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Commutative property of multiplication ; The ... more

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; Substitute 5 for, for, and 2 for into . ; ... more

**Verified Answer ✓**

; Substitute 8 for , for , and 7 for into . ; ... more

**Verified Answer ✓**

; Substitute 9 for , for , and for into . ; ... more

**Verified Answer ✓**

; Substitute 8 for , for , and for into . ; ... more

**Verified Answer ✓**

; Substitute for , for , and for into . ; ... more

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; Substitute for , for , and for into . ; ... more

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; Substitute 32 for , for , and for into . ; ... more

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; Substitute 15 for , for , and for into . ; ... more

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2 ; Substitute for , for , and for into . ; ... more

**Verified Answer ✓**

; Substitute for , 2 for , and for into . ; ... more

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; Substitute 5 for , for , and for into . ; ... more

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; Substitute for , for , and for into . ; ... more

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If the order is reversed, that is, giving water to... more

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Commutative property means that the order should ... more

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Washing clothes then drying and drying clothes and... more

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One needs to turn on the computer, and only then ... more

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Following the course of actions as given in the ... more

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All the three actions are independent of each ... more

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All the three actions are independent of each ... more

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All the three actions are independent of each ... more

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All the three actions are independent of each ... more

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To cook the egg, the given sequence of actions ... more

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Reading a book and playing footballSinging a song ... more

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Reading a book, playing football, and singing a ... more

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No, as the commutative property does not hold true... more

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; The given puzzle is made up of four rows and ... more

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Gerolamo Cardano, an Italian mathematician ... more

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; The product rule of exponents is .Apply the ... more

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; The quotient rule of exponents states that , ... more

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1 ; The zero rule of exponents states that , where... more

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; The negative rule of exponents states that , ... more

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; The power rule of exponents states that.Apply ... more

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10 ; Any number can be converted into scientific ... more

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; Move the decimal point to the left until the ... more

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; Move the decimal point to the left until the ... more

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; Move the decimal point to the right until the ... more

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; Move the decimal point to the right until the ... more

**Verified Answer ✓**

; Move the decimal point to the right until the ... more

**Verified Answer ✓**

; Move the decimal point to the right until the ... more

**Verified Answer ✓**

; Move the decimal point to the left until the ... more

**Verified Answer ✓**

; Move the decimal point to the left until the ... more

**Verified Answer ✓**

; Move the decimal point to the right until the ... more

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; Move the decimal point to the right until the ... more

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1600 ; The exponent on 10 is positive.Move the ... more

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53,000 ; The exponent on 10 is positive.Move the ... more

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; The exponent of 10 is negative.As the exponent ... more

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; The exponent of 10 is negative.As the exponent ... more

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; The exponent of 10 is negative.As the exponent ... more

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; The exponent of 10 is negative.As the exponent ... more

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; The exponent of 10 is 0.Apply Zero Exponent ... more

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46 ; The exponent of 10 is positive.As the ... more

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is the smallest number as it is the only number ... more

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The number, is the smallest number as the exponent... more

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is the smallest number as the exponent of base is... more

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Convert the number into scientific notation.Move ... more

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; Convert 319 million and billion into scientific... more

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; Convert billion and billion into scientific ... more

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; Convert 319 million and trillion into ... more

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1000 ; 1 meter has 1000 millimeters in it.1000 in ... more

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National Debt: trillion; Population: 328 million... more

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In the book Mathematics and Humor published in the... more

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Sequence ; A collection of numbers which are ... more

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terms ; A list of numbers that are related to each... more

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arithmetic ; An arithmetic sequence is a sequence ... more

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geometric ; A geometric sequence is a sequence in ... more

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ratio ; The common ratio of a geometric sequence ... more

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7, 13, 19, 25, 31 ; The first term of the given ... more

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9, 16, 23, 30, 37 ; The first term of the given ... more

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25, 20, 15, 10, 5 ; The first term of the given ... more

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, , , 4, 9 ; The first term of the given ... more

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5, 3, 1, , ; The first term of the given ... more

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, , , , ; The first term of the given arithmetic ... more

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44 ; Substitute 9 for , 4 for , and 5 for into ... more

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; Substitute 10 for , 9 for , and for into the ... more

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30 ; Substitute 11 for , for , and 5 for into ... more

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; Substitute 12 for , 7 for , and for into the ... more

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; Substitute 20 for , for , and for into the ... more

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9 ; Substitute 14 for , for , and for into the ... more

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; Subtract the first term, 1, from the second ... more

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; Subtract the first term, 2, from the second ... more

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; Subtract the first term, 1, from the second ... more

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; Subtract the first term, , from the second term... more

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1275 ; Substitute 50 for , 1 for , and 50 for ... more

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2550 ; Substitute 50 for , 2 for , and 100 for ... more

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2500 ; Substitute 50 for , 1 for , and 99 for ... more

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1325 ; Substitute 25 for , 5 for , and 101 for ... more

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340 ; Substitute 17 for , 100 for , and for into... more

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; Substitute 28 for , for , and for into the ... more

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3, 6, 12, 24, 48 ; The first term of the given ... more

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2, 6, 18, 54, 162 ; The first term of the given ... more

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5, 10, 20, 40, 80 ; The first term of the given ... more

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8, 4, 2, 1, ; The first term of the given ... more

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, 3, , 3, ; The first term of the given geometric ... more

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, 12, , 48, ; The first term of the given ... more

