The port of south louisiana, located along 54 miles of the mississippi river between new orleans and baton rouge, is the largest bulk cargo port in the world. the u. s. army corps of engineers reports that the port handles a mean of 4.5 million tons of cargo per week (usa today, september 25, 2012). assume that the number of tons of cargo handled per week is normally distributed with a standard deviation of .82 million tons. a. what is the probability that the port handles less than 5 million tons of cargo per week? b. what is the probability that the port handles 3 or more million tons of cargo per week? c. what is the probability that the port handles between 3 million and 4 million tons of cargo per week? d. assume that 85% of the time the port can handle the weekly cargo volume without extending operating hours. what is the number of tons of cargo per week that will require the port to extend its operating hours?

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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