amelia machine changes one red token into three white tokens and one white token into two red tokens. amelia has three red tokens and one white token. she uses the machine three times what is the smallest number of tokens she can end up with?

What is the value of x in the equation 6(x + 1) – 5x = 8 + 2(x – 1)?

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.

Suppose g(x) = f(x + 3) + 4. which statement best compares the graph of g(x) with the graph of f(x)?