The expression 10/12 (24/5 b - 36/5) and 2/3 (3b + 6) represent the lengths of the diagonals of parallelogram WXYZ. For what value of b is WXYZ a rectangle?

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).

Scott’s bank account showed a balance of $750 on sunday. during the next five days, he made one deposit of $140 and numerous withdrawals of $180 each. let x represent the number of withdrawals that scott made. write an inequality that can be used to find the maximum number of withdrawals that scott could have made and maintain a balance of at least $100. do not use a dollar sign ($) in your response.

32a³b² 8ab² simplify the following expression.