find the derivative of the function. ​

MEMORANDUM   To: English 2311 Students From: Mrs. Lauren Alfred, Instructor Date: March 3, 2026 Subject: Case Study for Midterm Exam You are the manager of a private swimming club. A member has written saying that she lost a contact lens (value $75) in your pool and she wants you to pay for the replacement. The contract that all members sign explicitly states that the management is not responsible for the loss of personal possessions. Write an adjustment letter denying the request. Invent any reasonable details. Remember to present yourself in a professional manner and proofread the document.  Letter Format- make sure the format is: Single spaced with extra line of space between paragraphs left-justified  Includes an inside address- you will need to make this up Attention line Subject line Salutation (Greeting) – make up the name of the person you are addressing this letter to Body paragraphs-a minimum of three that must include an introductory paragraph, a concluding paragraph, and one or more body paragraphs Complimentary closure Signature  

Once adopted, would any changes in accounting policy be allowed?  Why or why not?   [Hint:  Use the facts within the case description.]

9.  Operating expenses incurred for 2025 were $145,000, of which 80% had been paid in cash.     

10. A casino tracks the total money it keeps from a slot machine each day. While individual players may win or lose large amounts on single spins, the casino almost always makes money overall. Over many spins, the casino’s daily totals form a bell-shaped pattern centered around a profit. Why does this happen?

15. A researcher does not know the population standard deviation and uses the sample standard deviation instead. Which distribution should be used?

7. A researcher adds up the total waiting time for groups of customers at a coffee shop. Even though individual waiting times vary a lot, the totals look predictable. Why?

9. A scientist studies a population where individual measurements are very uneven and not bell-shaped. He still uses sample averages to estimate the population mean. Why is this reasonable?

12. A basketball player tracks how many shots he makes out of 50 attempts during practice to estimate how often he makes a basket. What is he calculating?

1. Why does the Central Limit Theorem help us estimate a population average when we only use samples?