The allen marble company has a target current ratio of 2.0 but has experienced some difficulties financing its expanding sales in the past few months. at present the firm has current assets of $2.5 million and a current ratio of 2.5. if allen expands its receivables and inventories using its short-term line of credit, how much additional short-term funding can it borrow before its current ratio standard is reached? the addition to current assets is

Panera bread is a chain of cafes serving sandwiches, soups, and freshly baked breads. the company began in 1981 with stores primarily located along the east coast of the united states. since then, the firm has expanded to over 1,300 locations throughout the united states and canada. the firm has strong earnings and has been designated by business week as a "significant growth company." panera bread executives are considering the idea of expanding globally by opening cafes in asia through a franchising strategy. which of the following, if true, supports the argument that panera bread should expand into asia through franchising? a: the panera bread menu changes rapidly, and each cafe's artisan bread bakers receive regular training on new recipes. b: panera bread executives want fast access to the asian market without a significant investment of capital. c: panera bread executives want to test the asian market with a short-term commitment that allows them to make quick profits. d: the panera bread mission is to make excellent bread available to customers around the world.

Onsider the following subscription behavior information from genie, a web site that provides tools for constructing a family tree (ancestor search). subscriptions cost $9.99 per month, but you are charged for the entire year at the time of purchase. there is a one-year minimum term when you sign up for the service. once purchased, subscriptions are set to renew automatically unless the subscriber cancels them. when a membership renews, it renews for a one-year term and again you are charged for the entire year. there are no variable costs associated with providing this service to an individual customer, but genie does engage in customer relationship activities that they believe will increase customer retention. these customer relationship activities cost genie about $10 per year per customer. based on a sample of 1000 customers that joined genie five years ago, near the time when the company was founded, they were able to determine how many of those customers remained subscribers in the second year, third year etc. based on this information, genie calculated the average annual retention rate to be 20%. genie uses an annual discount rate of 8%. a. last year, genie spent $10,000 placing advertisements on google. genie management believes that these advertisements were responsible for about 300 new subscribers. would you recommend to genie management that they purchase more google ads? b. suppose a newly-introduced loyalty program increases the number of customers that remained to 30%. does this new data change your answer to 9.a? c. do you have any hesitations or concerns about making recommendations to management based on your above estimate of customer lifetime value?

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.