2. Solve for X, show all calculation in binary number system only ((11111000)2 X = ((1101), – (0010)2)| + (100), - (11)2 - (100)2

Q: show that if x is an integer then x2+x-41= 0 produce prime numbers

A: Here show that if x is an integer then  produce prime numbers.

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: ..y yun.. 40mA B: Give the prime factorization of the number 34417

A: 34417= 127×271 The only divisors of 127 are 1 and 127 itself this implies that 127 is a prime…

Q: Compute C7,2. (Enter an exact number.)

A: A combination is a selection of all or part of a set of objects, without follow any order in which…

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: 3. Show that the weighted arithmetic mean of first n natural numbers whose weights are equal to the…

A:

Q: Let ab5c be all four-digit multiples of number 36 with different digits. If someone found 7 numbers…

A: Let ab5c be all four digit multiples number 36 with different digits.   As 36= 4x9, so the number…

Q: of the first 150 positive integers?

A:

Q: 1 101101, and 101, 2. 10111102 and 102 and 112 3. 1000012

A: Since there are multiple questions the first question is answered as per our guidelines. Kindly…

Q: 19 The number (B) of births of a city in the nth year after 2010 is estimated by B = 10…

A: Given:  The given function is B=100001.0136n. Find: The aim is to find the increase in the estimated…

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

A: To find the sum of squares of the first 2019 odd positive integers.

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

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

A:

Q: Prove by cases that n2−1 is divisible by 3 when n is an integer not divisible by 3.

A: The detailed solution is given below Thank you

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: Show that x2 + 9 is prime.

A: To show x2 + 9 is prime.

Q: Show that √17 is Irrational number

A:

Q: 5. Solve for X, show all calculation in binary number system only (1001101)2' X = ((1011), – (111)2)…

A: The given expression is: X=10112-11121001101210112+1012-112 Table for binary addition: 1+1=10…

Q: 7. Show that for every natural number n2 1, the integer ) + () +*(;) + - +) +22 +... +2" is…

A: Using binomial theorem:  n0+2n1+22n2....2nnn=n01n·20+n11n-1·21+n21n-2·22....nn1n-n·2n…

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: 27. Determine the number of n-digit numbers with all digits odd, such that 1 and 3 each occur a…

A:

Q: show that every integer greater than 11 is the sum of two composite integers

A: We need to prove that  every integer greater than 11 is the sum of two composite integers.

Q: 5. Given a real number x and a positive integer k, how many multiplications are used to find kx by…

A: Given,A real number x and positive integer kTo find: Total number of multiplications used with the…

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: How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0 if…

A:

Q: 3. Show that (5+ 13)e + (5- i3)-" is a real number if is also a real number.

A:

Q: Show that if n is an odd integer then []

A:

Q: Every natural number has a successor every number except 1 has a predecessor

A: We know that  Successor  is that number which can be find adding 1 in the given number  So if we…

Q: Solve for x: 34⁵⁰≡3x (mod26 )

A: Let us consider the equation ax≡b (mod n) is a modulo equation  where x is the solution of the…

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: The ISBN-10 of the sixth edition of Elementary Number Theory and Its Applications is 0-321-500Q1-8,…

A: Here, x1=0, x2=3, x3=2, x4=1, x5=5, x6=0, x7=0, x8=Q, x9=1, x10=8

Q: Find the sum of the first five natural even numbers using sigma notation.

A: We have to find sun of first 5 even natural numbers.

Q: Prove that 2^(27) - 1 is not a prime number.

A: A prime number is a natural number greater than 1 that is not a product of two smaller natural…

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: Prove that a natural number (an-1an-2a1ao)10 is divisible by 9 if and only if the sum of the digits…

A:

Q: How many integers from 1 to 99,999 contain exactly two consecutive 1s?

A:

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

A:

Q: How many can 3 digits be formed using the digits from 1 to 5 if the digit 2 is never there in the…

A:

Q: 1. IID00, and 10, 2. 11000012 and 1102

A:

Q: Compute 81^-3/4 without a calculator, writing your answer as a fraction

A: given that, 81-34

Q: Show that in any collection of 7 or more natural numbers there are ALWAYS TWO numbers whose sum or…

A: In the given problem we have to show that in any collection of 7 or more natural numbers there are…

Q: Show that, given a 7-digit number, where all digits except perhaps the last is non-zero, you can…

A:

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: (a). Show that the weighted arithmetic mean of firstn natural numbers whose weights are equal to the…

A:

Q: 1. Decimal System – base 10; 0,1,2,3,4,5,6,7,8,9 2. Binary System - base 2 3. Octal System - base 8…

A:

Q: Prove that the sum of two consecutive odd integers is divisible by 4.

A: Let the two consecutive integers be n and n+2 Then we need to prove that (n)+(n+2) is divisible by 4…

Q: 7-メナ メ= t ४%= +" Find az -1/3

A:

Q: 5. Find all integers 100 ≤ n ≤ 999 such that the last three digits of n² is same as n.

A: To find: All integers  100≤n≤999 such that the last three digits of n2 is same as n.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.