Answer:
The distance from the ship to the dock is approximately 5.24 miles
Step-by-step explanation:
From the parameters given in the question, we have;
The angle formed between the dock and the lighthouse = 70°
The angle formed between the dock and the lighthouse at the ship = 80°
The distance between dock and the lighthouse = 5 miles (From a similar question online)
By sine rule, we have;
Therefore, we have;
Therefore;
The distance from the ship to the dock ≈ 5.24 miles
The sample proportion, p-hat, of engineers who have master's degrees is 68.5% out of 200 engineers.
p-hat proportion:
In this proportion, "p" denotes the probability of a certain event occurring or a certain parameter being true for a certain population, but when a population is large, it may be impractical or impossible to measure it directly. So, we have used the proportion for that cases.
The general form for calculating p-hat proportion is,
where
x is the number of successes in the sample, and
y is the size of the sample.
Given,
In a random sample of 200 engineers, 137 have a master's degree.
Here we need to find the the sample proportion, p-hat, of engineers who have master's degrees
According to the question,
x = 137 (number of successes in the sample)
and y = 200 (size of the sample)
Now apply the value on the formula then we get,
So, the value of p-hat is
The results are usually reported as a percentage, which in this case would be
=> 0.685 x 100 = 68.5%
Therefore, the sample proportion, p-hat, of engineers who have master's degrees is 68.5% out of 200 engineers.
To know more about p-hat proportion here
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The trip was 6 hours long.
Step-by-step explanation:
Given,
The time to go to the island = 1 hours.
The return trip took 3/4 of the time of the original trip.
To find the time of the trip.
Let,
The time of the original trip is x hours.
The time for returning =
According to the problem,
1 +
= x
or, x - =
or, =
or, x = ×4 = 6 hours
Hence,
The trip was 6 hours long.
