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Question: what is the cosine of the angle between vectors u...

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What is the cosine of the angle between vectors u and v? Show how you set up the solution, and your actual calculations.
u = [ 4 2 0 -1 ] v = [ 3 -3 2 0 ]
II/ [ 2 points each] For each example below, state whether the feature is

i)    Numerical: discrete or continuous
ii)    Categorical or nominal: ordinal
If you’re doubtful about any part of an answer, add a few words of explanation.


a) Brightness outdoors as measured by a light meter.
b) Brightness outdoors as indicated by people’s subjective judgments (e.g. “it’s pretty bright”, “hard to see”).
c) Angles as measured in degrees between 0 and 360.
d) Telephone area code.
e) Bronze, silver, and gold medals as awarded at the Olympics.
f) Height above sea level in meters.
g) Number of patients in a hospital.
h) Ability to pass light in terms of the following values: opaque, translucent, transparent.
i) Military rank.
j) Density of a substance in grams per cubic centimeter.
k) Coat check number. (When you attend an event, you often can give your coat to someone who, in turn, gives you a number to use to claim your coat when leaving.)

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