An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Fill missing table entries: calculate each missing value using row and column totals.
Determine the number of officers: find the total number of officers from the completed table.
Calculate personnel who are either enlisted or have a civilian marriage: use the principle of inclusion-exclusion.
Calculate personnel who are neither enlisted nor have a civilian marriage: subtract those who are either enlisted or have a civilian marriage from the total personnel. 18 , 319 .
Explanation
Analyze the problem and data We are given a contingency table representing active Naval military personnel, cross-classified by pay grade and marital status. Our task is to fill in the missing entries and answer questions about the data.
Calculate missing entries First, we need to calculate the missing values in the table.
Missing entry in row M 2 column G 2 (Single with children, Officer): M 2 , G 2 = 16 , 361 − 14 , 786 = 1 , 575
Missing entry in row M 2 column G 3 (Single with children, Warrant): Since the sum of M 2 , G 1 , M 2 , G 2 and M 2 , G 3 must equal the total for M 2 (16,361), and we have values for M 2 , G 1 and M 2 , G 2 , we can deduce that M 2 , G 3 = 0 .
Missing entry in row M 3 column G 3 (Joint service marriage, Warrant): Let this entry be x . The total for column G 3 is 1,657. So, 72 + 0 + x + 1427 = 1657 , which means x = 1657 − 72 − 1427 = 158 .
Missing total for row M 3 (Joint service marriage): M 3 = 14 , 723 + 2 , 688 + 158 = 17 , 569 .
Missing entry in column G 2 (Officer): G 2 = 13 , 919 + 1 , 575 + 2 , 688 + 32 , 036 = 50 , 218 .
Answer the questions Now, let's answer the questions: b. How many are officers? The number of officers is the value we calculated for the total in column G 2 , which is 50,218. c. How many are enlisted and have a civilian marriage? This information is directly available in the table: 124,971. d. How many are either enlisted or have a civilian marriage? We use the principle of inclusion-exclusion: ∣ E n l i s t e d ∪ C i v i l ian ∣ = ∣ E n l i s t e d ∣ + ∣ C i v i l ian ∣ − ∣ E n l i s t e d ∩ C i v i l ian ∣ .
∣ E n l i s t e d ∣ = 272 , 591 , ∣ C i v i l ian ∣ = 158 , 434 , ∣ E n l i s t e d ∩ C i v i l ian ∣ = 124 , 971 .
Therefore, ∣ E n l i s t e d ∪ C i v i l ian ∣ = 272 , 591 + 158 , 434 − 124 , 971 = 306 , 054 .
e. How many are neither enlisted nor have a civilian marriage? We subtract the number of personnel who are either enlisted or have a civilian marriage from the total number of personnel: T o t a l − ∣ E n l i s t e d ∪ C i v i l ian ∣ = 324 , 373 − 306 , 054 = 18 , 319 .
State the final answer a. The missing entries are: 1,575; 0; 158; 17,569; 50,218. b. There are 50,218 officers. c. There are 124,971 that are enlisted and have a civilian marriage. d. There are 306,054 that are either enlisted or have a civilian marriage. e. There are 18,319 that are neither enlisted nor have a civilian marriage.
Examples
Contingency tables are useful in many real-world scenarios, such as analyzing customer demographics in marketing, assessing risk factors in healthcare, or evaluating the effectiveness of educational programs. For instance, a company might use a contingency table to understand the relationship between customer age and product preference, helping them to tailor marketing campaigns to specific age groups. Similarly, in healthcare, a contingency table could be used to study the association between smoking habits and the incidence of lung cancer, providing valuable insights for public health initiatives. These tables provide a structured way to examine relationships between different categories and make informed decisions based on the data.
In 30 seconds, approximately 2.81 × 1 0 21 electrons flow through the device which delivers a current of 15.0 A . This is calculated by first finding the total charge using the formula Q = I × t , and then converting that charge into the number of electrons using the charge of a single electron. The calculation shows the direct relationship between electrical current, time, and the flow of charge at the electron level.
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