Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. however, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. an article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (mpa) was 51.9 and the sample standard deviation was 1.2. suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 mpa. does the data provide compelling evidence for concluding that true average strength for the wsf/cellulose composite exceeds this value? (use α = 0.05.)

How many different three-digit numbers can be formed using the digits 1 comma 2 comma 9 comma 6 comma 4 comma 3 comma and 8 without repetition? for example, 664 is not allowed.

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? )

What is the area of the original rectangle? 8 cm² 20 cm² 25 cm² 40 cm²