in a class of 100 students, 45 students read physics, 52 students read chemistry and 15 students read both physics and chemistry. find the number of students who study neither physics nor chemistry​

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

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.

Which statement is true about the function f(x)= square root -x ? the domain of the graph is all real numbers. the range of the graph is all real numbers. the domain of the graph is all real numbers less than or equal to 0. the range of the graph is all real numbers less than or equal to 0.