As a math teacher, Josie frequently makes photocopies of fun activities for her students to do. When the copies come out of the copy machine, they form a stack.

Question

As a math teacher, Josie frequently makes photocopies of fun activities for her students to do. When the copies come out of the copy machine, they form a stack.
This table shows the relationship between the number of copies in the stack, x, and the height (in millimeters) of the stack, y.
x (copies)	y (millimeters)
20	2
50	5
60	6
70	7
According to the values in the table, do x and y have a proportional relationship?
yes
no

GPT-4o mini · Answer

To determine if $ x $ (number of copies) and $ y $ (height in millimeters) have a proportional relationship, we need to check if the ratio $ \frac{y}{x} $ is constant for the values given in the table. Let's calculate the ratio $ \frac{y}{x} $ for each pair of values: 1. For $ x = 20 $: $$ \frac{y}{x} = \frac{2}{20} = \frac{1}{10} = 0.1 $$ 2. For $ x = 50 $: $$ \frac{y}{x} = \frac{5}{50} = \frac{1}{10} = 0.1 $$ 3. For $ x = 60 $: $$ \frac{y}{x} = \frac{6}{60} = \frac{1}{10} = 0.1 $$ 4. For $ x = 70 $: $$ \frac{y}{x} = \frac{7}{70} = \frac{1}{10} = 0.1 $$ Since the ratio $ \frac{y}{x} $ is the same (0.1) for all values of $ x $ and $ y $, we conclude that $ x $ and $ y $ do have a proportional relationship. So the answer is: **yes**.

cesat · Answer

What is the constant of proportionality? Write your answer as a whole number or decimal. millimeters per copy

GPT-4o mini · Answer

The constant of proportionality $ k $ can be found from the ratios $ \frac{y}{x} $ that we previously calculated, which is the same for all pairs of values. The constant of proportionality is: $$ k = \frac{y}{x} = 0.1 \text{ millimeters per copy} $$ Thus, the constant of proportionality is: **0.1 millimeters per copy**.