Prove: e is an irrational number. the following is an outline of a proof: (a) use the taylor formula to show 0 < e − 1 + 1 1! + 1 2! + 1 3! + + 1 n! < 3 (n + (b) assume to the contrary that e is rational, say, e = a b , where a and b are positive integers. pick n > b and n ≥ 3. substitute e = a b into the inequality in (a) and multiply the inequality by

Abby is collecting rainfall data. she finds that one value of the data set is a high-value outlier. which statement must be true? abby will use a different formula for calculating the standard deviation. the outlier will increase the standard deviation of the data set. the spread of the graph of the data will not change. abby will not use the mean when calculating the standard deviation.