Question

the linear model ( y = 0.17x + 2.45 ) represents the data a principal collects to determine the relationship between the number of hours of sleep a student gets each night, ( x ), and the students gpa, ( y ). based on the linear model, what gpa can be expected of a student who gets 9 hours of sleep each night?

Explanation:

Step1: Substitute \(x = 9\) into the linear model

Given the linear model \(y=0.17x + 2.45\), when \(x = 9\), we have \(y=0.17\times9+2.45\).

Step2: Calculate the product

First, calculate \(0.17\times9\). Using the rule of decimal - multiplication: \(0.17\times9=(0.1 + 0.07)\times9=0.1\times9+0.07\times9=0.9+0.63 = 1.53\).

Step3: Calculate the sum

Then, add the result of the product to \(2.45\). So \(y=1.53+2.45\). According to the rule of decimal - addition, align the decimal points: \(1.53+2.45=(1 + 2)+(0.53+0.45)=3+0.98 = 3.98\).

Answer:

\(3.98\)