Middle School

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Is the data set approximately periodic?
If so, what are its period and amplitude?

A. not periodic
B. periodic with period of 4 and amplitude of about 7.5
C. periodic with period of 4 and amplitude of about 15
D. periodic with period of 5 and amplitude of about 15
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Is the data set approximately periodic If so what are its period and amplitude A not periodicB periodic with period of 4 and amplitude of

Answer :

Based on the calculations, the data set is approximately: C. periodic with period of 4 and amplitude of about 15.

What is a periodic function?

A periodic function can be defined as a type of function that has its values being repeated at regular interval of time (period).

In this scenario, we are giving the following data:

Hours 1 2 3 4 5 6 7 8 9 10 11 12

Number of boats 24 41 10 32 26 38 9 31 25 29 12 34

From the above, we can deduce that the values are being repeated at regular interval of four (4). Thus, its period is equal to four (4).

For the amplitude:

[tex]Amplitude =\frac{38-9}{2}\\[/tex]

Amplitude = 14.5 ≈ 15.

Find more information on periodic function here: https://brainly.com/question/9718382

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Rewritten by : Barada

Answer:

Option: C is the correct answer.

C. Periodic with period 4 and amplitude of about 15.

Step-by-step explanation:

We are given the table of values as:

Hour 1 -- 2 -- 3 -- 4 -- 5 -- 6 -- 7 -- 8 -- 9 -- 10 -- 11

Number 24-41-10-32-26-38-9-31-25-39-12

of boats

As we could see that after every 4 value the values are approximately repeating.

Hence,the data set is approximately periodic.

Also, the amplitude is calculated as:

Average of the maximum and minimum value of each set

We divide the set into 3 sets as follows:

Hour 1 2 3 4

Number of boat 24 41 10 32

Here we have amplitude as:

(41-10)/2=15.5

Hour 5 6 7 8

Number of boat 26 38 9 31

Amplitude is:

(38-9)/2=14.5

Hour 9 10 11 12

Number of boat 25 39 12

Amplitude is:

(39-12)/2=13.5

Hence, we see that the amplitude is about 15.