Assume that you manage a risky portfolio with an expected rate of return of 12% and a standard deviation of 39%. The T-bill rate is 6%A client prefers to invest in your portfolio a proportion (y) that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio's standard deviation will not exceed 30%. a. What is the investment proportion, y

He aldermanalderman company has prepared a sales budget of 42 comma 00042,000 finished units for a 3-month period. the company has an inventory of 10 comma 00010,000 units of finished goods on hand at december 31 and has a target finished goods inventory of 11 comma 00011,000 units at the end of the succeeding quarter. it takes 44 gallons of direct materials to make one unit of finished product. the company has inventory of 64 comma 00064,000 gallons of direct materials at december 31 and has a target ending inventory of 53 comma 00053,000 gallons at the end of the succeeding quarter. how many gallons of direct materials should aldermanalderman company purchase during the 3 months ending march 31? select the labels and enter the amounts to calculate the direct materials (gallons) to be purchased.

At april 1, 2019, the food and drug administration is in the process of investigating allegations of false marketing claims by hulkly muscle supplements. the fda has not yet proposed a penalty assessment. hulkly’s fiscal year ends on december 31, 2018. the company’s financial statements are issued in april 2019. required: for each of the following scenarios, determine the appropriate way to report the situation. 1. management feels an assessment is reasonably possible, and if an assessment is made an unfavorable settlement of $13 million is reasonably possible. 2. management feels an assessment is reasonably possible, and if an assessment is made an unfavorable settlement of $13 million is probable. 3. management feels an assessment is probable, and if an assessment is made an unfavorable settlement of $13 million is reasonably possible. 4. management feels an assessment is probable, and if an assessment is made an unfavorable settlement of $13 million is probable.

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.