The perimeters of a rectangle and an equilateral triangle are equal. The length of the rectangle is twice the width, and the side of the triangle is 8 more than the width of the rectangle. Which statements about this scenario are true if we use the variable w to represent the width of the rectangle? Check all that apply. The side of the triangle is w – 8. The length of the rectangle is 2w. A multistep equation will represent the scenario. A key word to identify is equal. A key word to identify is variable.

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).