A worker takes a random sample of 150 bolts and finds that 18 of them are either too long or too short, thus making them unusable. Estimate the number of unusable bolts in a production of 11,000 bolts.

1,320 bolts
860 bolts
340 bolts
450 bolts

Which is the equation of an ellipse with directrices at x = ±4 and foci at (2, 0) and (−2, 0)?

Lena reflected this figure across the x-axis. she writes the vertices of the image as a'(−2, 8), b'(−5, 6), c'(−8, 8), d'(−4, 2).

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?