Show that there are no idempotent commutative latin squares of order 2 , where $n\geq 1$ . [hint: the symbol 1 occurs in an even number of cells off the diagonal. if you use the hint, you need to justify why it is true.]

Peaches cost $4.29 per pound. find the cost of two and a quarter pounds of peaches.

Karen is financing $291,875 to purchase a house. she obtained a 15/5 balloon mortgage at 5.35%. what will her balloon payment be? a. $220,089.34 b. $219,112.46 c. $246,181.39 d. $230,834.98

Thompson and thompson is a steel bolts manufacturing company. their current steel bolts have a mean diameter of 127 millimeters, and a variance of 36. if a random sample of 35 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 0.5 millimeters? round your answer to four decimal places.