(after 3.1) Say we have linear transformations T : R 3 → R 2 and S : R 2 → R 4 . Let S ◦ T : R 3 → R 4 be the composition (that is, R 3 T −−→ R 2 S −−→ R 4 ). Can S ◦ T be one-to-one? (Hint: Start by thinking about all x such that T(x) = 0.)

At the beginning of the day, stock xyz opened at $6.12. at the end of the day, it closed at $6.88. what is the rate of change of stock xyz? a. 1.17% b. 11.0% c. 12.4% d. 81.5%

Which represents the solution set of the inequality 5x-9 < 21? a. x < 12/5 b. x > 12/5 c. x > 6 d. x < 6

At the olympic games, many events have several rounds of competition. one of these events is the men's 100-meter backstroke. the upper dot plot shows the times (in seconds) of the top 8 finishers in the final round of the 2012 olympics. the lower dot plot shows the times of the same 8 swimmers, but in the semifinal round. which pieces of information can be gathered from these dot plots? (remember that lower swim times are faster.) choose all answers that apply: a: the swimmers had faster times on average in the final round. b: the times in the final round vary noticeably more than the times in the semifinal round. c: none of the above.