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The table shows the amount of property damage (in dollars) due to automobile accidents in California in recent years. In this exercise we are interested in the total amount of property damage due to automobile accidents over the 8-year period from mid-2000 to mid 2008, using the data for the 9 years. a. One approach is to sum up the numbers in the second column, but only count half of the first and last numbers. Give the answer to this calculation. b. Approximate the amount of property damage over the 8-year period 2000–2008 by taking the average of the left endpoint sum and the right endpoint sum. Explain why this is equivalent to the calculation done in part a

 Year  Property Damage ($)2000309,5692001317,5672002335,8672003331,0552004331,2082005325,4532007313,3572008278,986\begin{array}{cc} {\text { Year }} & {\text { Property Damage }(\$)} \\ \hline 2000 & {309,569} \\ {2001} & {317,567} \\ {2002} & {335,867} \\ {2003} & {331,055} \\ {2004} & {331,208} \\ {2005} & {325,453} \\ {2007} & {313,357} \\ {2008} & {278,986} \end{array}

c. Explain why the answer from part a is the same as using the trapezoidal rule to approximate the amount of property damage over the 8-year period 2000–2008. d.Find the equation of the least squares line for this data, letting x=0 correspond to 2000. Then integrate this equation over the interval [0, 8] to estimate the amount of property damage over this time period. Compare with your answer to part a.

Bed Bath & Beyond is a nationwide chain of retail stores that sell a wide assortment of merchandise, including domestics merchandise and home furnishings, as well as food, giftware, and health and beauty care items. The number of stores open at the end of the fiscal year from 1997 to 2013 is stored in Bed & Bath and shown in right column.

YearStores OpenedYearStores Opened19971082006    80919981412007    88819991862008    971200024120091,037200131120101,100200239620111,139200351920121,173200462920131,4712005721\begin{array}{cc|cc} \textbf{Year} & \textbf{Stores Opened} & \textbf{Year} & \textbf{Stores Opened}\\ \hline 1997 & 108 & 2006 & \ \ \ \ 809\\ 1998 & 141 & 2007 & \ \ \ \ 888\\ 1999 & 186 & 2008 & \ \ \ \ 971\\ 2000 & 241 & 2009 & 1,037\\ 2001 & 311 & 2010 & 1,100\\ 2002 & 396 & 2011 & 1,139\\ 2003 & 519 & 2012 & 1,173\\ 2004 & 629 & 2013 & 1,471\\ 2005 & 721\\ \end{array}

a. Plot the data.

b. Compute a linear trend forecasting equation and plot the results.

c. Compute a quadratic trend forecasting equation and plot the results.

d. Compute an exponential trend forecasting equation and plot the results.

e. Using the forecasting equations in (b) through (d), what are your annual forecasts of the number of stores open for 2014 and 2015?

f. How can you explain the differences in the three forecasts in (e)? What forecast do you think you should use? Why?

Question

See, Inc. is an American corporation that sells eyewear over the Internet on its Web site, seeeyewear.com, which it registered as a domain name in 1998. See, Inc. owns federal trademarks on SEE and SEE SELECTIVE EYEWEAR ELEMENTS. See, Inc. has also filed for a trademark on SEE EYEWEAR. The Defendant, Imago Eyewear Party, Ltd., is an Australian company that also sells eyewear over the Internet. Imago uses the Web site “seeyewear.com” to sell its products. This Web site domain name was registered in 2002. Image has filed for a United States trademark on SEEYEWEAR. See, Inc. sued Imago Eyewear in Michigan Federal Court. See, Inc. claimed that Imago, by using the Web site seeyewear.com, had violated Federal trademark law and Michigan’s unfair trade practices statutes. Imago argued that there is no jurisdiction for See, Inc. to sue in Michigan. Imago argued that See, Inc. is an Australian corporation and that, although Michigan residents can access its Web site on the Internet, no Michigan resident has every contacted See, Inc. via its Web site. Therefore, a U.S. Court does not have jurisdiction to hear this case. Source: See, Inc. v. Imago Eyewear Party, Ltd., 167 Fed.Appx. 518 (6th Cir. 2006)

Can See, Inc. sue Imago Eyewear in Michigan?

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For this activity, we are to determine if the court has jurisdiction in the given scenario.

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