A source of laser light sends rays AB and AC toward two opposite walls of a hall. The light rays strike the walls at points B an
d C, as shown below:
A source of laser light is at point A on the ground between two parallel walls. The walls are perpendicular to the ground. AB is a ray of light which strikes the wall on the left at point B. The length of AB is 60m.AC is a ray of light which strikes the wall on the right at point C which is 40m above the ground. The ray AB makes an angle of 60 degrees with the ground. The ray AC makes an angle of 45 degrees with the ground.
What is the distance between the walls?
A source of laser light is at point A on the ground between two parallel walls. The walls are perpendicular to the ground. AB is a ray of light which strikes the wall on the left at point B. The length of AB is 60m.AC is a ray of light which strikes the wall on the right at point C which is 40m above the ground. The ray AB makes an angle of 60 degrees with the ground. The ray AC makes an angle of 45 degrees with the ground.
What is the distance between the walls?
2 answers:
Answer: 70 meters.
Step-by-step explanation:
Observe the figure attached.
The distance between the walls is:
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Both triangles are right triangles. Therefore, you can calculate the distance between the walls as following:
- Calculate the distance AD:
- Calculate the distance AE:
Therefore the distance between the walls is:
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Answer:
n=1041 or higher
Step-by-step explanation:
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".
The population proportion have the following distribution
2) Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
Since we don't have a prior estimation for th proportion of interest, we can use this value as an estimation And replacing into equation (b) the values from part a we got:
And rounded up we have that n=1041 or higher.
Using the binomial distribution, it is found that there is a 0.0231 = 2.31% probability that the first person to say yes will occur with the seventh customer.
For each person, there are only two possible outcomes, either they say yes, or they say no. The probability of a person saying yes is independent of any other person, which means that 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:
- The probability that the seventh person is the first to say yes is P(X = 0) when n = 6(first six say no) multiplied by 0.37(probability the seventh say yes).
- 37% say yes, hence
Then:
0.0231 = 2.31% probability that the first person to say yes will occur with the seventh customer.
A similar problem is given at brainly.com/question/24863377