An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate 'e' (No Softball): e = 32 − 20 = 12 .
Calculate 'd' (Do Not Swim Total): d = 32 − 22 = 10 .
Calculate 'c' (Do Not Swim & Softball): c = 10 − 5 = 5 .
Calculate 'a' (Swim & Softball) and 'b' (Swim & No Softball): a = 20 − 5 = 15 and b = 22 − 15 = 7 . The answer is a = 15 , b = 7 , c = 5 , d = 10 , e = 12 .
Explanation
Understanding the Problem We are given a table representing the activities of campers at a summer camp. The goal is to find the missing values in the table, which represent the number of campers participating in different activities. We know the total number of campers, the number who swim, the number who play softball, and the number who do not participate in either activity.
Calculating e First, let's find the value of 'e', which represents the number of campers who do not play softball. We can calculate this by subtracting the number of campers who play softball from the total number of campers: e = Total − Softball = 32 − 20 = 12
Calculating d Next, let's find the value of 'd', which represents the total number of campers who do not swim. We can calculate this by subtracting the number of campers who swim from the total number of campers: d = Total − Swim = 32 − 22 = 10
Calculating c Now, let's find the value of 'c', which represents the number of campers who do not swim and play softball. We know that 5 campers do not swim or play softball, and 'd' represents the total number of campers who do not swim. So, we can find 'c' by subtracting 5 from 'd': c = d − 5 = 10 − 5 = 5
Calculating a Now, let's find the value of 'a', which represents the number of campers who swim and play softball. We know that 20 campers play softball in total, and 'c' represents the number of campers who do not swim but play softball. So, we can find 'a' by subtracting 'c' from 20: a = 20 − c = 20 − 5 = 15
Calculating b Finally, let's find the value of 'b', which represents the number of campers who swim but do not play softball. We know that 22 campers swim in total, and 'a' represents the number of campers who swim and play softball. So, we can find 'b' by subtracting 'a' from 22: b = 22 − a = 22 − 15 = 7
Final Answer Therefore, the values that complete the table are: a = 15 , b = 7 , c = 5 , d = 10 , e = 12 .
Examples
Understanding how to fill in tables like this is useful in many real-life situations. For example, if you're organizing a school event, you might use a table to track which students are participating in different activities. By knowing the total number of students and how many are in each activity, you can quickly figure out how many students are doing multiple activities or none at all. This helps with planning and making sure everyone is included.
In an electric device delivering 15.0 A for 30 seconds, approximately 2.81 billion billion electrons flow through it. This is calculated using the relationship between current, charge, and the charge of an electron. The total charge is found by multiplying the current and time, and the number of electrons is calculated using the charge of a single electron.
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