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 proportion of each duck type in both samples.
Determine the mean frequency of each duck type using both samples.
Assess the variability between the samples by calculating the variance.
Conclude that both samples can be used to find the mean frequency of each duck.
The correct statement is: Eldrick can use both of these samples to find the mean frequency of each duck.
Explanation
Analyze the problem and data We are given two samples of duck populations and need to determine which statement about the samples is true. The options relate to whether the samples can be used to find the mean frequency of each duck, whether another sample is needed due to variability, or whether only one of the samples should be used.
Calculate total ducks in each sample First, let's calculate the total number of ducks in each sample: Sample 1: 21 + 4 + 9 + 6 = 40 Sample 2: 8 + 17 + 15 + 0 = 40
Calculate proportions in each sample Next, we calculate the proportion of each duck type in each sample: Sample 1:
Mallard: 40 21 = 0.525
Wood Duck: 40 4 = 0.1
Green Wing Teal: 40 9 = 0.225
American Widgeon: 40 6 = 0.15
Sample 2:
Mallard: 40 8 = 0.2
Wood Duck: 40 17 = 0.425
Green Wing Teal: 40 15 = 0.375
American Widgeon: 40 0 = 0
Calculate mean frequency Now, let's calculate the mean frequency of each duck type across both samples:
Mallard: 2 0.525 + 0.2 = 0.3625
Wood Duck: 2 0.1 + 0.425 = 0.2625
Green Wing Teal: 2 0.225 + 0.375 = 0.3
American Widgeon: 2 0.15 + 0 = 0.075
Assess variability To assess the variability between the two samples, we can calculate the variance for each duck type:
Mallard: Va r = 2 ( 0.525 − 0.3625 ) 2 + ( 0.2 − 0.3625 ) 2 = 0.02640625
Wood Duck: Va r = 2 ( 0.1 − 0.2625 ) 2 + ( 0.425 − 0.2625 ) 2 = 0.02640625
Green Wing Teal: Va r = 2 ( 0.225 − 0.3 ) 2 + ( 0.375 − 0.3 ) 2 = 0.005625
American Widgeon: Va r = 2 ( 0.15 − 0.075 ) 2 + ( 0 − 0.075 ) 2 = 0.005625
The total variance is 0.02640625 + 0.02640625 + 0.005625 + 0.005625 = 0.0640625
Conclusion Since the sample sizes are the same and the total variance isn't extremely high, it is reasonable to use both samples to find the mean frequency of each duck. If the variance was significantly higher, taking another sample might be considered. However, based on the given data, using both samples is appropriate.
Final Answer Therefore, the statement that is true is: Eldrick can use both of these samples to find the mean frequency of each duck.
Examples
In wildlife management, understanding population distributions is crucial for conservation efforts. By taking samples at different times or locations, biologists can estimate the average frequency of different species within a region. This information helps in making informed decisions about habitat management, resource allocation, and conservation strategies. For example, if the mean frequency of a certain duck species is declining, conservationists can investigate the causes and implement measures to protect their habitat or reduce threats.
When a device delivers a current of 15.0 A for 30 seconds, approximately 2.81 x 10^21 electrons flow through it. This calculation is based on the total charge delivered and the charge of a single electron. Therefore, knowing the relationship between current, charge, and electrons helps us arrive at this conclusion.
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