An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Calculate the minimum acceptable weight: 18 − 4 1 = 17.75 .
Calculate the maximum acceptable weight: 18 + 4 1 = 18.25 .
Express the unacceptable weights as an inequality: w < 17.75 or 18.25"> w > 18.25 .
The graph should represent the inequality w < 17.75 or 18.25"> w > 18.25 .
Explanation
Understanding the Problem Let's analyze the problem. We know that a box of cereal should weigh 18 ounces. However, the weight can vary by 4 1 of an ounce. This means the acceptable range of weights is 18 − 4 1 to 18 + 4 1 ounces. We need to find the weights that are not acceptable, meaning they are either too light (underfilled) or too heavy (overfilled).
Calculating Minimum Acceptable Weight First, let's calculate the minimum acceptable weight. This is the weight below which the box is considered underfilled and cannot be sold as a full box. We calculate it as: 18 − 4 1 = 17.75 So, any box weighing less than 17.75 ounces is underfilled.
Calculating Maximum Acceptable Weight Next, let's calculate the maximum acceptable weight. This is the weight above which the box is considered overfilled and cannot be sold as a full box. We calculate it as: 18 + 4 1 = 18.25 So, any box weighing more than 18.25 ounces is overfilled.
Expressing Unacceptable Weights as an Inequality Now, we need to express the unacceptable weights as an inequality. Let w be the weight of the cereal box. The unacceptable weights are those less than 17.75 ounces or greater than 18.25 ounces. This can be written as: 18.25"> w < 17.75 or w > 18.25 This means the graph should show two separate intervals: one extending to the left from 17.75 (but not including 17.75) and one extending to the right from 18.25 (but not including 18.25).
Conclusion Therefore, the graph that represents the possible weights of boxes that are overfilled or underfilled and cannot be sold as full boxes should have open circles at 17.75 and 18.25, with the line shaded to the left of 17.75 and to the right of 18.25.
Examples
Imagine you're working in a factory that produces cookies. Each cookie should weigh 2 ounces, but there's a tolerance of 0.1 ounces. If a cookie weighs less than 1.9 ounces or more than 2.1 ounces, it can't be sold. This problem helps you determine which cookies are within the acceptable weight range and which ones need to be discarded, ensuring quality control.
