Answer :
Final answer:
The absolute value inequality to represent the toddler's sleep pattern is |T - 15| ≤ 0.5, where T is the total sleep time. Hence, the total time lengths for the child's total nap and nighttime sleep could vary between 14.5 hours and 15.5 hours.
Explanation:
The problem deals with the total sleeping time for a child, which includes naptime and nighttime sleep. The total average sleeping time for the child is two hours for nap time plus 13 hours for nighttime sleep, which adds up to a total of 15 hours. Each of these periods of sleep can vary by about 15 minutes, meaning the total sleep duration can also vary by about 30 minutes.
Here, we will use an absolute value inequality to represent the variability in sleep time.
Let T be the total sleeping time. The average total sleeping time is 15 hours, but it can vary by about 0.5 hours (30 minutes). Therefore, the absolute difference between the actual total sleep time T and the average total sleep time 15 should be less than or equal to 0.5, which is represented as: |T - 15| ≤ 0.5
Therefore, this inequality concludes that the child's total sleep could vary between 14.5 hours and 15.5 hours.
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