Define γs, t to be the position in Chomp consisting of two rows of blocks, the top row of length s and the bottom of length t. We assume s ≤ t and t ≥ 1. Use induction on s + t to prove that γs, t is type P if and only if t = s + 1.

An optical inspection system is used to distinguish among different part types. the probability of a correct classification of any part is 0.92. suppose that three parts are inspected and that the classifications are independent. let the random variable x denote the number of parts that are correctly classified. determine the probability mass function of x. round your answers to four decimal places (e.g. 98.7654). x f(x) 0 1 2 3

Use sigma notation to represent the following series for 9 terms.

The line plot below represents the number of letters written to overseas pen pals by the students at the waverly middle school.each x represents 10 students. how many students wrote more than 6 and fewer than 20 letters. a.250 b.240 c.230 d.220