Fill in the average number of hours each living being sleeps in a day by looking at the charts. Select the appropriate hours from this list: 15, 2.5, 20, 8, 3.5, 13, 10.5, 18.

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Homi · Accepted Answer

Each circular diagram shows the proportion of a 24-hour day that a living being spends sleeping (blue section) and awake (orange section). We need to match the blue section's size for each animal to the given list of sleep hours.

Step 1 — Understand the proportions

The entire circle represents 24 hours in a day. The blue part of the circle shows the average number of hours each living being sleeps. We will calculate the fraction of a day for each given sleep duration.

Let $S$ be the sleep duration in hours. Let $F$ be the fraction of the day spent sleeping. The total hours in a day is 24 hours.

$F = \frac{S}{24}$

Let us calculate the fraction for each sleep duration provided in the list: For 2.5 hours: $F = \frac{2.5}{24} = 0.104$

For 3.5 hours: $F = \frac{3.5}{24} = 0.146$

For 8 hours: $F = \frac{8}{24} = 0.333 \quad (\text{which is } \frac{1}{3})$

For 10.5 hours: $F = \frac{10.5}{24} = 0.4375 \quad (\text{which is } \frac{7}{16})$

For 13 hours: $F = \frac{13}{24} = 0.542$

For 15 hours: $F = \frac{15}{24} = 0.625 \quad (\text{which is } \frac{5}{8})$

For 18 hours: $F = \frac{18}{24} = 0.75 \quad (\text{which is } \frac{3}{4})$

For 20 hours: $F = \frac{20}{24} = 0.833 \quad (\text{which is } \frac{5}{6})$

Diagram 1

Step 2 — Match sleep hours to each living being

We will now visually compare the blue section in each diagram to the fractions calculated in Step 1. We will assign the most appropriate sleep duration from the given list to each living being.

Giraffe: The blue section is the smallest. This visually matches the fraction for 2.5 hours ( $0.104$ ).
Elephant: The blue section is slightly larger than the giraffe's. This visually matches the fraction for 3.5 hours ( $0.146$ ).
Boy: The blue section is approximately one-third of the circle. This visually matches the fraction for 8 hours ( $0.333$ ).
Dog: The blue section is less than half but more than one-third. This visually matches the fraction for 10.5 hours ( $0.4375$ ).
Cat: The blue section is slightly more than half of the circle. This visually matches the fraction for 13 hours ( $0.542$ ).
Squirrel: The blue section is clearly more than half, appearing to be about five-eighths of the circle. This visually matches the fraction for 15 hours ( $0.625$ ).
Snake: The blue section is exactly three-quarters of the circle. This visually matches the fraction for 18 hours ( $0.75$ ).
Bat: The blue section is the largest, covering about five-sixths of the circle. This visually matches the fraction for 20 hours ( $0.833$ ).

Answer

Giraffe: 2.5 hours Elephant: 3.5 hours Boy: 8 hours Dog: 10.5 hours Cat: 13 hours Squirrel: 15 hours Snake: 18 hours Bat: 20 hours

Question 14

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