Evaluate the given integral by making an appropriate change of variables, where r is the rectangle enclosed by the lines x - y = 0, x - y = 7, x + y = 0, and x + y = 6.

Formulate the indicated conclusion in nontechnical terms. be sure to address the original claim. the foundation chair for a hospital claims that the mean number of filled overnight beds is over 523, and she is therefore justified starting a funding campaign to add a wing to the hospital. assuming that a hypothesis test has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

Rose and andrew are financing $128,000 to purchase a condominium. they obtained a 15-year, fixed-rate loan with a rate of 5.05%. they have been given the option of purchasing up to four points to lower their rate to 4.81%. how much will the four points cost them?

Similarly fie each expression 18,19,20