answer:The harmonic mean is calculated as the reciprocal of the average of the reciprocals of the given numbers. Given numbers: frac{39}{2}, 17, 11, frac{33}{2} Their reciprocals are: frac{2}{39}, frac{1}{17}, frac{1}{11}, and frac{2}{33} The average of these reciprocals is: frac{left(frac{2}{39}right) + left(frac{1}{17}right) + left(frac{1}{11}right) + left(frac{2}{33}right)}{4} Calculating this gives: frac{frac{770}{6543}}{4} = frac{770}{26172} Now, the harmonic mean (HM) is the reciprocal of this average: HM = frac{26172}{770} = frac{2431}{159} So, the harmonic mean is frac{2431}{159}.

answer:Both solutions you presented are correct and achieve the desired O(n log n) time complexity. The difference lies in their implementation and assumptions about the set representation. Your solution involves sorting the set and performing binary searches, which is a straightforward approach. It assumes that elements in the set can be accessed by index, which might not be the case for a traditional mathematical set (where elements are typically unordered and have no duplicates). The book's solution, while more complex, emphasizes using only sorting and merging. It creates a new set S' and removes duplicates to avoid issues with repeated elements. This approach may be more suitable for certain data structures, like sorted linked lists, where binary search is not efficient. In summary, neither solution is inherently wrong. They represent different ways to solve the problem, and each has its own advantages and disadvantages depending on the context and data structure used. It's beneficial to have multiple solutions available to choose the best one for a specific situation.

answer:Moctezuma II, also known as Montezuma, was the ninth and last emperor of the Aztec Empire. He ruled from 1502 to 1520, during a time of great upheaval and change for the Aztec people. Moctezuma was a skilled warrior and administrator, but he was also known for his cruelty and arrogance. He was eventually captured and killed by Spanish conquistadors led by Hernán Cortés.

answer:The timing of income recognition for tax purposes is governed by three primary methods of accounting: 1. Cash Basis Method: - Income is recognized when cash is received from a customer for goods or services. - Expenses are deductible only when cash is paid for deductible expenses. - Test: The taxpayer must have actual or constructive receipt of the income. 2. Accrual Basis Method: - Income is recognized when the taxpayer earns the income, regardless of when payment is received. - Expenses are deductible when incurred, regardless of when payment is made. - Test: The taxpayer must have an unconditional right to the income and a clear obligation to pay the expense. 3. Modified Accrual Basis Method: - A hybrid method that combines elements of both the cash and accrual methods. - Income is recognized when cash is received or when services are performed, whichever is earlier. - Expenses are deductible when paid or when incurred, whichever is later. - Test: The taxpayer must meet the tests for either the cash or accrual method, depending on the specific income or expense item. Notable Exceptions: - Long-term contracts: Income from long-term contracts may be recognized using the percentage-of-completion method or the completed-contract method. - Installment sales: Income from installment sales may be recognized over the period the payments are received. - Prepaid income: Income received in advance for services not yet performed is generally not recognized until the services are performed.