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112 ; Substitute 7 for , 2 for , and 5 for into ... more

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49,152 ; Substitute 3 for , 4 for , and 8 for ... more

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1 ; Substitute 64 for , for , and 7 for into the... more

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; Substitute for , for , and 8 for into the ... more

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; Substitute for , 3 for , and 7 for into the ... more

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; Substitute for , for , and 7 for into the ... more

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; Divide the second term, 25, by the first term, ... more

**Verified Answer ✓**

; Divide the second term, 12, by the first term, ... more

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; Divide the second term, 1, by the first term, 2... more

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; Divide the second term, 12, by the first term, ... more

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; Divide the second term, , by the first term, , ... more

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; Divide the second term, 6, by the first term... more

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189 ; Substitute 6 for , 3 for , and 2 for into ... more

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1093 ; Substitute 7 for , 1 for , and 3 for into ... more

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; Substitute 6 for , for , and 4 for into the ... more

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; Substitute 9 for , for , and 5 for into the ... more

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14,348,906 ; Substitute 15 for , 2 for , and 3 for... more

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4,194,300 ; Substitute 20 for , 4 for , and 2 for... more

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5050 ; The first 100 natural numbers are .The ... more

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10,000 ; The first 100 odd natural numbers are .... more

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3825 ; The first 50 multiples of 3 are .The ... more

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ft ; The jumping ball forms a geometric ... more

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billion ; Substitute for , for , and 16 for ... more

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billion ; The increase in the population after 1 ... more

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; Substitute 82 for , for , and 6 for into the ... more

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; The given sequence is an arithmetic sequence.... more

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267 ; The first number, , divisible by 6 between 7... more

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: 8; : 3 ; The common ratio, , is the ratio of ... more

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ft. ; The pattern of the bouncing of the ball is ... more

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Fibonacci ; In the sequence, the first two numbers... more

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Golden ; The number is known as Golden number and... more

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Divine ; The golden proportion, which is equal to ... more

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Rectangle ; A rectangle of length and width , ... more

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Ratio ; The ratio will have a value equal to the ... more

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Proportion ; Each ratio in the proportion will ... more

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Fibonacci-type sequence;Next two terms: 42,68 ; ... more

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Fibonacci-type sequence;Next two terms: 55,89 ; ... more

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Not a Fibonacci-type sequence ; Check if each term... more

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Not a Fibonacci-type sequence ; Check if each term... more

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Fibonacci-type sequence;Next two terms: 3,5 ; ... more

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Fibonacci-type sequence;Next two terms: , ; Check ... more

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Fibonacci-type sequence;Next two terms: 105,170 ; ... more

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Fibonacci-type sequence;Next two terms: , ; ... more

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1,1,2,3,5,8,13,21,34,55,89,144,233,377,610 ; The ... more

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Entire Proof Answer: Take the first 6 numbers of ... more

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21, 34, and 55 are the Fibonacci numbers, and the ... more

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The line should be marked at from one end to ... more

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Entire Proof Answer:The divine proportion, , can ... more

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;;; ; Assess the Fibonacci sequence, that is, 1, 1... more

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Fibonacci, also known as Leonardo of Pisa, was ... more

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Hindu-Arabic numerals are the set of 9 symbols, ... more

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The golden ratio is closely linked with the ... more

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GCD: 14LCM: 210 ; Write 42 as a product of prime ... more

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GCD: 9;LCM: 756 ; Write 63 as a product of prime ... more

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45 ; Find the LCM of the train which stops every ... more

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; The first addend is positive, so draw an arrow ... more

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; The first addend is negative, so draw an arrow ... more

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; The first addend is negative, so draw an arrow ... more

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10 ; Apply Quotient rule to rewrite the given ... more

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Natural numbers are those numbers that contain ... more

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Real numbers are a set of the sum of rational and ... more

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Irrational numbers are those numbers that cannot ... more

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; In the given decimal notation, move the decimal... more

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; In the given decimal notation, move the decimal... more

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; The given exponent is positive.So, move the ... more

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388 ; Divide the distance from planet E to planet ... more

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$ ; To determine the contribution of each person, ... more

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10 ; Substitute for , 9 for , and 2 for into the... more

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25 ; Substitute for , 10 for , and 5 for into ... more

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48 ; Substitute 3 for , 5 for , and 2 for into ... more

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; Substitute for , 10 for , and 3 for into the ... more

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3825 ; Substitute 50 for , 3 for , and 150 for ... more

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; Substitute 20 for , for , and for into the ... more

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45 ; Substitute 4 for , 3 for , and 2 for into ... more

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; Substitute 6 for , 1 for , and for into the ... more

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Arithmetic sequence; ; Calculate the difference ... more

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Geometric sequence; ; Find the ratio of the ... more

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1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ... more

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No ; In the Fibonacci sequence, the sum of two ... more

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Yes; ; ; In the Fibonacci sequence, the sum of two... more

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3; 5; 9 ; Divisible byTestResult2The number is ... more

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; The smallest prime number that divides 825 is 3... more

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8 ; Add the integers, and 7 in the first ... more

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Yes, set of integers is closed under ... more

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Distributive property of multiplication over ... more

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64 ; Use the quotient rule of exponents, , to ... more

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1024 ; Use the product rule of exponents, , to ... more

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; The given sequence is an arithmetic sequence.... more

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; The given sequence is a geometric sequence.... more

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1, 1, 2, 3, 5, 8, 13, 21, 34, 55 ; The first and ... more