Show that the distance measure defined as the angle between two data vectors, x and y, satisfies the metric axioms given on page 70. Specifically, angle between two data vectors is arccos( cos(x, y) ), so d(x, y) = arccos( cos(x, y) )Show for distance measure arccos( cos(x, y) )A) Positivity1) d(x, x) >= 0 for all x and y,2) d(x, y) == 0 onlY if x == y. B) Symmetryd(x, y) == d(y, x) for all x and y. C) Triangle Inequalityd(x, z) < d(x, y) + d(y, z) for all points x, y, and z. D) Explain in simple English the intuition for why would arccos( cos(x, y) ) satisfy the same properties (A, B,C above) as the Euclidean distance.

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.

Simplify. −4x^2 (5x^4−3x^2+x−2) −20x^6−12x^4+8x^3−8x^2 −20x^6+12x^4−4x^3+8x^2 −20x^8+12x^4−4x^2+8x −20x^6+12x^4+4x^3−8x^2

Kendra had twice as much money as kareem. kendra later spent $8 and kareem earned $6. by then,the two had the same amount of money. how much money did each have originally?