Suppose that you wish to cross a river that is 3900 feet wide and flowing at a rate of 5 mph from north to south. Starting on th
e eastern bank, you wish to go directly across the river to a point on the western bank opposite your current position. You have a boat that travels at a constant rate of 11 mph.
a) In what direction, measured clockwise from north, should you aim your boat? Include appropriate units in your answer.
b) How long will it take you to make the trip? Include appropriate units in your answer.\
Please show your work so I may understand. Thank you so much!
a) In what direction, measured clockwise from north, should you aim your boat? Include appropriate units in your answer.
b) How long will it take you to make the trip? Include appropriate units in your answer.\
Please show your work so I may understand. Thank you so much!
1 answer:
Answer:
a) 297°
b) 4.52 minutes
Step-by-step explanation:
a) Consider the attached figure. The boat's actual path will be the sum of its heading vector BA and that of the current, vector AC. The angle of BA north of west has a sine equal to 5/11. That is, the heading direction measured clockwise from north is ...
270° + arcsin(5/11) = 297°
__
b) The "speed made good" is the boat's speed multiplied by the cosine of the angle between the boat's heading and the boat's actual path. That same value can be computed as the remaining leg of the right triangle with hypotenuse 11 and leg 5.
boat speed = √(11² -5²) = √96 ≈ 9.7980 . . . . miles per hour
Then the travel time will be ...
time = distance/speed
(3900 ft)×(1 mi)/(5280 ft)×(60 min)/(1 h)/(9.7980 mi/h) ≈ 4.523 min
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Answer:
a) The best estimator for the population mean is given by the sample mean
b) The 99% confidence interval would be given by (4.969;6.431)
c) We are 99% confident that the true mean for th number of gallons of gasoline sold to his customers is between 4.969 and 6.431.
Step-by-step explanation:
1) Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean for the sample
population mean (variable of interest)
represent the population standard deviation
n=45 represent the sample size
2) Part a
The best estimator for the population mean is given by the sample mean
3) Part b. Develop a 99 percent confidence interval for the population mean.
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 99% confidence interval would be given by (4.969;6.431)
4) Part c. Interpret the meaning of part (b).
On this case we can say this: We are 99% confident that the true mean for th number of gallons of gasoline sold to his customers is between 4.969 and 6.431.