An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
A current of 15.0 A flowing for 30 seconds results in approximately 2.81 × 1 0 21 electrons moving through the circuit. This is calculated using the total charge formula and the charge of a single electron. Therefore, the number of electrons flowing through the device is significant and demonstrates the relationship between current, charge, and time.
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Calculate the mean frequency of each duck type using both samples.
Assess the variability between the two samples for each duck type.
Evaluate each of the given statements based on the calculated means and variability.
Determine that Monique can use both samples to find the mean frequency of each duck.
M o ni q u e c an u se b o t h s am pl es t o f in d t h e m e an f re q u e n cy o f e a c h d u c k .
Explanation
Analyze the problem We are given two samples of duck populations and need to determine which statement about the samples is true. The options involve using both samples, taking another sample due to variability, or using only one of the samples.
Calculate the mean frequency First, let's calculate the mean frequency for each duck type using both samples. This will help us assess the overall population distribution. The mean is calculated as follows:
M e an = 2 S am pl e 1 + S am pl e 2
For Mallards: M e an = 2 17 + 21 = 19
For Wood Ducks: M e an = 2 8 + 7 = 7.5
For Green Wing Teal: M e an = 2 10 + 8 = 9
For American Widgeon: M e an = 2 5 + 6 = 5.5
Assess the variability Next, let's assess the variability between the two samples for each duck type. This will help us determine if the samples are consistent. The variability is calculated as the absolute difference between the counts in the two samples:
Va r iabi l i t y = ∣ S am pl e 1 − S am pl e 2∣
For Mallards: Va r iabi l i t y = ∣17 − 21∣ = 4
For Wood Ducks: Va r iabi l i t y = ∣8 − 7∣ = 1
For Green Wing Teal: Va r iabi l i t y = ∣10 − 8∣ = 2
For American Widgeon: Va r iabi l i t y = ∣5 − 6∣ = 1
Evaluate the statements Now, let's evaluate each statement:
"Monique can use both samples to find the mean frequency of each duck." This is true. Using both samples provides a more representative estimate of the population. The mean frequencies calculated above (19, 7.5, 9, 5.5) are reasonable estimates.
"Monique should take another sample because there is too much variability in the two samples." The variability is relatively low (4, 1, 2, 1). Taking another sample might provide more data, but the current variability doesn't necessarily warrant it.
"Monique should use only the first sample to find the mean frequency of each duck." This is not ideal because it ignores the information from the second sample.
"Monique should use only the second sample to find the mean frequency of each duck." This is also not ideal because it ignores the information from the first sample.
Conclusion Based on the analysis, the most accurate statement is that Monique can use both samples to find the mean frequency of each duck.
Examples
In wildlife management, estimating population sizes is crucial for conservation efforts. By taking multiple samples and calculating the mean frequency of different species, biologists can get a more accurate representation of the overall population. This helps in making informed decisions about habitat management, hunting regulations, and other conservation strategies. For example, if the mean frequency of a particular duck species is declining, conservationists might implement measures to protect their breeding grounds or reduce hunting pressure.
