What is the units' digit of the sum of the squares of the first 2019 odd positive integers?

Q: Prove that the difference of squares of any two odd numbers is multiple of 8. (SOlve this task…

A: To proveDifference of squares of any two odd numbers is multiple of 8.

Q: What are fermat numbers? What is the first fermat number?

A: In mathematics, a Fermat number, named after Pierre de Fermat, who first studied them, is a positive…

Q: show that SZ+5 is irrational number

A: If a number cannot be written in ab form, where a and b are integers is known as an irrational…

Q: How many perfect squares are there between 1,000,000 and 9,000,000?

A:

Q: What is the smallest positive integer n such that 80325 divides n!

A:

Q: What is an integer

A:

Q: Show that the sum of the cubes of the first n positive integers is (n(n + 1)/2)^2

A:

Q: Show that a number with 30 digits cannot have more than 100 prime factors.  

A: Prime factor: A factor of a number which is a prime number. For example: consider a number 26. The…

Q: Find the smallest positive integer that leaves a remainder of 1 when divided by 2, a remainder of 2…

A: Let N be such a number N=10a+9:  N+1 = 10a+10 N=9b+8: N+1 = 9b+9 N=8c+7: N+1 = 8c+8 N=7d+6 and so on…

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: Find three consecutive integers Such thate Hour times the sauare Of theo third less three times the…

A: Let consecutive integers are x-1,x,x+1

Q: What is the smallest positive integer that has 6, 8, and 10 as factors?

A:

Q: All composite number can represent as product of primes numbers

A:

Q: Derive an expression for the sum of the first n positive even integers.

A: We Use the A.P series. Find The sum of the first n positive even integer.

Q: Can a number N, sum of whose digits is 21345, be a square of a natural number?

A: Given: a number N, sum of digit is 21345

Q: Set C is the set of positive two-digit even numbers less than 56 that are divisible by 5.

A:

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: What two nonnegative real numbers with a sum of 23 have thelargest possible product?

A: we have to find the two non negative real number with a sum of 23 which will have largest possible…

Q: Is there a smallest decimal that is greater than the number 2?

A:

Q: Find a three-digit positive integer such that the sum of all three digits is 14, the tens digit is…

A:

Q: 6.) Find the sum of the first 50 positive integers ending in 6.

A:

Q: (b) Find the sum of the first 110 positive odd integers.

A: Our Aim is to find the sum of the first 110 positive odd integers.

Q: is an even integer then n square is .A Negative

A: Suppose n=m is an even integer.Since n=m , then n2=m2

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 & an odd number is even

Q: Every odd prime number is greater than 2.

A: Given: "Every odd prime number is greater than 2." To find: Statement in the form "If p, then q"…

Q: what is the smallest integer greater than the square root of 117

A: Given, To find smallest integer  greater than the square root of 117

Q: Show that 3 + V5 is irrational number

A:

Q: What is the sum of the first 6 terms in Diagonal 5 of the Pascal's Triangle?

A: First draw the Pascal's triangle. The starting diagonal is called as diagonal 0 .

Q: what is the smallest integer greater than the square root of 48

A: First perfect square after 48 is 49. First perfect square before 48 is 36 Square root of 49 is 7 and…

Q: How far did they calculate out before making that decision … 1000 places ….10, 000 places? How many…

A: Given: To explain the given statement as follows,

Q: Write down the 7th row of Pascal's Triangle.

A: We have to find the 7th row of Pascal's Triangle

Q: Show that 2 + V5 is irrational number

A: To prove that 2+53 is irrational number. (It is evident that 2 is irrational, but here providing its…

Q: b. Assume prior studies have shown that about 40% of full-time students earn bachelor's degrees in…

A: It is given that margin of error (E) is 0.05 and the confidence level is 0.90.

Q: Choose two distinct integers, x and y, between 0 and 9. Derive the number of 9- digit integers that…

A:

Q: Determine all natural numbers divisible by 8 whose sum of digits is less than 10 and the product of…

A: Permutation and combination concepts will be used to filter out all the 3 scenarios in getting…

Q: is there integer that has reminder of 2 when its devided by 5?

A: There are infinite number of integers that has reminder of 2 when its divided by 5

Q: How many times greater is the value of the digit 6 in 536,807 than value of the digit 6 in 392,601?…

A: GivenDigit 6 in 536807Digit 6 in 392601

Q: What is the smallest sum possible sum of 25 consecutive positive integers which s a perfect square?

A: Let's take the 25 consecutive positive numbers as an Arithmetic Progression with first term a.…

Q: What is the last digit when you expand 3^2005 ?

A: Topic - exponents

Q: 4. Find The Three cube Meots of 1

A:

Q: Is the geometric mean of the first 100 natural numbers greater, equal or less than 50? Show your…

A:

Q: What is the number of integers with (a) at most n (decimal) digits; (b) exactly n digits…

A: What is the number of integers with (a) at most n (decimal) digits; (b) exactly n digits (don’t…

Q: Fermat's theorem is true for only prime number. إختر واحداً.

A:

Q: Prove that 13,050.046 is not the square of a natural number.

A: Use the fact that an even number is perfect square the number is divisible by 4

Q: 5. Prove that the sum of a two digit number and its reversal is a multiple of 11.

A:

Q: Find the sum of all  natural numbers between 250 and 1000 which are exactly divisible

A:

Q: Find for the sum of the first 50 negative even integers.

A: Negative even integers :-    -2,-4,-6,-8, ....... This is AP series with a=-2, d=-2

Q: What is the sum of the first 7 terms in diagonal 10 of the Pascal’s triangle?

A: Given :   Pascal's triangle

Statements and Logic

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