Question

the height of a stack of dvd cases is in a proportional relationship to the number of cases in the stack. a stack of 8 cases and its height are shown. find the constant of proportionality. then use the constant of proportionality to find the height of a stack of 12 cases. the constant of proportionality is \boxed{} millimeters per dvd case. enter your answer in the answer box and then click check answer.

Explanation:

Step1: Identify the given values

We know that for 8 DVD cases, the height is 104 mm (from the table, assuming the height of 8 cases is 104 mm as it's a common problem setup). Let \( h \) be the height and \( n \) be the number of cases. Since \( h \) is proportional to \( n \), we have \( h = k \cdot n \), where \( k \) is the constant of proportionality (height per case).

Step2: Calculate the constant of proportionality

To find \( k \), we use the formula \( k=\frac{h}{n} \). Substituting \( h = 104 \) mm and \( n = 8 \) cases, we get \( k=\frac{104}{8} \).

Step3: Simplify the fraction

\( \frac{104}{8}=13 \). So the constant of proportionality \( k \) is 13 millimeters per DVD case.

Answer:

13