Question

in a meadow filled with wildflowers, a hiker observes 450 butterflies. scientists have been studying this meadow for years and have discovered that the number of butterflies depends on the number of flowers in the field. the line of best - fit that they calculated is shown below: number of butterflies = 88 + 0.2(number of flowers). if the hiker’s observation is analyzed, the residual for the number of butterflies is - 14. how many flowers are there in the field?
there are \\(\square\\) flowers in the field.

Explanation:

Step1: Recall residual formula

Residual = Observed value - Predicted value

Step2: Define variables and plug in values

Let $F$ = number of flowers. Observed butterflies = 450, Residual = -14, Predicted butterflies = $88 + 0.2F$.
$-14 = 450 - (88 + 0.2F)$

Step3: Simplify the equation

$-14 = 450 - 88 - 0.2F$
$-14 = 362 - 0.2F$

Step4: Isolate the term with $F$

$0.2F = 362 + 14$
$0.2F = 376$

Step5: Solve for $F$

$F = \frac{376}{0.2}$

Answer:

1880