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.

The number of members f(x) in a local swimming club increased by 30% every year over a period of x years. the function below shows the relationship between f(x) and x: f(x) = 10(1.3)xwhich of the following graphs best represents the function? graph of f of x equals 1.3 multiplied by 10 to the power of x graph of exponential function going up from left to right in quadrant 1 through the point 0, 0 and continuing towards infinity graph of f of x equals 10 multiplied by 1.3 to the power of x graph of f of x equals 1.3 to the power of x