It is a characteristic that can be used for classification but has no numerical value.
For example, the colours of the cars in your street, or the favourite fruit of people in your class are qualitative variables.
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There is no such word in maths (or math, if you prefer). There are vertices and verticals. They mean different things so find out which one you want and re-submit your question.
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I hope this helps
yes
An arc is part of the circumference of a circle.