Suppose that we have a right triangle $abc$ with the right angle at $b$ such that $ac = \sqrt{61}$ and $ab = 5.$ a circle is drawn with its center on $ab$ such that the circle is tangent to $ac$ and $bc.$ if $p$ is the point where the circle and side $ac$ meet, then what is $cp$?

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. (a) what is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips, inclusive? (b) what is the probability that a randomly selected bag contains fewer than 1125 chocolate chips? (c) what proportion of bags contains more than 1225 chocolate chips? (d) what is the percentile rank of a bag that contains 1425 chocolate chips?

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.

Write a function rule for the table. hours worked pay 2 $16.00 4 $32.00 6 $48.00 8 $64.00 p = 16h p = 8.00h p = h + 16 h = 8.00p