Suppose you are choosing between the following three algorithms: algorithm a solves problems by dividing them into ve subproblems of half the size, recursively solving each subproblem, and then combining the solutions in linear time. algorithm b solves problems of size n by recursively solving two subproblems of size n 1 and then combining the solutions in constant time. algorithm c solves problems of size n by dividing them into nine subproblems of size n=3, recursively solving each subproblem, and then combining the solutions in o(n2) time. what are the running times of each of these algorithms (in big-o notation), and which would you choose

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? )