Most frequent pattern mining algorithms consider only distinct items in a transaction. however, multiple occurrences of an item in the same shopping basket, such as four cakes and three jugs of milk, can be important in transactional data analysis. how can one mine frequent itemsets efficiently considering multiple occurrences of items? propose modifications to the well-known algorithms, such as apriori and fp-growth, to adapt to such a situation.

Florence invested in a factory requiring. federally-mandated reductions in carbon emissions. how will this impact florence as the factory's owner? a. her factory will be worth less once the upgrades are complete. b. her factory will likely be bought by the epa. c. florence will have to invest a large amount of capital to update the factory for little financial gain. d. florence will have to invest a large amount of capital to update the factory for a large financial gain.

Define the marginal rate of substitution between two goods (x and y). if a consumer’s preferences are given by u(x, y) = x3/4y1/4, compute the consumer’s marginal rate of substitution as a function of x and y. calculate the mrs if the consumer has chosen to consumer 48 units of x and 16 units of y. show your work. (use the back of the page if necessary.

Under t, the point (0,2) gets mapped to (3,0). t-1 (x, y) →