There are two machines available for cutting corks intended for use in wine bottles. the first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.08 cm. the second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation 0.03 cm. acceptable corks have diameters between 2.9 cm and 3.1 cm.

what is the probability that the first machine produces an acceptable cork? (round your answer to four decimal places.)

what is the probability that the second machine produces an acceptable cork? (round your answer to four decimal places.)

explain the math behind your answer so i am able to understand! (

What is the greatest number of parts of a circle that can be formed by cutting the circle with 7 straight cuts? (note: the parts do not have to be equal in size)

Abakery recorded the number of muffins and bagels it sold for a seven day period. for the data presented, what does the value of 51 summarize? a) mean of bagels b) mean of muffins c) range of bagels d) range of muffins sample # 1 2 3 4 5 6 7 muffins 61 20 32 58 62 61 56 bagels 34 45 43 42 46 72 75

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? )