An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Determine the total number of players: e = 65 .
Calculate the number of left-handed players: d = 65 − 52 = 13 .
Calculate the number of right-handed male players: c = 34 − 6 = 28 .
Calculate the number of left-handed female players: a = 13 − 6 = 7 , and the total number of female players: b = 24 + 7 = 31 . The final answers are: a = 7 , b = 31 , c = 28 , d = 13 , e = 65 .
Explanation
Understanding the Problem We are given a two-way frequency table that summarizes data from a survey of 65 baseball players. The table categorizes players by gender (Female, Male) and favored hand (Right, Left). Our goal is to determine the values of the variables a, b, c, d, and e in the table. We will use the information provided to fill in the missing values.
Finding the Total Number of Players First, we determine the value of 'e', which represents the total number of baseball players surveyed. We know that 65 players were surveyed, so e = 65 .
Calculating the Number of Left-Handed Players Next, we calculate 'd', which represents the total number of players favoring the left hand. We know that the total number of players is 65 and 52 players favor the right hand. Therefore, the number of players favoring the left hand is: d = 65 − 52 = 13 .
Calculating the Number of Right-Handed Male Players Now, we calculate 'c', which represents the number of male players favoring the right hand. We know that there are 34 male players in total, and 6 of them favor the left hand. Therefore, the number of male players favoring the right hand is: c = 34 − 6 = 28 .
Calculating the Number of Left-Handed Female Players We can now calculate 'a', which represents the number of female players favoring the left hand. We know that the total number of players favoring the left hand is 13, and 6 of them are male. Therefore, the number of female players favoring the left hand is: a = 13 − 6 = 7 .
Calculating the Total Number of Female Players Finally, we calculate 'b', which represents the total number of female players. We know that 24 female players favor the right hand, and 7 favor the left hand. Therefore, the total number of female players is: b = 24 + 7 = 31 .
Final Answer In summary, we have found the following values: a = 7 b = 31 c = 28 d = 13 e = 65 These values complete the two-way frequency table.
Examples
Two-way frequency tables are commonly used in market research to analyze customer preferences. For example, a company might survey customers about their favorite product features, categorizing responses by age group and gender. The resulting table helps the company understand which features are most popular among different demographics, informing product development and marketing strategies. This allows for targeted improvements and advertising campaigns, maximizing customer satisfaction and sales.
A device with a current of 15.0 A for 30 seconds will have approximately 2.81 x 10^21 electrons flow through it. This is calculated by first finding the total charge and then relating it to the number of electrons. Using the equations for current and charge allows us to solve for the total number of electrons accurately.
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