Sam’s utility function is u(x1, x2) = 2x1 + x2, where x1 is the number of units of good 1 he consumes per week and x2 is the number of units of good 2 he consumes per week. sam has $200 a week to spend. the price of x1 is $4. sam currently doesn’t consume good 2, as it is way too expensive. sam has received an invitation to join a club devoted to the consumption of good 2. if he joins the club, sam can get a discount on the purchase of good 2. if he belonged to the club, he could buy good 2 for $1 a unit. how much is the most sam would be willing to pay to join this club?

In triangle abc, the length of side ab is 12 cm, the length of side bc is 5 cm, and the length of side ca is 9 cm. find the measure of angle a using the law of cosines.

Scott’s bank account showed a balance of $750 on sunday. during the next five days, he made one deposit of $140 and numerous withdrawals of $180 each. let x represent the number of withdrawals that scott made. write an inequality that can be used to find the maximum number of withdrawals that scott could have made and maintain a balance of at least $100. do not use a dollar sign ($) in your response.

In a study of the relationship between socio-economic class and unethical behavior, 129 university of california undergraduates at berkeley were asked to identify themselves as having low or high social-class by comparing themselves to others with the most (least) money, most (least) education, and most (least) respected jobs. they were also presented with a jar of individually wrapped candies and informed that the candies were for children in a nearby laboratory, but that they could take some if they wanted. after completing some unrelated tasks, participants reported the number of candies they had taken. it was found that those who were identiď¬ed as upper-class took more candy than others. in this study, identify: (a) the cases, (b) the variables and their types, (c) the main research question, (d) identify the population of interest and the sample in this study, and (e) comment on whether or not the results of the study can be generalized to the population, and if the ď¬ndings of the study can be used to establish causal relationships.