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A student conducts an experiment to study whether temperature affects the timing of a cricket's chirps. The student keeps a cricket in an enclosed box, heated to different temperatures each day for twelve days, and records the chirps using a sound-activated microphone. The results are recorded in the table below:

| Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|-----|----|----|----|----|----|----|----|----|----|----|----|----|
| Temperature (°C) | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 |
| Average time between chirps (sec) | 2.5 | 2.6 | 2.2 | 2.3 | 2.0 | 1.8 | 1.9 | 1.8 | 1.4 | 1.2 | 1.5 | 1.1 |

Which generalization can be made from the data in the table?

A. The higher the temperature, the fewer chirps there will be in 10 seconds.
B. The chirps occur closer together as the temperature increases.
C. The chirps become farther apart as the temperature increases.
D. There is no relationship between temperature and the time between chirps.



Answer :

GinnyAnswer
Let's determine the general trend between temperature and the timing of the cricket's chirps.

First, let's analyze the difference in time between chirps as the temperature increases:

- From Day 1 to Day 2: [tex]\( 2.5 - 2.6 = -0.1 \)[/tex]
- From Day 2 to Day 3: [tex]\( 2.6 - 2.2 = 0.4 \)[/tex]
- From Day 3 to Day 4: [tex]\( 2.2 - 2.3 = -0.1 \)[/tex]
- From Day 4 to Day 5: [tex]\( 2.3 - 2.0 = 0.3 \)[/tex]
- From Day 5 to Day 6: [tex]\( 2.0 - 1.8 = 0.2 \)[/tex]
- From Day 6 to Day 7: [tex]\( 1.8 - 1.9 = -0.1 \)[/tex]
- From Day 7 to Day 8: [tex]\( 1.9 - 1.8 = 0.1 \)[/tex]
- From Day 8 to Day 9: [tex]\( 1.8 - 1.4 = 0.4 \)[/tex]
- From Day 9 to Day 10: [tex]\( 1.4 - 1.2 = 0.2 \)[/tex]
- From Day 10 to Day 11: [tex]\( 1.2 - 1.5 = -0.3 \)[/tex]
- From Day 11 to Day 12: [tex]\( 1.5 - 1.1 = 0.4 \)[/tex]

Next, we sum these differences to understand the overall trend:

[tex]\[ -0.1 + 0.4 - 0.1 + 0.3 + 0.2 - 0.1 + 0.1 + 0.4 + 0.2 - 0.3 + 0.4 = 1.4 \][/tex]

A positive total time difference of [tex]\(1.4\)[/tex] indicates that the average time between chirps generally decreases as the temperature increases.

Therefore, the correct generalization we can make is:

The chirps occur closer together as the temperature increases.

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