Use the pigeonhole principle to show that if one picks nine numbers between 2 (inclusive), at...

Use the pigeonhole principle to show that if one picks nine numbers between 2 (inclusive), at least two of the numbers chosen must have a common divisor d ≥ 2

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orchestra answered 3 years ago

Using only real numbers between 0 and 100, inclusive, show the set of three numbers whose...

Using only real numbers between 0 and 100, inclusive, show the set of three numbers whose product is 64 and whose sum is minimal is give by {4, 4, 4}. (a) When is an absolute minimum or maximum guaranteed? (b) State the steps to find an absolute minimum and maximum. (c) Is the space closed and bounded? Explain. (d) Use Lagrange Multipliers to find the minimum and maximum please label and write neatly.

State and prove a generalized version of pigeonhole principle and use it to prove the following...

State and prove a generalized version of pigeonhole principle and use it to prove the following statement: If 22 numbers are selected at random, at least 4 of them will have the same remainder when divided by 7.

IN C++: Using a single for loop, output the even numbers between 2 and 1004 (inclusive)...

IN C++: Using a single for loop, output the even numbers between 2 and 1004 (inclusive) that iterates (loops) exactly 502 times. The outputted numbers be aligned in a table with 10 numbers per row. Each column in the table should be 5 characters wide. Do not nest a loop inside of another loop.

Use pigeonhole principle to solve please: will upvote! Let V = {v1,…,vk} be any set of...

Use pigeonhole principle to solve please: will upvote! Let V = {v1,…,vk} be any set of vectors in R^2 (Real Numbers to the power of 2). Suppose n agents each start at (0,0) and each takes a mV-walk where a mV-walk consists of a sequence of exactly m steps and each step moves the agent along a vector in V. Prove that, if n > (m + k − 1 , k − 1) (these are two separate terms in...

1.) Using excel. A random number generator picks a number from one to nine in a...

1.) Using excel. A random number generator picks a number from one to nine in a uniform manner. X ~ _________ Graph the probability distribution. f(x) = _________ μ = _________ σ = _________ P(3.5 < x < 7.25) = _________ P(x > 5.67) P(x > 5|x > 3) = _________ Find the 90th percentile. 2) using excel A subway train on the Red Line arrives every eight minutes during rush hour. We are interested in the length of time...

Use pigeonhole principle to prove the following (need to identify pigeons/objects and pigeonholes/boxes): a. How many...

Use pigeonhole principle to prove the following (need to identify pigeons/objects and pigeonholes/boxes): a. How many cards must be drawn from a standard 52-card deck to guarantee 2 cards of the same suit? (Note that there are 4 suits.) b. Prove that if four numbers are chosen from the set {1, 2, 3, 4, 5, 6}, at least one pair must add up to 7.

Write a program that prints the count of all prime numbers between A and B (inclusive),...

Write a program that prints the count of all prime numbers between A and B (inclusive), where A and B are defined as follows: A = The 5 digit unique number you had picked at the beginning of the semester B = A + 5000 Just a recap on prime numbers: A prime number is any number, greater or equal to 2, that is divisible ONLY by 1 and itself. Here are the first 10 prime numbers: 2, 5, 7,...

(Write in PythonUse a for statement to print 10 random numbers between 25 and 35, inclusive....

(Write in PythonUse a for statement to print 10 random numbers between 25 and 35, inclusive. (Write in Python)in python The Pythagorean Theorem tells us that the length of the hypotenuse of a right triangle is related to the lengths of the other two sides. Look through the math module and see if you can find a function that will compute this relationship for you. Once you find it, write a short program to try it out. (Write in PythonSearch on...

1. Use cardinality to show that between any two rational numbers there is an irrational number....

1. Use cardinality to show that between any two rational numbers there is an irrational number. Hint: Given rational numbers a < b, first show that [a,b] is uncountable. Now use a proof by contradiction. 2. Let X be any set. Show that X and P(X) do not have the same cardinality. Here P(X) denote the power set of X. Hint: Use a proof by contradiction. If a bijection:X→P(X)exists, use it to construct a set Y ∈P(X) for which Y...

Use cardinality to show that between any two rational numbers there is an irrational number. Hint:...

Use cardinality to show that between any two rational numbers there is an irrational number. Hint: Given rational numbers a < b, first show that [a, b] is uncountable. Now use a proof by contradiction

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