Answer:
![\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D)
Step-by-step explanation:
The given ratio is ![\frac{18}{27}](https://tex.z-dn.net/?f=%5Cfrac%7B18%7D%7B27%7D)
9 is the common factor of 18 and 27
divide numerator and denominator by 9
![\frac{18/9}{27/9} =\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B18%2F9%7D%7B27%2F9%7D%20%3D%5Cfrac%7B2%7D%7B3%7D)
hence
is proportion with ![\frac{18}{27}](https://tex.z-dn.net/?f=%5Cfrac%7B18%7D%7B27%7D)
we know that
The measurement of the exterior angle is the semi-difference of the arcs which comprises
In this problem
∠FGH is the exterior angle
∠FGH=![50\°](https://tex.z-dn.net/?f=50%5C%C2%B0)
∠FGH=
-----> equation A
![arc\ FEH+arc\ FH=360\°](https://tex.z-dn.net/?f=arc%5C%20FEH%2Barc%5C%20FH%3D360%5C%C2%B0)
--------> equation B
Substitute equation B in equation A
![100\°=(arc\ FEH-[360\°-arc\ FEH])](https://tex.z-dn.net/?f=100%5C%C2%B0%3D%28arc%5C%20FEH-%5B360%5C%C2%B0-arc%5C%20FEH%5D%29)
![100\°=2arc\ FEH-360\°](https://tex.z-dn.net/?f=100%5C%C2%B0%3D2arc%5C%20FEH-360%5C%C2%B0)
![2arc\ FEH=360\°+100\°](https://tex.z-dn.net/?f=2arc%5C%20FEH%3D360%5C%C2%B0%2B100%5C%C2%B0)
![arc\ FEH=230\°](https://tex.z-dn.net/?f=arc%5C%20FEH%3D230%5C%C2%B0)
therefore
<u>The answer is</u>
The measure of arc FEH is equal to ![230\°](https://tex.z-dn.net/?f=230%5C%C2%B0)
Enrolement increased by 30% that means last year=100%
incease of 30%=30+100=130% now
now=182
percent means parts out of 100 so
130%=130/100=13/10
182=13/10 of x (x represents the number last year)
of means multipy so
182=13/10 times x
multiply both sides by 10/13 to clear fraction
182 times 10/13=x=140
140 students last year
20% of 100 is 20. divide that by 2 to get 20% of 50. 20/2 is 10. 20% of 50 is 10. There are 10 blue marbles.
Hope it helped :)
Ali