He nine ring wraiths want to fly from barad-dur to rivendell. rivendell is directly north of barad-dur. the dark tower reports t
hat the wind is coming from the west at 68 miles per hour. in order to travel in a straight line, the ring wraiths decide to head northwest. at what speed should they fly (omit units)?
1 answer:
This problem is better understood with a given figure. Assuming that the flight is in a perfect northwest direction such that the angle is 45°, therefore I believe I have the correct figure to simulate the situation (see attached).
Now we are asked to find for the value of the hypotenuse (flight speed) given the angle and the side opposite to the angle. In this case, we use the sin function:
sin θ = opposite side / hypotenuse
sin 45 = 68 miles per hr / flight
flight = 68 miles per hr / sin 45
<span>flight = 96.17 miles per hr</span>
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Answer:
0.2%
Step-by-step explanation:
The given parameters are;
The percentage of product within the correct range = 95%
The percentage of the times the sensor reject boxes of incorrect weight = 98%
The percentage of the times the company reject boxes with correct weight = 1%
We have, FN = 0.9, TN = 9.8, TP = 90 - 0.9 = 89.1, FP = 10 - 9.8 = 0.2
FNR = FN/(FN + TP) = 0.9/(0.9 + 89.1) = 0.01
FPR = 0.2/(0.2 + 9.8) = 0.02
TPR = 89.1/(89.1 + 0.9) = 0.99
TNR = 9.8/(9.8 + 0.2) = 0.98
P(C/A) = TPR × P(C)/((TPR × P(C) + FPR×(1 - P(C)))
Where;
P(C/A) = The probability that a correct weight package is accepted
∴ P(C/A) = 0.99*0.9/(0.99*0.9 + 0.02*0.1) ≈ 0.99776
The probability that a correctly weighed package is rejected, P(C/R), is given as follows;
P(C/R) = 1 - P(C/A)
∴ P(C/R) ≈ 1 - 0.99776 = 0.00224 ≈ 0.2%
The probability that a correctly weighed package is rejected, P(C/R) ≈ 0.2%