A fisherman illegally drops some fish into a pond, and they quickly propagate (reproduce). The population growth of the new specifies is modeled by P(x) = 6b^x, where x is the time in weeks following the moment he dropped the fish into the pond and b is a positive unknown base. Find b if you know the lake contains 51 fish after 6 weeks.

a. 1.43

b. 8.5

c. 7.5

d. 1.23

For the equation below, x is the input and y is the output. y = -4x + 3 if the input is -8, then the output is

Rachel reads 1/5 of the pages of a book plus 12 pages on the first day. on the second day, she reads 1/4 of the remaining pages plus 15 pages. on the third day, she reads 1/3 of the remaining pages plus 18 pages. on the fourth day, she reads the remaining 70 pages. how many total pages are in the book?

Jeffery conducted a survey in his school and found that 30 of the 50 eighth grade students' favorite subject is mathematics. based on the results, jeffery concluded that out of the 200 students in his school, 120 students' favorite subject is mathematics. select the statement that is true about jeffery's conclusion. a. jeffery's conclusion is not valid because the sample was biased since only 200 students were surveyed. b. jeffery's conclusion is valid because the sample was random since all of the students were eighth grade students. c. jeffery's conclusion is valid because the sample was random. d. jeffery's conclusion is not valid because the sample was biased since all of the students were eighth grade students.