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A fence is to be built to enclose a rectangular area of 280 square feet. The fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 14 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.
Vanilla Box Company is going to make open-topped boxes out of 19 × 11-inch rectangles of cardboard by cutting squares out of the corners and folding up the sides. What is the largest volume box it can make this way?
The cost of Cynthia's dinner is $15.20. She pays an additional tip that is 20% of the cost of the dinner. What is the best estimate for the amount of the tip?
Information on a packet of seeds claims that the germination rate is 92%. The packet contains 160 seeds. We will treat the packet as a random sample of seeds. Find the standard error of the proportion. Show 4 decimal places in your answer.
Facebook reports that the average number of Facebook friends worldwide is 175.5 with a standard deviation of 90.57. If you were to take a sample of 25 students, what is the probability that the mean number Facebook friends in the sample will be 19..
eighty percent of drivers wear seat belts. If three drivers are pulled over, what is the probability that all would be wearing their seat belts?
A bag contains 5 yellow marbles, 16 green marbles, and 2 red marbles. What is the chance of drawing a yellow marble? If a yellow marble is drawn the first time and then a second marble is drawn without replacement
A company wishes to manufacture a box with a volume of 56 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material.
A spherical weather balloon is being inflated. Beginning at 25 cm, the radius of the balloon is increasing at the rate of 4 cm per second. Express the surface area of the balloon as a function of time t.
Show how to construct a triangle given the length of one side, the distance from an adjacent vertex to the incenter and the radius of the incircle.
The probabilities that a person A and a person B will live an additional 15 years are 0.76 and 0.59 respectively. Assuming that their lifespans are independent, what is the probability that A or B will live an additional 15 years?
find the intervals on which f(x) is increasing and decreasing and find the x- and y- coordinates of all the local extrema
a man has $34,000 to invest. he invests some at 5% and some at 4%. his total annual interest income is %1,545. find the amount he invests at each rate.
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