How many different rays can be formed from five collinear points?
2 answers:
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The value of tangent theta is equal to the negative 1. At this value the value of secant theta is .
<h3>What is tangent theta?</h3>
The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,
Given information-
The value of tangent theta is equal to the negative 1.
The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,
The value of tangent theta is equal to the negative 1. Thus put the value in above expression as,
Simplify it further as,
When the value of cosine and sine theta is equal, then the angle exist in 4th quadrant with the value of . Which extent to the
for the cosine function.
In the trigonometry cosine theta is the reciprocal of the secant theta. Thus,
Thus the value of secant theta is
Learn more about the tangent theta here;
Answer:
a) 0.259
b) 0.297
c) 0.497
Step-by-step explanation:
To solve this problem, it is important to know the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central limit theorem
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
a. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes?
Here we have that
This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.
X = 11.2
By the Central Limit Theorem
has a pvalue of 0.6293.
X = 10.8
has a pvalue of 0.3707.
0.6293 - 0.3707 = 0.2586
0.259 probability, rounded to three decimal places.
b. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.5 and 11 minutes?
Subtraction of the pvalue of Z when X = 11 subtracted by the pvalue of Z when X = 10.5. So
X = 11
has a pvalue of 0.5.
X = 10.5
has a pvalue of 0.2033.
0.5 - 0.2033 = 0.2967
0.297, rounded to three decimal places.
c. If you select a random sample of 100 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes?
Here we have that
This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.
X = 11.2
By the Central Limit Theorem
has a pvalue of 0.7486.
X = 10.8
has a pvalue of 0.2514.
0.7486 - 0.2514 = 0.4972
0.497, rounded to three decimal places.