Clara found the product of 3 – 6y2 and y2 + 2. her work is shown below. (3 – 6y2)(y2 + 2) = 3(y2) + (–6y2)(2) = 3y2 – 12y2 = –9y2 is the student’s work correct? no, she did not multiply –6y2 by 2 correctly. no, she did not add 3y2 and –12y2 correctly. no, she did not use the distributive property correctly. yes, she multiplied the binomials correctly.

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.