the sum of ages of anna, emma and karen are 27years. Anna is 2 years older than Karen and Emma is 4 years younger than. Anna. write a system of equations that represents each of the ages.

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 16 cubic feet per minute. the diameter of the base of the cone is approximately three times the altitude. at what rate is the height of the pile changing when the pile is 12 feet high? (hint: the formula for the volume of a cone is v = 1 3 πr2h.)

7. if the value of x varies directly with the value of y, and x = 3 when y = 21. what is the valu y, and x = 3 when y = 21. what is the value of x when y = 105?

According to a study conducted in 2015, 18% of shoppers said that they prefer to buy generic instead of name-brand products. suppose that in a recent sample of 1500 shoppers, 315 stated that they prefer to buy generic instead of name-brand products. at a 5% significance level, can you conclude that the proportion of all shoppers who currently prefer to buy generic instead of name-brand products is higher than .18? use both the p-value and the critical-value approaches.