Yes, (2,4) is the solution of 2x-7y<-10
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There are 16 outcomes. You’d multiply the number of coins there are (4) by itself (4) and get 16.
How to find rapidly the coordinates of Q:
since Q is the center of gravity of the triangle ABC, so we have the following vector relationship
vecQA +vecQB +vecQC =<span>vec0
</span><span>vecQA=(x-3, y+2)
</span><span>vecQB=(x-1, y+5)
</span><span>vecQC=(x-7, y+5)
</span><span>vec0=(0, 0)
</span>
so, vecQA +vecQB +vecQC =<span>vec0 is equivalent to
</span>x-3 +x-1+x-7 =0, and y+2+y+5+<span>y+5=0 so 3x-11=0 implies x=11/3
</span><span>and 3y+12=0 implies y=-12/3
finally the </span><span>the coordinates of point Q is (11/3, -4)</span><span>
</span>
Take the 2/5 and multiple it by 3 to get 6/15....then take the 1/3 and multiple it by 5 to get 5/15. Then add this together (6/15+5/15=....) to get 11/15