Question 1182658
Here's how to solve this problem:

1. **Let 'f' represent the number of flowers.** The equation given is:

   Number of butterflies = 86 + 0.25f

2. **The hiker observed 450 butterflies.**  This is the *actual* (observed) number of butterflies.

3. **The residual is -27.** The residual is the difference between the actual value and the predicted value from the line of best fit.  So:

   Residual = Actual number of butterflies - Predicted number of butterflies

   -27 = 450 - (86 + 0.25f)

4. **Solve for 'f' (number of flowers):**

   -27 = 450 - 86 - 0.25f
   -27 = 364 - 0.25f
   0.25f = 364 + 27
   0.25f = 391
   f = 391 / 0.25
   f = 1564

Therefore, there are **1564** flowers in the field.