Define signal x(t) = u(t−1)−u(t−2.5)−2δ(t− 4)+δ(t −6). (a) sketch y(t) = $ t −[infinity] x(τ )dτ . (b) describe a simple change that can be made to the right-most delta function in x(t) so that y(t) = $ t −[infinity] x(τ )dτ has finite energy. (c) sketch z(t) = $ [infinity] t x(τ )dτ . (d) determine real constants a and b so that w(t) = x ? t−a b ? has a region of support

Questions 9-10. use the table of educational expenditures to answer the questions. k-12 education expenditures population indiana $9.97 billion 6.6 million illinois $28.54 billion 12.9 million kentucky $6.58 billion 4.4 million michigan $16.85 billion 9.9 million ohio $20.23 billion 11.6million 9. if the amount of k-12 education expenses in indiana were proportional to those in ohio, what would have been the expected value of k-12 expenditures in indiana? (give the answer in billions rounded to the nearest hundredth) 10. use the value of k-12 education expenditures in michigan as a proportion of the population in michigan to estimate what the value of k-12 education expenses would be in illinois. a) find the expected value of k-12 expenditures in illinois if illinois were proportional to michigan. (give the answer in billions rounded to the nearest hundredth) b) how does this compare to the actual value for k-12 expenditures in illinois? (lower, higher, same? )