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Answer:

The maximum value is 3.

Step-by-step explanation:

The given trigonometric function is

[tex]y=-2+5\sin(\frac{\pi}{12}(x-2))[/tex]

The amplitude of this function is 5.

[tex]|A|=5[/tex]

[tex]-5\le A\le5[/tex]

The function is shifted vertically down by two units.

To find the maximum value, we add -2 to the upper boundary of A.

The maximum values is 5-2=3

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