To find the ratio of dogs to birds at the second adoption center, we first simplify the given ratio from the first adoption center, which is 4:24.

1. Simplify the Ratio:
   • Divide both terms by 4: $\frac{4}{4} : \frac{24}{4} = 1 : 6$

The simplified ratio of dogs to birds at the first adoption center is 1:6.

2. Find Equivalent Ratios: Now we need to find which of the given options (2:10, 6:25, 7:42, 9:72) is equivalent to 1:6.

   • Check Each Option:
     • 2:10: Simplifies to $\frac{2}{2} : \frac{10}{2} = 1 : 5$ (not equivalent)
     • 6:25: Simplifies to $\frac{6}{6} : \frac{25}{6} = 1 : \frac{25}{6}$ (not equivalent)
     • 7:42: Simplifies to $\frac{7}{7} : \frac{42}{7} = 1 : 6$ (equivalent)
     • 9:72: Simplifies to $\frac{9}{9} : \frac{72}{9} = 1 : 8$ (not equivalent)

Therefore, the ratio of dogs to birds at the second adoption center is 7:42.

Summary:

• The answer is 7:42.

Would you like any further details or explanations? Here are some related questions to consider:

1. What other ratios can you create using the numbers from the first adoption center?
2. How can you determine if two ratios are equivalent?
3. What is the significance of ratios in comparing quantities?
4. Can you provide real-life examples where ratios are commonly used?
5. How would you convert the ratio of 7:42 into a percentage for each animal?

Tip: When simplifying ratios, always divide both terms by their greatest common divisor (GCD).