Emma elected as an “S” Corp in 2011. The corporation had operating loss for $50,000 in the first year. The total net income for the following 6 years was $120,000. In 2017, it made distributions ($30,000 each) to its 3 equal shareholders. What’s the balance for AEP account at the end of 2017?

You are the manager of a firm that produces output in two plants. the demand for your firm's product is p = 20 − q, where q = q1 + q2. the marginal costs associated with producing in the two plants are mc1 = 2 and mc2 = 2q2. how much output should be produced in plant 1 in order to maximize profits?

Label each scenario with the term that best describes it. use the midpoint method when applicable. marcel duchamp was a famous artist prior to his death, and was known for his dada artwork, including works such as "soft toilet". all of his original sculptures and paintings go on sale. paul owns a tim horton's, a famous donut and coffee franchise. he is willing to sell as many maple glazed donuts as customers want at a price of $1.00 each, but he refuses to sell any donuts for any price lower than $1.00 . the price of facial tissues rises from $2.85 per box to $3.15 . as a result, p& g increases production from 15 million boxes to 25 million boxes of facial tissue. with the school semester starting for both high school and college, papermate chooses to increase production of pens from 38 million to 42 million after global prices of writing instruments increase from $1.90 a package to $2.10 a package. bright ideas increases its production of lightbulbs by 15% after a 400% increase in the price of fluorescent bulbs. labels: elastic supply; perfectly inelastic supply; perfectly elastic supply; inelastic supply; unit-elastic supply.

Describe three scenarios in which you might utilize mathematics to investigate a crime scene, accident scene, or to make decisions involving police practice. be sure to explain how math is used in police as they work through each scenario.