Aman and a woman agree to meet at a certain location about 12: 30 p. m. if the man arrives at a time uniformly distributed between 12: 15 and 12: 45 and the woman independently arrives at a time uniformly distributed between 12: 30 and 1 pm, find the probability that the man arrives first

We define the spaces of the man and the woman's independent arrivals.
In this case, 
f(man) = 1 (45-15) = 1/30
f(woman)=1/(60-0)= 1/60
f(man)*f(woman) = 1/1800

Probability = P 
P (man-woman)< 5 = 1/1800* integral of (y ) with limits of (x+5) and (x-5) from 45 to 15. 
P (man-woman) <5 = 1/6

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.