1. If f(x) is differentiable for the closed interval [-4, 0] such that f(-4) = 5 and f(0) = 9, then there exists a value c, -4 < c < 0 such that: a, f(c) = 0
b, f '(c) = 0
c, f (c) = 1
d, f'(c) = 1
2. If f(x) = |(x2 - 8)|, how many numbers in the interval 0 ≤ x ≤ 2.5 satisfy the conclusion of the mean value theorem?
a, 1
b, 2
c, 3
d, None

Colby and jaquan are growing bacteria in an experiment in a laboratory. colby starts with 50 bacteria in his culture and the number of bacteria doubles every 2 hours. jaquan starts with 80 of a different type of bacteria that doubles every 3 hours. let x equal number of days. colbys experiment follows the model: a.) y=50*2^x b.) y=50*2^8x c.) y=50*2^12x jaquans experiment follows the model: a.)80*2^x b.)80*2^8x c.)80*2^12x

Standard deviation of 19,29,21,22,23

Questions 9-10. use the table of educational expenditures to answer the questions. k-12 education expenditures population indiana $9.97 billion 6.6 million illinois $28.54 billion 12.9 million kentucky $6.58 billion 4.4 million michigan $16.85 billion 9.9 million ohio $20.23 billion 11.6million 9. if the amount of k-12 education expenses in indiana were proportional to those in ohio, what would have been the expected value of k-12 expenditures in indiana? (give the answer in billions rounded to the nearest hundredth) 10. use the value of k-12 education expenditures in michigan as a proportion of the population in michigan to estimate what the value of k-12 education expenses would be in illinois. a) find the expected value of k-12 expenditures in illinois if illinois were proportional to michigan. (give the answer in billions rounded to the nearest hundredth) b) how does this compare to the actual value for k-12 expenditures in illinois? (lower, higher, same? )