Amarine manufacturer will sell n(x) power boats after spending $x thousand on advertising, as given by upper n (x )equals 970 minus startfraction 3 comma 780 over x endfractionn(x)=970− 3,780 x, 5 less than or equals x less than or equals 305≤x≤30. (a) find upper n prime (x )n′(x). (b) find upper n prime (10 )n′(10) and upper n prime (20 )n′(20). write a brief verbal interpretation of these results.

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? )

Aculture started with 4,000 bacteria. after 5 hours, it grew to 5,200 bacteria. predict how many bacteria will be present after 19 hours. round your answer to the nearest whole number.

Solve the system of equations using the substitution method. {y=−3x+7x=−2y−16 enter your answers in the boxes.