Question

a horse owner has 50 lbs of hay that is 6% protein by weight. he adds x lbs of oats that is 12% protein by weight. the function y = (0.06(50) + 0.12x)/(50 + x) models the percent of protein, y, in the final mixture of feed. what is the y-intercept of the function that models the percent of protein in the final mixture? the y-intercept is \boxed{}

Explanation:

Step1: Recall y-intercept definition

The y-intercept of a function is the value of \( y \) when \( x = 0 \).

Step2: Substitute \( x = 0 \) into the function

Given the function \( y=\frac{0.06(50)+0.12x}{50 + x} \), substitute \( x = 0 \):

$$ y=\frac{0.06(50)+0.12(0)}{50+0} $$

Step3: Simplify the expression

First, calculate the numerator: \( 0.06(50)=3 \) and \( 0.12(0) = 0 \), so the numerator is \( 3+0 = 3 \). The denominator is \( 50+0 = 50 \). Then \( y=\frac{3}{50}=0.06 \), which is \( 6\% \).

Answer:

\( 0.06 \) (or \( 6\% \))