Calculate the pH of a buffer solution made from 0.20 M HC2H3O2 and 0.50 M C2H3O2- that has an acid dissociation constant for HC2H3O2 of 1.8 x 10-5.
pH = pKa + log ([A-]/[HA]) pH = pKa + log ([C2H3O2-] / [HC2H3O2]) pH = -log (1.8 x 10-5) + log (0.50 M / 0.20 M) pH= 5.1 [A-] = concentration of base (C2H3O2- in this problem) [HA] = concentration of acid (HC2H3O2 in this problem) To determine the acid or base when it is not explicitly stated, use knowledge of conjugate acids and bases.
Four political candidates are deciding whether or not to enter a race for an elected office where the decision depends on who else is throwing his or her hat into the ring. Suppose a candidate A prefers not to enter if candidate B is expected to enter; otherwise, A prefers to enter. Candidate B prefers not to enter if she expects either candidate A and/or candidate D to enter; otherwise she prefers to enter. Candidate C prefers not to enter if he expects candidate A to enter and prefers to enter in all other cases. candidate D prefers not to enter if either candidate B and/or C are expected to enter; otherwise she prefers to enter. If we assume that their choices are consistent with Nash equilibrium, who will enter the race?
If Nash equilibrium was assumed for their choices, candidates A and D would enter a race and B and C would enter a race. This is due to their payoff being higher than 0 when the other candidate is running in the same race against them. For example, A and B cannot run together as there is a better payout/preference if B does not run for A as A would prefer not to run if B were to run. This trend follows suit for A and C, A and B, C and D, and B and D.
Explain why we care about using linear regression models at all. After all, if we have two continuous variables Y and X , we can simply compute the correlation coefficient between them. Why would we care about using this regression stuff at all?
These models are significant in that they are an accurate predictor (to an extent) of an expected output given the input. Linear regression models also help in demonstrating correlation between two data points to either validate the significance of the correlation or the lack thereof. Although correlation is determined from these models a more in depth approach to even the most simple of problems may shed light on various confounding variables.