An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate a by summing the first row: a = 0.2 + 0.73 = 0.93 .
Calculate b by summing the second row: b = 0.8 + 0.28 = 1.08 .
The completed values for the conditional relative frequency table are a = 0.93 and b = 1.08 .
Therefore, the final answers are: a = 0.93 ; b = 1.08 .
Explanation
Understand the problem We are given a conditional relative frequency table with some missing values, denoted as a and b . Our goal is to find these missing values. The table represents the distribution of towns based on their population size and land area.
Calculate a To find the value of a , we need to sum the conditional relative frequencies for towns with a land area less than 20 sq. mi. This means adding the values in the first row: 0.2 + 0.73 .
Sum the values Calculating the sum, we have: a = 0.2 + 0.73 = 0.93
Calculate b To find the value of b , we need to sum the conditional relative frequencies for towns with a land area greater than 20 sq. mi. This means adding the values in the second row: 0.8 + 0.28 .
Sum the values Calculating the sum, we have: b = 0.8 + 0.28 = 1.08
State the final answer Therefore, the values that complete the conditional relative frequency table are a = 0.93 and b = 1.08 .
Examples
Conditional relative frequency tables are useful in many real-world scenarios. For example, a marketing company might use such a table to analyze customer demographics and purchasing behavior. By categorizing customers based on age and income, the company can determine the probability that a customer in a certain age group will purchase a particular product. This information can then be used to target marketing efforts more effectively, increasing sales and improving customer satisfaction. Similarly, public health officials could use these tables to study the relationship between lifestyle factors and disease prevalence, helping them to design more effective prevention programs.
Approximately 2.81 x 10^{21} electrons flow through the device when a current of 15.0 A is delivered for 30 seconds. We calculate this by using the relationship between current, charge, and time, and then converting charge to the number of electrons. This illustrates how electric charge in a circuit can be quantified through basic physics principles.
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