1. a researcher firm finds that the average number of customers that are in Somerset Mall on a
Saturday varies sinusoidally with time. The mall is open from 9:00 am to 9:00 pm; the minimum number of customers is at 9:00 am and 9:00 pm when there are zero customers. The maximum
number of customers is at 3:00 pm when there are 875 customers in the mall.

a) Sketch and label this situation. [3pts.]

b) Write an equation to represent this relationship where y represents the number of customers in
the mall and x represents the number of hours past 9:00 am. Note: The domain of this function will be
[0, 12]. [5pts.)

c) On a particular Saturday, the mall decides to have a prize for the 500th customer to arrive.
Determine at what time the prize will be given. [3pts.]

step-by-step explanation:

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a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.

i believe it is 0.1m because the measurement of 30.4m limits how precise you can be

you can only be as precise as the least precise measurement