Question

8.4.3 test (cst): data and mathematical modeling
a company produces items in small batches. the machinery needs to warm up before the items can be produced. the scatterplot shows the time needed to produce batches of different numbers of items.
based on the line of best fit, which of these statements is true?
a. the equipment starts producing items after about 25 minutes of warming up.

Explanation:

Step1: Find the y - intercept

The line of best fit in a linear model \(y = mx + b\) (where \(y\) is production time and \(x\) is the number of items) has a \(y\) - intercept. The \(y\) - intercept represents the time when \(x = 0\) (before any items are produced, i.e., the warm - up time).
Looking at the scatter - plot and the line of best fit, when \(x = 0\), \(y\approx25\). This means that when no items are being produced (\(x = 0\)), the time (\(y\)) is about 25 minutes. So the equipment has a warm - up time of about 25 minutes before it starts producing items (when \(x>0\)).

Answer:

A. The equipment starts producing items after about 25 minutes of warming up.