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Consider the set of integers, Z. A binary operation ⊗ on Z is called a "pseudo-multiplication" if it satisfies all of the three properties:⊗ is commutative: m ⊗ n = n ⊗ m,⊗ is associative: (m ⊗ n) ⊗ p = m ⊗ (n ⊗ p), and⊗ is distributive over + (the usual addition of integers): m ⊗ (n + p) = m ⊗ n + m ⊗ p.Find all possible pseudo-multiplication operations ⊗ on Z. For each operation you find, prove it has the three properties so you know it really is a pseudo-multiplication. If you don't find all, find at least one (besides ·) and find as many as you can.(This is part of the project.) For each pseudo-multiplication you found, answer the following questions if you can:Does it have a pseudo-multiplicative identity element?Does it have the cancellation property?Find all integers that have pseudo-multiplicative inverses.
If the solution to an equation is imaginary or irrational, it takes a bit more effort to check. Replace x by each given number to verify the following statement.
One hundred stones are placed on the ground 3 feet apart, the first being 3 feet from a basket. If the basket and all of the stones are in a straight line, how far does a person travel who starts from the basket and brings the stones to it one by ..
Compute the surface integral over the given oriented surface.
Draw the diagram for each and discuss the part of the solution that would be different to finding the requested probabilities.
The second number is 5 less than the first. What are the possible values for the first of the two numbers? In your answer, denote the first number by X
Write the statement in symbolic form (Let p: The tent is pitched. q: The bonfire is burning. #40, The bonfire is not burning, however the tent is pitched.
Find whether the given statements are true or false - Which of the following are statement?
find the equation of the straight line from the given data.find the equation of the indicated curve subject to the
with end of month contributions of 251.33 an investment account is expected reach 100000 in value after 15 years and 5
An initial population of 895 quail increases at an annual rate of 7%. Write an exponential function to model the quail population.
Can you think of situations in the business world or other real life situations where you would need to calculate or estimate probabilities?
The median weight was 130 grams. The mean weight was 150 grams, and the mode weight was 110 grams and what is the only sequence of seven weights to fit this description?
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