Flip a fair coin n times. using markov's and
chebyshev'sinequalities ,prove that the length of the longest
constant run inthe resulting list of heads and tails is (1 +
o(1))log_{2}(n). inother words, for every a> 0, almost no list
has at least(1+a)log_{2}(n) consecutive identical flips, and almost
every listhas at least (1-a)log_{2}(n) consecutive identical
flips.

In the proof of the triangle angle sum theorem, you must draw an auxiliary line. which construction must you use to draw this line?

The manufacturer of a new product developed the following expression to predict the monthly profit, in thousands of dollars, from sales of the productwhen it is sold at a unit price of x dollars.-0.5x^2 + 22x - 224what is represented by the zero(s) of the expression? a.the profit when the unit price is equal to 0b.the unit price(s) when the profit is equal to 0c.the profit when the unit price is greatestd.the unit price(s) when profit is greatest

Common binomial factor of 6x(3x+7)+5(3x+7)