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Let n > 1 be a fixed natural number.
(a) Prove the following: if x is of the form x = nk + 1 for some natural number k, then x^2 ≡ 1 mod n.
(b) Find a y ∈ N and an n ∈ N such that y (not congruent) 1 mod n and y^2 ≡ 1 mod n.
If each unit of labor costs $500 and each unit of capital $200, and the amount allocated to labor and capital is $300,000, use Lagrange multipliers to determine the number of units of labor and capital which maximizes the level of production.
MUNICIPAL BONDS Maya paid $10,000 for a 7-yr bond issued by a city. She received interest amounting to $3500 over the life of the bonds.
Does your college or university sell any of its student data? If your institution sells student data, what data do they sell, to whom, and for how much?
in the 2010 winter olympics germany canada and the united states won a combined total of 93 medals. germany won seven
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A student studying for a vocabulary test knows the meanings of10 words from a list of 20 words. If the test contains 10 words from the study list, what is the probability that at least 8 of the words on the test are words that the student knows? (Rou..
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Calculate the break-even level of sales, assuming: $1.4 million fixed costs, $400,000 depreciation expense, variable costs-to-sales ratio of 65%.
Before proceeding, review the formal definition of congruence modulo n.
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