An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Find the number of students who have been to Alaska: 14. Relative frequency: 50 14 .
Find the number of students who have been to Hawaii but not Alaska: 15. Relative frequency: 50 15 .
Find the number of students who have not been to Alaska or Hawaii: 21. Relative frequency: 50 21 .
The relative frequencies are: Alaska: 50 14 , Hawaii but not Alaska: 50 15 , Neither: 50 21 .
Explanation
Understand the problem We are given a two-way table that summarizes survey data about students' visits to Alaska and Hawaii. The goal is to find the relative frequencies for three specific categories of students based on their travel history.
Define relative frequency The relative frequency is calculated by dividing the number of students in the specified category by the total number of students surveyed. The total number of students is 50.
Calculate relative frequency for Alaska
Students who have been to Alaska:
From the table, we see that 14 students have been to Alaska.
The relative frequency is 50 14 .
Calculate relative frequency for Hawaii but not Alaska
Students who have been to Hawaii but not Alaska:
From the table, we see that 15 students have been to Hawaii but not Alaska.
The relative frequency is 50 15 .
Calculate relative frequency for neither Alaska nor Hawaii
Students who have not been to Alaska or Hawaii:
From the table, we see that 21 students have not been to Alaska or Hawaii.
The relative frequency is 50 21 .
State the final answer Therefore, the relative frequencies are:
Alaska: 50 14
Hawaii but not Alaska: 50 15
Neither Alaska nor Hawaii: 50 21
Examples
Understanding relative frequencies is useful in many real-world scenarios. For example, if a school wants to start a new club, they might survey students to see what activities they are interested in. The relative frequencies of the responses can help the school decide which clubs are most likely to be popular and successful. In this case, the school could use the relative frequencies to determine the proportion of students interested in different types of clubs, such as sports, arts, or academics. This information can guide the school's decision-making process and ensure that they are offering clubs that meet the needs and interests of their students.
