A number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome.
Give the sample space describing all possible outcomes.
Then give all of the outcomes for the event of rolling a number from 3 to 6.
If there is more than one element in the set, separate them with commas.

Prove that 16^4-2^13-4^5 is divisible by 11.

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.

What's for breakfast? all people who ate at a certain restaurant were surveyed as to what they ordered on a particular sunday morning. 40 ate eggs 42 ate sausage 32 ate pancakes 13 ate sausage and eggs 15 ate pancakes and sausage 11 ate eggs and pancakes 6 ate all three items 3 people didn't eat any of the items how many people ate only pancakes? how many people ate at the resturant that morning? how many people didn't eat eggs?