Using mathematical induction, prove that for any integer n, with n≥1, n(n2-1)(n+2) is divisible by 4.
Using mathematical induction, prove that for any integer n, with n≥1, n(n2-1)(n+2) is divisible by 4.
A company conducts a survey every spring to measure the morale of its employees. A group to be surveyed is randomly selected from all employees who have been with the company for exactly 5 years....
(a) Please count how many functions f : D → {0, 1} can be defined if the domain D is a finite set with the cardinality |D| = n. (b) Can you find a bijection between the set of all such...
Suppose a machine on average takes 108 seconds to execute a single algorithm step. What is the largest input size for which the machine will execute the algorithm in 2 seconds assuming the number...
let T = {(x,y) ∈ R x R(real numbers) | y = √x / (√(x-3)) Let D = {y ∈ R, | (x,y) ∈ T for x ∈ R}. for each one, decide if true or false a) 1/4 ∈ D b) 4 ∈ D why...
let T = {(x,y) ∈ R x R(real numbers) | y = √x / (√(x-3)) Let D = {y ∈ R, | (x,y) ∈ T for x ∈ R}. for each one, decide if true or false a) 1/4 ∈ D b) 4 ∈ D why...
Let S = {(x, y) ∈ R × R | 2x + 3y < 8}, T = {(x, y) ∈ R | y^2 + y > 6x^2}. (a) Exists a ∈ R so that (a, −10) ∈ ST? Why? (b) Exists b...
Prove by induction that ∀n≥3 : n^2+1≥3n
In how many ways can 10 identical laptops be distributed among five electronic stores if (a) there are no restrictions? (b) each store gets at least one? (c) the largest store gets...
A classroom has 12 students. The teacher would like to pick a group of 4 students to present on a topic. How many different combinations of 4 students could the teacher choose from?
There are 100 students majoring in engineering. There are three math classes offered to the engineering student's this semester: Calculus, Discrete Math, and Statistics. 28 students take...
Suppose you are to prove the statement "The difference of any two odd integers is even." Re-write this statement as a universal conditional statement. What should the first sentence of a...
A sphere is growing at a rate proportional to the radius. At t=0 the radius is 8in and at t=30 the radius is 12in. What is the radius at t=15? I'm stumped on this one. I've worked with...
Suppose you can afford $476 per month starting on march 1,2012. You save this much a month until January 1, 2013. Now, suppose you continue to pay $475 per month. how long would it take you to pay...
Subject of Combinations and Permutations
Find the smallest number k such that s(n) = O(n^k). (Big Oh) s(n) = sqrt(n^2-1)
Calculate 314^163 mod 7 by using: a) Modular exponentiation b) Fermat's little theory
Please indicate whether each variable is a discrete or continuous variable? Variable 1. The time it takes to shower in the morning. Variable 2. The number of trees...
The family (Mama, Papa, and the three kids, Ed, Lisa, and Judy) were about to go on a camping vacation. They decided to take their five dogs with them, and they needed to know how many cans of dog...
A={ -4 ,-3 ,-2 ,-1 ,0 ,1 ,2 ,3 ,4} R is defined on A as follows: For All (m,n) ∈A,m R n ⇔ 5 | (m^2- n^2 )