An office building loses a third of its heat between sundown and midnight and an additional half of the original amount of heat between midnight and 4 AM. If five-eighths of the remaining heat is lost between 4 AM and 5 AM, what proportion of the total heat loss occurs between 5 AM and sunrise?

Step-by-step explanation:

Proportion of Heat Loss Between sundown and midnight

Proportion of Heat Loss between midnight and 4 AM  

Proportion of Total Heat Already Lost

Proportion of Remaining Heat

Between 4 AM and 5 AM, five-eighths of the remaining heat is lost.

Proportion of Heat Loss between 4 AM and 5 AM=

Therefore, Proportion of Remaining Heat Left

We therefore say that:

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this

a=24; b=12

step-by-step explanation:

a/b=2: 1

a=2b

36/(1+2)=12

b=12

a=24