Show that the following decimals are Rational 0,444444444......

Q: Determine if the numbers are irrational or rational:  0.343434343434343434...

A: This is a problem related to type of the number. Based on the general formula we will answer the…

Q: show that the following number is rational by writing it as a ratio of two integers 5.6077

A: Rewrite the given number as: 5.6077 = 5+0.6077            = 5+607710000 only factors of 10000 are 5…

Q: Prove that the hundreds digit of n20 is even.

A: To Prove that the hundreds digit of n20 is even.

Q: every rational number is a decimal true or false?

A: We know that rational numbers are of the form of terminating and repeating decimals whereas…

Q: Show that every rational number has exactly two finite simple continued fraction expansions.

A: To Show : Show that every rational number has exactly two finite simple continued fraction…

Q: Consider the following number. 0.59595959.. Show that the number is rational by writing it as a…

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Q: Find a counterexample to show that the following conjecture is false. Conjecture: For all counting…

A: Conjecture : For all counting numbers n , n3 + 5n +66 is an even counting number. This conjecture is…

Q: Prove that the sum of an irrational number and a rational number is irrational using a proof by…

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Q: Show that the following number is rational by writing it as a ratio of two integers. 8/9 +2/5

A: A rational number is a real number that is the ratio of two integers. There are certain criteria for…

Q: Consider all positive integers that are mueiples of 20 and that are less than or equal to 300. What…

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Q: For the first 5 odd primes, show that Wilsn's theorem holds to be true.

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Q: does there exists   ______such that if n is divided by 5 the remainder is 2 and  if   ?

A: We have to check whether there exist n such that if n is divided by 5 then remainder is 2. Let if n…

Q: Suppose that the prime factorizations of two positive integers x and y are expressed using a common…

A: The prime factorization is breaking down a number into the product of only prime numbers. These…

Q: 1. 0.0861861861861, when expressed as a rational number, is:

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Q: . Prove that between every rational number and every irrational number there is an irrational…

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Q: Show that the following number is rational by writing it as a ratio of two integers.…

A: Consider the given decimal number 52.4744174417441… Suppose that, x=52.4744174417441. Rewrite the…

Q: Every even integer greater than 2 is sum of two primes? Give your views on this?

A: We know that 2 is even prime. And all other primes are odd.

Q: Show that the following number is rational by writing it as a ratio of two integers.…

A: Given information: The rational number 52.4699169916991... Consider x=52.4699169916991...

Q: Are the irrational numbers closed under multiplication?

A: Use closure property.

Q: Determine whether the statement Every decimal with a repeating pattern of digits is a rational…

A: Consider the given statement, Every decimal with a repeating pattern of digits is a rational number…

Q: Show that there is no positive integer n for which In-1+ In+1 is rational.

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Q: Prove that a positive integer n is prime number.if no prime p less than or equal to n divides n.

A: Let us assume that the contradiction of the statement , let  n ≥ 0 be a composite number .  Thus , n…

Q: Consider the following statement. If the decimal expansion of r is terminating, then r is rational.…

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Q: prove that the one's digit of any integer,n, is the remainder when one divides n by 10.

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Q: Determine if 0.762050555854466... is rational or irrational and give a reason for your answer.

A: follow next step

Q: Is there an integer that has a remainder of 2 when it is divided by 5 and a remainder of 3 when it…

A: (a)The fill up for the statement to rewrite the given statement: Is there an integer n such that n…

Q: If the rational number r is also an algebraic integer, prove that r must be an ordinary integer.

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Q: Find the rational number which has the following repeating decimal expansion:…

A: Let us determine the rational number of the repeating decimal expansion using the rule of 9 in the…

Q: Is the set of integers a subset of the set of rationalnumbers?

A: We know that set of integer, Z=..., -3, -2, -1, 0, 1, 2, 3, ... And set of rational number,…

Q: Why do these rational numbers have terminating decimal? 1/30, 1/32, 1/40, and 3/60.

A: The number is said to be terminating if its denominator is in form of 2x5y. Simplify each number and…

Q: Show that there is no rational number r satisfying 2" = 6. Where does your proof break down if we…

A: Let us consider that, suppose a rational number r exists such that r=pq; q≠0. Now,  2pq=6 On taking…

Q: What is the limo+x².In(x) For answers that are fractions infinity negative infinity write... in…

A: L' Hospital Rule  :   If limx→a f(x)g(x) = 00 and ±∞±∞ form , then               limx→a f(x)g(x) =…

Q: Of addition of integers, subtraction of whole numbers and division of rationals, which operation and…

A: Note: The natural numbers along with zero form the collection of whole numbers. Remark: Let * is a…

Q: 3. Show that 3.141592592592592... is a rational number, by expressing it as a ratio of two integers.

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Q: "For all integers n, n(n² – 1) is divisible by 6." (You may use quotient-remainder theorem and…

A: Let us consider, for all integers n a = n3 – n a = n (n2 – 1) a = n (n + 1)(n – 1)

Q: Find a counterexample to show that the following conjecture is false. Conjecture: For all numbers…

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Q: Use the quotient remainder theorem and division into cases to show for all integers n, the integer…

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Q: Determine whether the number is rational or irrational. 3.789778977789.. Is 3.789778977789...…

A: The given number is: 3.789778977789...

Q: There is no integer that has a reciprocal that is an integer.

A: As per the instructions, we will be answering only the first question. For (32), Notice that the…

Q: Prove, that (nezond n73) If x"=5,+hen x is not a rational number.

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Q: Consider the set of rational numbers under the operation of addition. What is the inverse of 9?

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Q: Find a counterexample to show that the following conjecture is false. Conjecture: For all counting…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Find an irrational number between 5 and 9. 9.6767767776... 5.677      8.6767767776... 8.6 8.766

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Q: Let S be the set of all rational numbers that can be expressed as a repeating decimal in the form…

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Q: Show that the following number is rational by writing it as a ratio of two integers 0.79797979.

A: We have to write number 0.79797979... In the ratio of two integers . Lets=0.79797979...we can writ…

Q: Show

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Q: Use a proof by contradiction to show that the difference of any rational number and any irrational…

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Q: Prove or disprove the following: n+1 For any odd integer n, H= ()) 2

A: Let  n=2k+1         -  (1) Where k is an integer. Then n is any odd integer. Now, LHS= n24        -…

Statements and Logic

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