A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides. The graph below shows how the volume of the box in cubic inches, V, is related to the length of the side of the square cutout in inches, x. (1.7,81.87) V a. The point (1.25, 77.188) is on the graph. This means that when the volume of the box is 77.188 v cubic inches when the cutout length is |1.25 v inches. b. When the cutout length is 3 inches, the volume of the box is 54 cubic inches. This means that the point (3,54) is on the graph above. c. Suppose the largest possible cutout length is 4.5 inches. Over what interval of x does the volume of the box decrease as the cutout length gets larger? (Enter your answer as an interval.) Preview no answer given
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Suppose the largest possible cutout length is 4.5 inches. Over what interval of xx does the volume of the box decrease as the cutout length gets larger? (Enter your answer as an interval.)
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