Consider the problem of reasoning about the identity of a set from the size of its intersections with other sets. You are given a finite set U of size n, and a collection A1, . . . , Am of subsets of U. You are also given numbers c1, . . . , cm. The question is: 1. Does there exist a set X ⊂ U so that for each i = 1, 2, . . . , m, the cardinality of X ∩ Ai is equal to ci?

We will call this an instance of the Intersection Inference Problem, with input U, {Ai}, and {ci}.

2. Prove that Intersection Inference is NP-complete.

On the way home from visiting his family, vincent’s plane cruised at an altitude of 3.2 × 104 feet. he had heard that a man named felix baumgartner skydived from an altitude of 1.28 × 105 feet. vincent wants to know how much higher felix went on his skydiving trip. question 1 you have already seen how adding numbers works in either scientific notation or standard notation. but can you subtract numbers in scientific notation and get the same results as subtracting in standard notation? to find out, first solve vincent’s problem in standard notation. part a write the cruising altitude of vincent’s plane in standard notation.

Me on this one i will give you 20pts. answer should be in detail . this is the discussion topic. one of the most fiercely debated topics in sports is the hot hand theory. the hot hand theory says that success breeds success. in other words, rather than each shot a basketball player takes or each at-bat a baseball player has being an independent event, the outcome of one event affects the next event. that is, a player can get hot and make a lot of shots in a row or get a lot of hits in a row. the hot hand theory, however, has been shown to be false in numerous academic studies. read this article, which discusses the hot hand theory as it relates to a professional basketball player. state whether you agree or disagree with the hot hand theory, and give reasons for your opinion. be sure to use some of the terms you’ve learned in this unit, such as independent event, dependent event, and conditional probability, in your answer.

What is the ratio for the surface areas of the cones shown below, given that they are similar and that the ratio of their radil and altitudes is 4: 3? 23