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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).

Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (-1+i)+(21+5i)+0

Arectangle has a width of 5 cm and a length of 10 cm. if the width is increased by 3, how does the perimeter change?