Alan

The sum of the coefficients of a polynomial is easily obtained by setting x = 1.

Like so:

So x = 13

This graph should help:

These graphs should help you answer this:

Suppose that f(x) is a function such that f(xy) + x = xf(y) + f(x) for all real numbers x and y. If f(-1) = 5 then compute f(-1001).

This is a right-angled triangle with QR as the hypotenuse.  Let PQ be the Opposite to angle at R, and PR be the Adjacent.

tanR = 4sinR  means 1/cosR = 4, or cosR = 1/4

But cosR = PR/QR = PR/20

So PR/20 = 1/4

Hence PR = 5

Guest #1 has the right idea, but has missed a minus sign. 

\(\frac{c-1}{6-(-3)}=\frac{1-5}{-3-5}\\\frac{c-1}{6+3}=\frac{-4}{-8}\\\frac{c-1}{9}=\frac{1}{2} \\c-1=\frac{9}{2}\\c=\frac{11}{2}\)

There is a difference between your question and the one answered by heureka at : https://web2.0calc.com/questions/a-fair-coin-is-flipped-7-times-what-is-the-probability-that-at-least-5-of-the-flips-come-up-heads; namely you are asking for 5 consecutive heads, whereas the other questions just asked for 5 heads (not necessarily consecutive)..

For your case, have you ignored HHHHHTH and HTHHHHH ?

Hmm.  I'm afraid the answers here are wrong!  The original clearly says "diagram not to scale".  The diagram is drawn as it is to be misleading! If you don't believe me try to draw it using the specified lengths and angles.

Here is the correct answer:

Calculate the circumference of the complete circle. Take 3/4 of that and add to it the lengths of OP and OQ (which are radii of the circle).