Topchop sells hairstyling franchises. topchop receives $50,000 from a new franchisee for providing initial training, equipment, and furnishings that have a stand-alone selling price of $50,000. topchop also receives $30,000 per year for use of the topchop name and for ongoing consulting services (starting on the date the franchise is purchased). carlos became a topchop franchisee on july 1, 2021, and on august 1, 2021, had completed training and was open for business. how much revenue in 2021 will topchop recognize for its arrangement with carlos?

Astock is selling today for $50 per share. at the end of the year, it pays a dividend of $3 per share and sells for $58. a. what is the total rate of return on the stock? (enter your answer as a whole percent.) b. what are the dividend yield and percentage capital gain? (enter your answers as a whole percent.) c. now suppose the year-end stock price after the dividend is paid is $42. what are the dividend yield and percentage capital gain in this case? (negative amounts should be indicated by a minus sign. enter your answers as a whole percent.)

Connors academy reported inventory in the 2017 year-end balance sheet, using the fifo method, as $154,000. in 2018, the company decided to change its inventory method to lifo. if the company had used the lifo method in 2017, the company estimates that ending inventory would have been in the range $130,000-$135,000. what adjustment would connors make for this change in inventory method?

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.