Prove that 4.999...=5.000...=5

Q: Prove that Va - Vb is irrational number if 'a' and 'b’ are prime number?

A: Given To prove that a-b is irrational number if a and b are prime number.

Q: 3. If today is Thursday, what day is it 500 days from now?

A: Given that today is Thursday. Now, we have to find the day which will fall 500 days from now. Divide…

Q: Use a direct proof to show that the sum of two odd integers is even.

A: Types of integers : Odd integers : The integer which is not divided by 2 . It has the form 2k+1…

Q: O In 17 lo 6

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Q: plz solve q4

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Q: . Show that 1729 is a Carmichael number.

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Q: Prove that the last two digits of 2" cannot be 02 and the last three digits cannot be 108.

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: prove : 1+1/(3)2+1/(5)2+1/(7)2+...=(pie)2/8

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Q: 3 when atrucken came to his second toll booth ina 169 mile. stretch ofroad he handed in a ticker…

A: It is given that  the time stamp on the toll booth was 2 hours earlier, it means that time taken to…

Q: Prove dis prove that the or smallest non- commutative ving is of order 4-

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Q: 1. Show that subtraction is not associative for the set of integers.

A: Definition :Let "." be a binary operation and A is a setThen "." is said to be associative for A if…

Q: Without using any theorems from the book, prove the following statement: The sum of any two odd…

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Q: Prove by mathematical induction

A: The principle of mathematical induction is a technique or method that is used to prove the statement…

Q: Find the smallest distinct postive numbers that provide a counterexample to show the statement is…

A: Let the odd numbers be 1 and 3 and the even number be 2, According to the question, The sum of any…

Q: Prove or disprove the following statement: The product of an odd number with any integer is odd.

A: The product of an odd number with any integer is odd.

Q: Prove by induction that it is possible to pay, without requiring change, any whole number of…

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Q: Prove that 2^10 + 5^12 is a composite number.

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Q: Prove that the sum of any five consecutive positive integers is always a multiple of five.

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Q: Prove that a three-digit number is a multiple of 9 whenever the sum of the digits is a multiple of…

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Q: How do we proof that 2logn = n?

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Q: Prove that an odd number multiplied by an odd number is odd.

A: The objective is to prove that an odd number multiplied by an odd number is odd.

Q: a number whose decimal reoresentation repeats is a rational number. true or false

A: A number is rational if and only if its decimal representation is repeating or terminating (i.e.…

Q: Prove through mathematical induction that...

A: Mathematical induction is a method of proving a statement, formula, or expression. In this, the…

Q: Prove that the Ving of ComPelX numbers C¢,+.)is fielol

A: Solution is given as below:

Q: 2) express the given reapeating decimal as a fractional : 0.9999..., 0•159159159…, 0·782178217821… ,…

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Q: a) Prove or disprove = . 3

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Q: Determine the smallest integer that can be expressed as a sum of two primes in three different ways

A: Let us have smallest prime numbers  are, 2,3,5,7,11,13 17,19.....

Q: () - (" ;')-(,".) Show that: n+1

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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: : a number is even  if

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Q: Find te Qea of He triandle camy intermediate computocions o at least four decimal places. Round…

A: Let the lengths of the sides of a triangle be a, b, c . The area, A , of this triangle is calculated…

Q: Prove that a four-digit number is a multiple of 8 whenever the number formed by the first three…

A: The solution is given by using the expanded form of number as follows

Q: Assume that all four-digit integers (numbers from and including 1000 to and including 9999) are…

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Q: - 1, 1, 9; degree: 3 omial with integer coeffi

A: Is an expression consisting of variables (also called indeterminants) and coefficients, that…

Q: Prove that the number in between twin primes is always a multiple of 6.

A: A Twin prime are those numbers which are prime and having a difference of two ( 2 ) between the two…

Q: Show that 1729 is a Carmichael number.

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Q: 2. May plans to from Bank A 12% per ann decides to pa ordinary time

A: Given: May makes a loan on 15 January 2011 with a simple interest of 12% per annum. To determine the…

Q: Prove: If the sum or the difference of two irreducible fractions is an integer, the denominators of…

A: Proof: Let two irreducible fractions are ab and cd Since the fractions are irreducible, (a,b)=1 and…

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

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Q: 1. Show that 1105 is a Carmichael number.

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Q: Determine the smallest integer that can be expressed as a sum of two primes in three different ways.

A: The number is 22 and all others smallest integer can not be written as sum of two primes in three…

Q: Find odd and general

A: Given,       f(x)=x-π3;   0≤x≤π

Q: Prove by contradiction that 2020 cannot be written as a sum of 3 odd integers.

A: The objective is to prove  that 2020 cannot be written as a sum of 3 odd integers by the…

Q: Prove that no integer congruent to 3 modulo 4 can be written as the sum of two squares.

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Q: Suppose that p is a prime number greater than 30. Prove that when p is divided by 30, the remainder…

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Q: Define β1 stands for?

A: β1 is mainly used in linear regression.  The linear regression is defined as the mathematical linear…

Q: Find a number that provides a counterexample to show that the given statement is false.

A: We have to find counter example for each of the given statement.

Q: How many corresponding integers are made up of 1443 digits taken from (1-2-3-4-5-6) provided that no…

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Q: $550.45(1 + 0.0875 × 195/365) − $376.29 / (1 + 0.0875 × 99/365)

A:

Statements and Logic

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