A geometric series G has common ratio r and an arithmetic series A has first term a and common difference d , where a and d are non-zero. The first three terms of G are equal to the third, fourth and sixth terms of A respectively. The sum of the first four terms of A is 6 .

A80-foot piece of siding is cut into three pieces so that the second piece is four times four times as long as the first piece and the third piece is five times as long as the first piece. if x represents the length of the first piece, find the lengths of all three pieces.

(a) (8%) compute the probability of an even integer among the 100 integers 1! , 2! , 3! , until 100! (here n! is n factorial or n*(n-1)*(n-2) *… 1) (b) (16%) compute the probability of an even integer among the 100 integers: 1, 1+2, 1+2+3, 1+2+3+4, …., 1+2+3+… + 99, and 1+2+3+… + 100

Awater holding tank measures 105 m long, 50 m wide, and 8 m deep. traces of mercury have been found in the tank, with a concen- tration of 60 mg/l. what is the total mass of mercury in the tank? answer in units of kg.