Mai, Kiran, and Clare are baking cookies together. They need 34 3 4 cup of flour and 13 1 3 cup of butter to make a batch of cookies. They each brought the ingredients they had at home. Mai brought 2 cups of flour and 14 1 4 cup of butter. Kiran brought 1 cup of flour and 12 1 2 cup of butter. Clare brought 114 1 1 4 cups of flour and 34 3 4 cup of butter. A measuring cup and spoon. If the students have plenty of the other ingredients they need (sugar, salt, baking soda, etc.), how many whole batches of cookies can they make? Explain your reasoning.

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.