Trevor took one of his friends out to lunch. The lunches cost $248.40 and he paid 12.5% sales tax. If Trevor left a 15% tip on t
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Answer:
The height of the tree is approximately 21.4 feet
Step-by-step explanation:
We list out the question parameters first as follows;
The distance from the base of the tree where the angle of elevation is measured, d = 10 feet
The angle of elevation to the top of the tree from 10 feet from the base, θ = 65°
Let 'h' represent the height of the tree, then we have;
The line formed by the angle 65° angle, the height of the tree, 'h', and the distance 'd', form a right triangle with 'h' being the opposite leg to the given reference angle, 65°, and 'd' being the adjacent leg
By trigonometric ratio, we have;
∴ h = d × tan(θ)
Plugging in the given values, we get;
h = 10 feet × tan(65°) = 21 feet inches
∴ By rounding to the nearest tenth of a foot, the height of the tree, h ≈ 21.4 feet.
Answer:
a) 0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.
b) 0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.
Step-by-step explanation:
For each component, there are only two possible outcomes. Either they last more than 1,000 hours, or they do not. Components operate independently, 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.
One subsystem has eight identical components, each with a probability of 0.1 of failing in less than 1,000 hours.
So 1 - 0.1 = 0.9 probability of working for more, which means that
a. exactly two of the four components last longer than 1000 hours.
This is P(X = 2) when . So
0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.
b. the subsystem operates longer than 1000 hours.
The subsystem has 8 components, which means that
It will operate if at least 4 components are working correctly, so we want:
In which
So
Then
0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.