The volume v, in liters, of air in the lungs during a four-second respiratory cycle is approximated by the model v = 0.1729t + 0.1522t2 − 0.0374t3, where t is the time in seconds. approximate the average volume of air in the lungs during one cycle. (round your answer to four decimal places.)

Look at the hyperbola graphed below. the hyperbola gets very close to the red lines on the graph, but it never touches them. which term describes each of the red lines? o o o o a. asymptote b. directrix c. focus d. axis

Acompany produces packets of soap powder labeled “giant size 32 ounces.” the actual weight of soap powder in such a box has a normal distribution with a mean of 33 oz and a standard deviation of 0.7 oz. to avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. to avoid losing money, it labels the top 5% (the heaviest 5%) overweight. how heavy does a box have to be for it to be labeled overweight?

Find the maximum value of p= 4x + 5y subject to the following constraints :