[tex]\mathbf{\frac{23}{90}}[/tex] fraction of all shapes are circles.
Given that the ratio of the number of white shapes to black shapes is 7:3
Let the number of white shapes be [tex]7n[/tex]
Then the number of black shapes be [tex]3n[/tex]
So total number of shapes [tex]=7n+3n=10n[/tex]
Now ratio of white circles to white squares is 2:7
So the fraction of circles to all white shapes [tex]=\frac{2}{2+7}=\frac{2}{9}[/tex]
Hence the number of white circles [tex]=\frac{2}{9}\times7n=\frac{14n}{9}[/tex]
Again given that the ratio of black circles to the number of black sqaures is 1:2
So the fraction of circles in all black shapes [tex]=\frac{1}{1+2}=\frac{1}{3}[/tex]
The number of black circles [tex]=\frac{1}{3}\times3n=n[/tex]
Total number of circles [tex]=\frac{14n}{9}+n=\frac{14n+9n}{9}=\frac{23n}{9}[/tex]
The fraction of all shapes are circle is [tex]=\frac{\frac{23n}{9}}{10n}=\frac{23n}{90n}=\frac{23}{90}[/tex]
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