A Cepheid star is a type of variable star, which means its brightness is not constant. The relationship between the brightness of a
Cepheid star and its period, or length of its pulse, is given by M = -2.78(log P) - 1.35, where M is the absolute magnitude, or
brightness, of the star, and Pis the number of days required for the star to complete one cycle. What is the absolute magnitude of
a star that has a period of 45 days? Use a calculator. Round your answer to the nearest hundredth.

Adice is rolled 5 times. how many possible rolls are there? ( determine the number of outcomes using only the fundamental counting principal )

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.

Jane’s favorite fruit punch consists of pear, pineapple, and plum juices in the ratio 5: 2: 3. how many cups of pear juice should she use to make 20 cups of punch?