An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate the number of personnel who are either enlisted or have a civilian marriage using the inclusion-exclusion principle: 272 , 591 + 158 , 434 − 124 , 971 = 306 , 054 .
Calculate the number of personnel who are neither enlisted nor have a civilian marriage by subtracting the previous result from the total number of personnel: 324 , 373 − 306 , 054 = 18 , 319 .
Calculate the number of personnel who do not have a joint service marriage by subtracting the number of personnel with a joint service marriage from the total number of personnel: 324 , 373 − 17 , 476 = 306 , 897 .
The number of personnel who do not have a joint service marriage is 306 , 897 .
Explanation
Understand the problem and provided data We are given a contingency table for active Naval military personnel, cross-classified by marital status and pay grade. We need to find the number of personnel who are either enlisted or have a civilian marriage, the number of personnel who are neither enlisted nor have a civilian marriage, and the number of personnel who do not have a joint service marriage.
Calculate the number of personnel who are either enlisted or have a civilian marriage Let E be the event that a person is enlisted, and C be the event that a person has a civilian marriage. We want to find n ( E ∪ C ) , the number of personnel who are either enlisted or have a civilian marriage. We can use the inclusion-exclusion principle: n ( E ∪ C ) = n ( E ) + n ( C ) − n ( E ∩ C ) . From the table, n ( E ) = 272 , 591 and n ( C ) = 158 , 434 . We are given that n ( E ∩ C ) = 124 , 971 . Therefore, n ( E ∪ C ) = 272 , 591 + 158 , 434 − 124 , 971 = 306 , 054.
Calculate the number of personnel who are neither enlisted nor have a civilian marriage Let T be the total number of personnel. From the table, T = 324 , 373 . We want to find the number of personnel who are neither enlisted nor have a civilian marriage, which is n (( E ∪ C ) c ) = T − n ( E ∪ C ) . Therefore, n (( E ∪ C ) c ) = 324 , 373 − 306 , 054 = 18 , 319.
Calculate the number of personnel who do not have a joint service marriage Let J be the event that a person has a joint service marriage. We want to find the number of personnel who do not have a joint service marriage, which is n ( J c ) = T − n ( J ) . From the table, n ( J ) = 17 , 476 . Therefore, n ( J c ) = 324 , 373 − 17 , 476 = 306 , 897.
State the final answer The number of personnel who are either enlisted or have a civilian marriage is 306,054. The number of personnel who are neither enlisted nor have a civilian marriage is 18,319. The number of personnel who do not have a joint service marriage is 306,897.
Examples
Understanding contingency tables and set operations like unions and complements is crucial in many real-world scenarios. For instance, in marketing, companies use these concepts to analyze customer demographics and preferences. They might want to know how many customers are either subscribed to a newsletter or have made a purchase in the last month. Similarly, in public health, these methods can help determine the number of people who are vaccinated against a disease but do not have any pre-existing conditions, aiding in targeted healthcare interventions.
A device with a current of 15.0 A flowing for 30 seconds delivers approximately 2.81 x 10^21 electrons. This is calculated using the charge-current-time relationship and the charge of a single electron. Thus, around 2.81 trillion trillion electrons flow through the device in that time frame.
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