For any nonempty set $t$ whose elements are positive integers, define $f(t)$ to be the square of the product of the elements of $t$. for example, if $t=\{1,3,6\}$, then $f(t)=(1\cdot 3\cdot 6)^2 = 18^2 = 324$. consider the nonempty subsets $t$ of $\{1,2,3,4,5,6,7\}$ that do not contain two consecutive integers. if we compute $f(t)$ for each such set, then add up the resulting values, what do we get?

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Alandowner and his neighbor purchased adjoining undeveloped lots. after both built homes on their respective lots, the landowner suggested to the neighbor that a common driveway be built where the two lots joined. the neighbor agreed. the landowner and the neighbor split the cost of constructing the driveway and entered into a written agreement to equally share the costs of its upkeep and maintenance. the agreement was recorded in the county recorder's office. two years later, the neighbor built a new driveway located entirely on his lot. the common driveway, which the landowner continued to use but which the neighbor no longer used, began to deteriorate. the landowner asked the neighbor for money to maintain the common driveway, but the neighbor refused to contribute. three years later, the neighbor conveyed his lot to a friend. the friend entered into possession and used only the driveway built by the neighbor. by this time, the common driveway had deteriorated badly and contained numerous potholes. the landowner asked the friend to pay half of what it would take to repair the common driveway. the friend refused. the landowner repaired the driveway and sued the friend for 50% of the cost of repairs. will the landowner prevail?

Jamie is saving for a trip to europe. she has an existing savings account that earns 3 percent annual interest and has a current balance of $4,200. jamie doesn’t want to use her current savings for vacation, so she decides to borrow the $1,600 she needs for travel expenses. she will repay the loan in exactly one year. the annual interest rate is 6 percent. a. if jamie were to withdraw the $1,600 from her savings account to finance the trip, how much interest would she forgo? .b. if jamie borrows the $1,600 how much will she pay in interest? c. how much does the trip cost her if she borrows rather than dip into her savings?