Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false. Show work. 1^2 +4^2+7^2+…+(3n-2)^2=n(6n^2-3n-1)/2

Acyclist bike x distance at 10 miles per hour .and returns over the same path at 8 miles per hour.what is the cyclist average rate for the round trip in miles per hour ?

Afamily went out to dinner and their bill was $113.if they want to leave a 19% tip, how much should they leave.

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.