An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
The number of quarts is the input, and the number of liters is the output.
The table displays a relationship between liters and quarts.
The equation I = 0.95 q represents the table.
There are 0.95 liters in every quart.
This is a function because every input has exactly one output.
Explanation
Analyzing the Problem The problem presents a table showing the relationship between quarts (q) and liters (I). We need to determine which statements about this relationship are true.
Identifying Input and Output The table shows that as the number of quarts increases, the number of liters also increases. This suggests a relationship where quarts could be the input and liters the output.
Verifying the Equation Let's check if the equation I = 0.95 q represents the table. We can substitute the values of q from the table into the equation and see if we get the corresponding I values. For example, when q = 1 , I = 0.95 × 1 = 0.95 ; when q = 2 , I = 0.95 × 2 = 1.9 ; when q = 3 , I = 0.95 × 3 = 2.85 ; when q = 4 , I = 0.95 × 4 = 3.8 ; when q = 5 , I = 0.95 × 5 = 4.75 ; when q = 6 , I = 0.95 × 6 = 5.7 . The equation accurately represents the table.
Determining Liters per Quart Since the equation I = 0.95 q holds true, it means that for every quart, there are 0.95 liters.
Checking for Functionality Finally, we need to check if this relationship represents a function. A function requires that each input (number of quarts) has exactly one output (number of liters). Looking at the table, each value of q has a unique value of I. Therefore, this is a function.
Conclusion Based on our analysis, all the given statements are correct:
The number of quarts is the input, and the number of liters is the output.
The table displays a relationship between liters and quarts.
The equation I = 0.95 q represents the table.
There are 0.95 liters in every quart.
This is a function because every input has exactly one output.
Examples
Understanding the relationship between quarts and liters is useful in many real-life situations, such as when you're cooking and need to convert measurements, or when you're traveling and need to understand the volume of liquids in different countries. For example, if a recipe calls for 2 quarts of water, you can use the equation I = 0.95 q to determine that you need 1.9 liters of water. This kind of conversion is essential for ensuring accurate measurements and successful outcomes in various activities.
