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

Expert Solution

orchestra answered 2 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.

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.

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...

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,...

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

Let k ≥ 2. Use that R (the real numbers) is complete to show R^k is...

Let k ≥ 2. Use that R (the real numbers) is complete to show R^k is complete.

2) Suppose I use a random numbers table to randomly choose 900 numbers between 0 and 100....

2) Suppose I use a random numbers table to randomly choose 900 numbers between 0 and 100. In this particular sample, the mean of the 900 numbers is 50 and the standard deviation is 30. a)Approximately, what proportion of the 900 numbers should fall between 20 and 80 (inclusive)? b)Suppose each student in Static (class size = 140) repeats the experiment described above and computes the mean of his or her 900 numbers. Based on the information given above, estimate the...

Which of the following represent a number between 0 and 1, inclusive? Select one: a. Coefficient...

Which of the following represent a number between 0 and 1, inclusive? Select one: a. Coefficient of Kurtosis b. Coefficient of Skewness c. Coefficient of Determination d. Coefficient of Correlation e. None of these

Create a JAVA lottery game application. Generate four random numbers, each between 0 and 9 (inclusive). Allow the...

Create a JAVA lottery game application. Generate four random numbers, each between 0 and 9 (inclusive). Allow the user to guess four numbers. Compare each of the user’s guesses to the four random numbers and display a message that includes the user’s guess, the randomly determined four-digit number, and the amount of points the user has won as follows: No matches 0 points Any one digit matching 5 points Any two digits matching 100 points Any three digits matching 2,000 points All four...

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