Question

question 5
annabelle measured her heart rate every 5 minutes during a recent hour - long workout. a quadratic regression on the data resulted in the equation $y = - 0.09x^{2}+5.76x + 83.29$.
use the regression equation to determine annabelles heart rate after working out for 30 minutes. (round your answer to the nearest beat per minute.)

Explanation:

Step1: Substitute x=30 into equation

$y = -0.09(30)^2 + 5.76(30) + 68.29$

Step2: Calculate squared term

$30^2 = 900$, so $-0.09 \times 900 = -81$

Step3: Calculate linear term

$5.76 \times 30 = 172.8$

Step4: Sum all terms

$y = -81 + 172.8 + 68.29$

Step5: Compute final value

$y = 160.09$

Step6: Round to nearest integer

$y \approx 160$

Answer:

160 beats per minute