A frame B is rotated 90 about the z-axis, then translated 3 and 5 units relative to the nand o-axes respectively, then rotated another 90 about the n-axis, and finally, 90 about the y-axis. Find the new location and orientation of the frame. 0 1 0 1 1 0 0 1 B = 0 0 -1 1 0 0 0 1

(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

Asequence {an} is defined recursively, with a1 = 1, a2 = 2 and, for n > 2, an = an-1 an-2 . find the term a241

Amanda went into the grocery business starting with five stores. after one year, she opened two more stores. after two years, she opened two more stores than the previous year. if amanda expands her grocery business following the same pattern, which of the following graphs represents the number of stores she will own over time?