Q1) Show, by applying the definition of the O-notation, that each of the following is true. – If f(n)= n(n-1)/2, then f(n) = O(n^2). – If f(n)= n+ log n, then f(n) = O(n). – 1+ n+ n^2 + n^3 = O(n^3). Q2) State without proof whether each of the following is True or False. – 7 = O(1). – n + n^4 = O(n^3). – For any polynomial T(n), T(2n) = O(T(n)). – For any function T(n), T(2n) = O(T(n)). Q3) Show, by the definition of the O-notation, that n^3 != O(n^2). (Note != means not-equal.) Q4) Let T1(n)= O(f(n)) and T2(n)= O((g(n)). Prove by the definition of the O-notation, this implies T1(n) + T2(n)= O(f(n) + g(n)). Q5) Let T1(n)= O(f(n)) and T2(n)= O((g(n)). Prove by the definition of the O-notation, this implies T1(n) * T2(n)= O(f(n) * g(n)).

I have a timed homework quiz and was wondering if one of you can help me with it. my email is
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1)Comprehensive cycle problem: Perpetual system At the beginning of 2012, the Jeater Company had the following balances in its accounts: During 2012, the company experienced the following events. 1. Purchased inventory that cost $2,200 on account from Blue Company under terms 1y10, ny30. The merchandise was delivered FOB shipping point. Freight costs of $110 were paid in cash. 2. Returned $200 of the inventory that it had purchased because the inventory was damaged in transit. The freight company agreed to pay the return freight cost. 3. Paid the amount due on its account payable to Blue Company within the cash discount period. 4. Sold inventory that had cost $3,000 for $5,500 on account, under terms 2y10, ny45. 5. Received merchandise returned from a customer. The merchandise originally cost $400 and was sold to the customer for $710 cash during the previous accounting period. The customer was paid $710 cash for the returned merchandise. 6. Delivered goods FOB destination in Event 4. Freight costs of $60 were paid in cash. 7. Collected the amount due on the account receivable within the discount period. 8. Took a physical count indicating that $7,970 of inventory was on hand at the end of the accounting period. Required a. Identify these events as asset source (AS), asset use (AU), asset exchange (AE), or claims exchange (CE). b. Record each event in a statements model like the following one. c. Prepare an income statement, a statement of changes in stockholders’ equity, a balance sheet, and a statement of cash flows. 2)”The following data apply to Superior Auto Supply Inc. for May 2012. 1. Balance per the bank on May 31, $8,000. 2. Deposits in transit not recorded by the bank, $975. 3. Bank error; check written by Allen Auto Supply was charged to Superior Auto Supply’s account, $650. 4. The following checks written and recorded by Superior Auto Supply were not included in the bank statement: 5. Note collected by the bank, $500. 6. Service charge for collection of note, $10. 7. The bookkeeper recorded a check written for $188 to pay for the May utilities expense as $888 in the cash disbursements journal. 8. Bank service charge in addition to the note collection fee, $25. 9. Customer checks returned by the bank as NSF, $125. Required Determine the amount of the unadjusted cash balance per Superior Auto Supply’s books.”

There are certain big questions that philosophers have been puzzling over for millennia. Amazingly, many people ask these same questions in daily life. Reflect on the questions related to each of the six branches of philosophy below. Then, write 2–3 paragraphs describing a time in your life when you have asked similar questions. Talk about the specific circumstances that brought you to each question, and what conclusions you came to. The questions are as follows:

Metaphysics:

• What is real?
• Is the physical world more or less real than the spiritual or psychological world?
• Is there such a thing as a soul? And if so, how does it survive outside of a physical body?
• Do all people have free will, or are lives determined by fate?

Epistemology:

• How is anything known?
• What is the basis for knowledge? Is it innate reason, experience, or something else?
• Is all knowledge subjective, or are there some universal truths?
• What is the relationship between faith and reason?
• What can artificial intelligence teach people about knowledge?
• What are the limits of human understanding?

Ethics:

• What is the right thing to do?
• What does it mean to be a good person?
• Does virtue lead to happiness?
• Do the ends justify the means, or is a virtuous action virtuous in and of itself?
• How does living in a society affect morality?
• Is morality culturally based, individually based, or is there a universal morality?

Aesthetics:

• What is beautiful?
• Is beauty truly in the eye of the beholder, or are there some things that all cultures find beautiful?
• What is the purpose of art?
• How can a piece of art be successful or valuable? Does beauty matter?

Political philosophy:

• What is the best kind of government?
• How much power should the government have?
• What kind of people should be in power?
• How involved should the common citizen be in government?

Social philosophy:

• How should humans behave in a society?
• Do people give up certain rights when they choose to live in a society?
• How do social values affect individual beliefs? Do people behave differently in a crowd than they would individually?
• How does society affect language and other types of communication?

In APA format and reference page included.