a) The fraction of women is [tex]\frac{12}{577}[/tex]
b) The fraction of men is [tex]\frac{565}{577}[/tex]
Step-by-step explanation:
a)
In this part of the problem, we are asked to find what fraction of the prize winners are women.
We have:
[tex]w=24[/tex] (number of prizes awarded to women)
[tex]m=1130[/tex] (number of prizes awarded to men)
First of all, we calculate the total number of prizes awarded:
[tex]p=w+m=24+1130=1154[/tex]
Now we find the fraction of prize winners who were women, which is given by:
[tex]p(w) = \frac{w}{p}=\frac{24}{1154}[/tex]
And we can simplify by dividing both numerators and denominators by 2,
[tex]p(w)=\frac{24}{1154}=\frac{12}{577}[/tex]
b)
The total number of prizes awarded is
[tex]p=1154[/tex]
The number of prizes assigned to men is
[tex]m=1130[/tex]
Therefore, the fraction of prize winners who were men is
[tex]p(m)=\frac{m}{p}=\frac{1130}{1154}=\frac{565}{577}[/tex]
where we simplified the fraction by dividing both the numerator and the denominator by 2.
Learn more about fractions:
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