Approximately how much more quickly (in mph) does a pilot traveling 400 mph and rising at an angle of 30o gain altitude versus a
pilot traveling 300 mph and rising at an angle of 40o?
1 answer:
We can find the height of the altitude by the ratio of sin. See my attachment.
sin of angle = side in front of the angle / hypotenuse
sin x = height/distance
If the two pilot is rising in an hour, then the first distance is 400 miles, the second distance is 300 miles.
Find the height of first pilot
height/distance = sin x
height/400 = sin 30°
height = sin 30° × 400
height = 1/2 × 400
height = 200
Find the height of second pilot
height/distance = sin x
height/300 = sin 40°
height = sin 40° × 300
height = 0.642 × 300
height = 192
So the first pilot traveling 400 mph with 30° is more quickly to reach high altitude than the second pilot traveling 300 mph with 40°
sin of angle = side in front of the angle / hypotenuse
sin x = height/distance
If the two pilot is rising in an hour, then the first distance is 400 miles, the second distance is 300 miles.
Find the height of first pilot
height/distance = sin x
height/400 = sin 30°
height = sin 30° × 400
height = 1/2 × 400
height = 200
Find the height of second pilot
height/distance = sin x
height/300 = sin 40°
height = sin 40° × 300
height = 0.642 × 300
height = 192
So the first pilot traveling 400 mph with 30° is more quickly to reach high altitude than the second pilot traveling 300 mph with 40°
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Answer:
0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they pass, or they do not. The probability of an student passing is independent of other students, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Probability that all students pass in a class:
Class of 8 students, which means that
Each student has a 95% chance of passing their class independent of the other students, which means that
This probability is P(X = 8). So
Find the probability that, in exactly one of the two classes, all 8 students pass.
Two classes means that
0.6634 probability all students pass in a class, which means that .
This probability is P(X = 1). So
0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.