answer:The opportunity cost of producing a good is the value of the next best alternative that was not chosen. In this case, the opportunity cost of producing a unit of X for Agnes is the 1 unit of Y that she could have produced instead. Similarly, the opportunity cost of producing a unit of X for Brenda is the 2 units of Y that she could have produced instead. The opportunity cost of producing a unit of X for Agnes and Brenda in terms of Good Y is: - For Agnes: 1 unit of Y - For Brenda: 2 units of Y

answer:This topic has been studied extensively, particularly in the context of arithmetic, but the results apply to sf ZFC and similar theories as well. The process involves iteratively building theories by adding the consistency statement of the previous theory, operatorname{Con}(T), to create T + operatorname{Con}(T). This can be carried out transfinitely, up to the limit of recursive ordinals, omega_1^{CK}. The structure becomes complex due to the dependence of theories on the chosen notation at limit stages. Turing's 1938 thesis, "Systems of Logic Based on Ordinals," and works by Feferman provide insights into recursive ordinal notations and transfinite progressions of axiomatic theories. A formal description could involve a sequence of theories T_0 = sf ZFC, T_{n+1} = T_n cup {operatorname{Con}(T_n)}, and T_omega = bigcup_{nin omega} T_n, representing the "infinitely more strong" theory sf N. Intuitively, one might expect that sf N would prove its own consistency due to the consistency of all preceding theories. However, this is not the case. The issue lies in the interpretation of operatorname{Con}(T_n), which asserts that T_n has a model within the true universe of sets. When considering a model M of sf N, it only means that M satisfies sf ZFC and thinks it has models of each T_n. The "thinks" part is crucial, as M might be wrong about containing a model of some T_n. In summary, while we can formally describe the progression of theories, sf N cannot prove its own consistency due to the intricacies of operatorname{Con}(T_n) and the distinction between internal and external consistency. The incompleteness theorem and the subtleties of quantification over natural numbers within models further complicate the matter.

answer:Upon complete combustion of acetylene, the flue gas will contain both carbon dioxide (CO2) and water vapor (H2O). Therefore, the correct answer is D, which includes both B (CO2) and C (H2O).

answer:The eigenvalues of the matrix are ({0.112 - 5.449i, 0.112 + 5.449i, 0.776}).