You just got a free ticket for a boat ride, and you can bring along 2 friends! Unfortunately, you have 5 friends who want to com
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Answer:
84.5 m
Step-by-step explanation:
It is often helpful to draw a diagram for word problems involving geometric relationships. One for this problem is shown below.
The mnemonic SOH CAH TOA reminds you of the relationship between sides of a right triangle:
Tan = Opposite/Adjacent
Here we're given angles of depression measured from the horizontal (as shown in the diagram), but it is more convenient to use angles measured from the vertical. In particular, ∠BAO is the complement of 60°, and its tangent is the ratio OB/OA:
tan(30°) = OB/OA
OB = (200 m)·tan(30°) ≈ 115.47 m . . . . . . multiply by OA, use OA=200 m
Likewise, we have ...
OC = (200 m)·tan(45°) = 200 m
Then the width of the river is the difference between these values:
BC = OC -OB = 200 m - 115.47 m = 84.53 m
Using the binomial distribution, it is found that there is a 0.027 = 2.7% probability that he makes exactly 1 of the 3 free throws.
For each free throw, there are only two possible outcomes, either he makes it, or he misses it. The results of free throws are independent from each other, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- He makes 90% of the free throws, hence
.
- He is going to shoot 3 free throws, hence
.
The probability that he makes exactly 1 is P(X = 1), hence:
0.027 = 2.7% probability that he makes exactly 1 of the 3 free throws.
To learn more about the binomial distribution, you can take a look at brainly.com/question/24863377