Suppose that a positive number a is written in scien- tific notation as a = c × 10", where n is an integer and 1 sc< 10. Explain what n indicates about the size of a.

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: Prove the following:For any natural number n, if n 2 + 6 n is an even number, then n is an even…

A: To prve that n is an even integer under the given conditions

Q: 10. Show that the product of a+bi and b+ai always results in a purely imaginary number, given that a…

A: Given two complex numbers: a+bi and b+ai

Q: The square of an even integer is congruent to 0 (mod 4). Select one: O True O False

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Every natural number can be written as the products of prime numbers

A: Prime numbers are the numbers which have only two factors, 1 and the number itself.

Q: Show that if a positive integer is odd, then it's square is odd.

A: To show that if a positive integer is odd then its square is odd

Q: Find an explicit formula for an. 15) 0, -1, 0, 1, 0, -1, 0, 1, . . .

A:

Q: Show all formula, substitution and calculations. Round off to 2 decimals. In how many ways can…

A: The collection of items or elements arranged in a different way with ordering is called Permutations…

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

A:

Q: of the first 150 positive integers?

A:

Q: Every natural number greater than 1 can be written as the products of prime numbers.

A: Prove that  every natural number greater than 1 can be expressed as product of primes or the number…

Q: Prove that 2" >n For all nuatural numbers

A:

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

A:

Q: Are the irrational numbers closed under multiplication?

A: Use closure property.

Q: If 2x³ - 4x² + x + 1 = 0 so x = 4x² - 2x³ - 1 then |x5-x4] < €, X4 = 1.36603, x5 = 1.366024, is the…

A: As per the question we are given an equation and the approx root after 4th and 5th iteration of the…

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

A:

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: Define an odd number and show that the product of odd even numbers is also even.

A: We need to first define an odd number. And layer prove product of an odd and an even number is…

Q: If a = 17 (mod 3), then what is the remainder of a when divided by 3? Enter the numerical value.

A:

Q: "Every positive integer can be written as the sum of the square of 3 positive integers." prove…

A: Given: "Every positive integer can be written as the sum of the square of 3 positive integers." To…

Q: Show that n-lis divisible by 8, if n is an odd positive integer

A:

Q: Prove that the product of an even number and an odd number is even.

A: Here, objective is to prove that the product of an even number &amp; an odd number is even

Q: If 2x³-4x²+x+1=0 so x = 4x² - 2x³ - 1 then x5-x4|< €, X4 = 1.36603, x5 = 1.366024, is the error…

A:

Q: Prove: The product of an irrational number and a nonzero rational number is irrational.

A:

Q: 0alaEN,a is an even number and ac i4}

A: The set just contains those even natural numbers that are less than 14.

Q: Develop a simple expression for the entries of A", where n is a positive integer and 1 A = -IN -IN

A: To get a simple expression for the entries of An, where n is a positive integer. A=112012

Q: А. If p 2q 5 is a prime number, prove that p2-q? is divisible by 3.

A:

Q: Find out how many distinct three-digit numbers can be formed using al the digits of 1, 2, and 3. * O…

A: To find  Number of distinct three digit numbers can be formed using all the digits 1,2 and 3.

Q: (325)g and (154)8

A:

Q: If x is an odd integer then 5x – 7 is an even integer. (use direct proof)

A: Given that “x” is an odd integer then “5x-7” is an even integer.

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: Show that there da do not exist tworeal numbers which add to 7 and multply to 13. It is not…

A: According to the problem, we have

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

A:

Q: Provide proof of why is it that a positive real number multiplied by a negative real number yiclds a…

A: Let's find.

Q: Show that 5 – V7 is an algebraic number.

A:

Q: How large a subset of the integers from 1 to 50 must be chosen to guarantee that one of the numbers…

A: We have to determine How large a subset of integers from 1 to 50 must be chosen to guarantee that…

Q: ss the following as a factorial: 6 x 5 x 4 x 3x 2 x

A: The factorial function tells us to multiply all whole numbers down to 1 from the selected number.

Q: It is possible if the index of a radical number is even and its radicand is negative.

A: Note: According to bartleby we have to solve the first question only please upload the question…

Q: Is it true that for any odd n the number 2" +1 is divisible by 3? Prove your answer.

A: We prove this by using PMI(Principle of Mathematical induction)

Q: Define β1 stands for?

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

Q: Find mZD. 6. D Write your answer as an integer or as a decima mZD = %3D

A: We have a right-angled triangle right angled at F we have to find angle D

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: divisible

A: