Would you rather have the forces of demand and supply determine the price of gasoline which you pay at the pump, or would you prefer a government mandated price ceiling? What problems would a price ceiling on gasoline bring? There are two different schools of thought on how to lower gasoline prices and reduce US dependence on foreign oil. Increase SUPPLY of oil (drilling offshore) Decrease DEMAND (finding alternatives to oil). Think through how you might graph how these two changes will bring about lower gas prices. Which school of thought do you subscribe to?

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.

Simon, aged 10, is invited to a classmate's birthday party at an exclusive ski resort on march 15th. the day will include 4 hours of snowboarding, lunch and birthday cake. simon's mother checks a box on the invitation that says "yes, we will attend" and returns it to the classmate's address. unfortunately, they later don't attend the party when simon comes down with the flu. on march 17th, simon's mother receives an invoice in the mail from simon's classmate for $35 that says, "party no-show fee." can simon's classmate collect the fee?