Identify the transformation that maps the figure with center (7, 1) onto itself. Q: A: A) rotate 180° clockwise about (4, 1) and reflect across the x-axis B) rotate 180° clockwise about (4, 1) and reflect across the y-axis C) rotate 27

1- 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.2- 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 the first question?

How does the graph of g(x)=⌊x⌋−3 differ from the graph of f(x)=⌊x⌋? the graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted right 3 units. the graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted up 3 units. the graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted down 3 units. the graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted left 3 units.

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.