The differential equation below models the temperature of an 89°C cup of coffee in a 23°C room, where it is known that the coffee cools at a rate of 1°C per minute when its temperature is 73°C. Solve the differential equation to find an expression for the temperature of the coffee at time t. (Let y be the temperature of the cup of coffee in °C, and let t be the time in minutes, with t = 0 corresponding to the time when the temperature was 89°C.)

Following is a list of various costs incurred in producing replacement automobile parts. with respect to the production and sale of these auto parts, classify each cost as either variable costs, fixed costs, or mixed costs. 1. oil used in manufacturing equipment 2. plastic 3. property taxes, $165,000 per year on factory building and equipment 4. salary of plant manager 5. cost of labor for hourly workers 6. packaging 7. factory cleaning costs, $6,000 per month 8. metal 9. rent on warehouse, $10,000 per month plus $25 per square foot of storage used 10. property insurance premiums, $3,600 per month plus $0.01 for each dollar of property over $1,200,000 11. straight-line depreciation on the production equipment 12. hourly wages of machine operators 13. electricity costs, $0.20 per kilowatt-hour 14. computer chip (purchased from a vendor) 15. pension cost, $1.00 per employee hour on the job

Select the statement that indicates tina's company is a partnership. tina jones is a dancer specializing in latin dance styles. she always wanted to have her own dance studio where she could teach dancing to young and old alike. in 2006, she opened her first dance studio, electric diva, in madison triangle. it was a great choice as a business location because it's well-connected by highways to most places in the city. she leased the space for three years. her initial investment included a good sound system, cheerful interior design, and strong flooring. to raise capital for the business, tina turned to her brother-in-law, philip. philip made half the financial investment. he manages the accounts and social media needs of the business. he has a 30% share in trisha's business. together, they expanded the business to three dance studios in the city and plan to open franchises in other cities.

Read the following scenario and answer the question in 5-10 sentences. you are the owner of a small business that is a defendant in a lawsuit in federal court. you received bad news from your lawyer that the judge did not allow certain documents to be admitted as evidence in court and that the jury reached a $50,000 verdict in favor of the plaintiff. your lawyer tells you that it is within your legal right to hire him to file an appeal with the united states court of appeals. if the appellate court rules in your favor, you may be able to avoid paying part or all of the $50,000. evaluate your lawyer’s suggestion about appealing the decision.