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I will attach a file with the solution during the interview because it is difficult to type the solution in here.

A hypothesis test can be thought of as being somewhat similar to a court case. In a court case, we want to find out whether someone is either guilty, or not guilty, so we assume that they are not guilty, ...

Let the lines be:

r₁ = (a, b, c) + t(d, e, f)

r₂ = (g, h, i) + s(j, k, l)

Since t and s above are variables and the rest of the letters are constants, the only w...

Integrating this expression is a simple trick. We use integration by parts. For this we need a function we can integrate and a function we can differentiate. We know how to differentiate ln(x) which is 1/...

 We can start with the identity sin²(x)+cos²(x)=1 If we divide through the equation by cos²(x), we get: sin²(x)/cos²(x) + cos²(x)/cos^...