Answer:
[tex]\dfrac{1}{16}[/tex]
Step-by-step explanation:
Proportion of Heat Loss Between sundown and midnight[tex]=\dfrac{1}{3}[/tex]
Proportion of Heat Loss between midnight and 4 AM [tex]=\dfrac{1}{2}[/tex]
Proportion of Total Heat Already Lost [tex]=\dfrac{1}{3}+\dfrac{1}{2} =\dfrac{5}{6}[/tex]
Proportion of Remaining Heat [tex]=1-\dfrac{5}{6}=\dfrac{1}{6}[/tex]
Between 4 AM and 5 AM, five-eighths of the remaining heat is lost.
Proportion of Heat Loss between 4 AM and 5 AM= [tex]\dfrac{5}{8}$ X \dfrac{1}{6} = \dfrac{5}{48}[/tex]
Therefore, Proportion of Remaining Heat Left [tex]=\dfrac{1}{6}- \dfrac{5}{48}=\dfrac{1}{16}[/tex]
We therefore say that:
[tex]\dfrac{1}{16}$ of the total heat loss occurs between 5 AM and sunrise.[/tex]
