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Noor brought 21 sheets of stickers. she gave 1/3 of a sheet to each of the 45 students at recess. she wants to give teachers 1 1/2 sheets each.

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e.g. 98.76543).

Given that sin∅ = 1/4, 0 < ∅ < π/2, what is the exact value of cos∅? a. (√4)/4 b. (√15)/4 c. (4π)/2 d. (4√2)/4