Use DEDUCTIVE reasoning to prove that this conjecture is true: The sum of the digits for any two-digit whole number multiplied by 9 will always be 9 if you keep adding the digits until they equal a single digit. example: 98 x 9 = 882 8+8+2 = 18 1+8 = 9 20 x 9 = 180 1+8+0 = 9

Q: The Big-0 of 0(2n+1) is the same as O(n).

A: Answer: True

Q: Use Mathematical Induction to prove that sum of the first n odd positive integers is n2

A: Let us assume that P(k) is true for a k∈N. Let us show that P(k+1) is true aswell. Therefore we have…

Q: Let z and y be two n-digit base-4 numbers. If T(n) is the number of arithmetic operations needed to…

A: Consider two n digit base 4 numbers, x and y. Algorithm To compute T(n) :- if y = 0:    return 0 z =…

Q: he smallest positive integer which divides the expression (n+1)(n+2)(n+3)(n+4) is

A: The correct answer is given below:-

Q: log(n + 1) is O(log n) while log(n² + 1) is not. O True O False

A: Below is the answer with explanation:

Q: Find the decimal number represented by the machine number o 01100000101…

A: Step 1: Step 2: Signed bit is 0, So it is a positive decimal. Step 3: Take exponent bits…

Q: Write an algorithm to find the sum of n numbers. Calculate the time complexity of the same in terms…

A: ALGORITHM:- The algorithm is a step-by-step solution to any problem. The definition of an algorithm…

Q: What is the Theta notation for the ff. : foo(n): 1: if n == 1 then 2: return 1 3: else 4: return n·…

A: The algorithm is linear, running in O(n) time because it executes once every time it decrements the…

Q: Write two different algorithms for finding the given input as prime number or not? Compare which…

A: Let the number to be checked be n. Algorithm 1 for finding if the given input is a prime number or…

Q: x log x is O(x²) O True O False

A: Time complexity: It tells how long the particular statement in the code will be executed. It is…

Q: If Number1= 19.86 and Number2 = 2.04, then: a.Int(Number1) + Int(Number2) = Matlab إجابتك

A: The given question type is a fill in the blanks.

Q: Indicate the run time complexity: for i+0 to n - 1: for j+0 to n*n: x++; O(n") O(n") O(n*) O None of…

A: The run time of a loop can be found out by analyzing the number of iterations will be made.

Q: All complex numbers have an irrational part that causes problems when digital computers use…

A: A kind of mathematics known as floating-point arithmetic substitutes floating points for decimals.…

Q: Give the correct answer to the last quesiton show all steps

A: Solution of the given question is like asOn the apply of fermet theoremHence theorem is applicable…

Q: Prove that the following algorithmfor computing Fibonacci numbers is correct. function fib(n)…

A: To prove the correctness of the given algorithm for computing Fibonacci numbers, we need to show…

Q: The Fibonacci numbers are defined as follows: Fo = F; = 1 and for every i2 2, F, = Fi+ F;-2. We thus…

A: Given:

Q: may I ask why you multiplied it by 0.2

A: Answer:

Q: Prove that the following is true for all positive integers n by using the Principle of Mathematical…

A: In mathematical induction method, first proves that a statement is true for the initial value. Then…

Q: Compute the multiplicative inverses of the following (if they exist) using the extended Euclidean…

A:

Q: Write a program to compute the following summation. 1 1+√2 1 1 1 1 + √²+√3 + √³+√² + √A+√5 +i+…

A: NOTE - Here I have used the python programming language to code. I have imported the math module to…

Q: With your own understanding, explain the Mid-Square method of generating Pseudo–Random Numbers and…

A: Task: generate 5 Pseudo-Random Numbers from the seed number 2714. answer is in step 2.

Q: How many ways can one prove something? The sum of two even integers must be shown indirectly.

A: There are many ways to prove something, and the best approach often depends on the specific…

Q: Break down 42 into a sum of non consecutive Fibonacci numbers

A: Since it hasn't been specified whether you want this to be solved mathematically, i assume it is a…

Q: The gap between adjacent primes near the integer N is roughly log(N). By showing your calculations,…

A: Gap between adjacent primes near the integer N is roughly log(N). To find- Estimate the number of…

Q: Recall the Babylonian Algorithm for calculating a square root that we discussed in class. What will…

A: The idea is, we are given S for which we want to find S we first make an estimate x of S if x is…

Q: Use contradiction to prove that an even number multiplied by an odd number will equal an even…

A: In this proof, we aim to demonstrate that the product of an even number multiplied by an odd number…

Q: Prove that if x is odd, then x² + 3 is even. Hint: format for odd & even number as from the notes

A: SOLUTION - To prove,  If x is odd, then x2 + 3 is even   Proof -  if x is odd then it will be of  x…

Q: (a) For a number n base 9, find a test for determining if n is a multiple of 5 using the digits of n…

A: The question is very simple. Solution a) The test is you just have to check (if the sum of the last…

Q: What is the likely complexity of an algorithm that has the following empirical observations of the…

A: - We need to estimate the time complexity of the observation done with the size and count.

Q: c). Bagilah : (i). 101111 : 10011 (ii). 10111 : 100 = %3D .... ... ......

A: 1. Step by step solution :Step-1 :Set up the problem with long division bracket. Put dividend inside…

Q: Which time complexity has the highest growth rate?     a.     O(2n)     b.     O(1)       c.…

A: Time complexity is basically a time  taken by a program to execute the instructions less the time…

Q: Solve the following with Written Complete Solution. NO COMPLETE SOLUTIONS MEANS WRONG.   1.…

A: The solution to the given problem is below.     ***Note: According to Bartleby policy we are allowed…