What is the ratio of the blue triangles to all the triangles?

Stars = 6  
Triangles = 6  
Circles = 12

Ratio of stars : triangles : circles = $6 : 6 : 12$  
Divide all numbers by their greatest common divisor, which is 6.
$$
\frac{6}{6} : \frac{6}{6} : \frac{12}{6}
$$
$$
1 : 1 : 2
$$
The ratio is $\boxed{\text{1 : 1 : 2}}$.

Total marbles = 30  
Blue marbles = 17  
Red marbles = 4  
Green marbles = $30 - 17 - 4 = 9$

Ratio of blue : red : green = $17 : 4 : 9$  
These numbers do not have a common divisor other than 1, so the ratio is already in its simplest form.  
The ratio is $\boxed{\text{17 : 4 : 9}}$.

Blue triangles = 9  
Yellow triangles = 6  
Total triangles = $9 + 6 = 15$

Ratio of blue triangles : all triangles = $9 : 15$  
Divide both numbers by their greatest common divisor, which is 3.
$$
\frac{9}{3} : \frac{15}{3}
$$
$$
3 : 5
$$
The ratio is $\boxed{\text{3 : 5}}$.

Red circles = 4  
Green circles = 8  
Total circles = $4 + 8 = 12$

Ratio of red circles : all circles = $4 : 12$  
Divide both numbers by their greatest common divisor, which is 4.
$$
\frac{4}{4} : \frac{12}{4}
$$
$$
1 : 3
$$
The ratio is $\boxed{\text{1 : 3}}$.

Total marbles = 28  
Yellow marbles = 6  
Orange marbles = 20  
Purple marbles = $28 - 6 - 20 = 2$

Ratio of purple marbles : all marbles = $2 : 28$  
Divide both numbers by their greatest common divisor, which is 2.
$$
\frac{2}{2} : \frac{28}{2}
$$
$$
1 : 14
$$
The ratio is $\boxed{\text{1 : 14}}$.

Total horses = 22  
White horses = 12  
Black horses = $22 - 12 = 10$

Ratio of white horses : black horses = $12 : 10$  
Divide both numbers by their greatest common divisor, which is 2.
$$
\frac{12}{2} : \frac{10}{2}
$$
$$
6 : 5
$$
The ratio is $\boxed{\text{6 : 5}}$.