Sketch an angle theta in standard position such that theta has the least possible positive measure and the point (-2, Square roo
1 answer:
A sketch of the angle is attached and the six trigonometric functions for each angle are;
sinθ = -½
cosθ = -(√3)/2
tanθ = (√3)/3
cscθ = -2
secθ = -(2√3)/3
cotθ = √3
<h3>How to find the trigonometric ratios?</h3>
We can use the unit circle to figure out the trigonometric functions of θ.
Both the x- and y- coordinates are in the third quadrant, so θ is an obtuse angle (210°), as seen in the figure below.
An angle in standard position is an angle measured with respect to the +x semi-axis. In this question we must derive the six trigonometric functions from the distances between a given point and the origin. The trigonometric functions are described below:
sinθ = -2/4 = -½
cosθ = (-2√3)/4 = -(√3)/2
tanθ = -2/(-2√3) = 1/√3 = (√3)/3
cscθ = 1/sin θ = 1/-½ = -2
secθ = 1/cosθ = 4/(-2√3) = -2/√3 = -(2√3)/3
cotθ = 1/tan θ = -2√3/(-2) = √3
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Answer:
Probablity of getting six in at most three roll= 0.199.
Step-by-step explanation:
Given: Dice rolled at most 3 times untill a 6 occurs.
First, finding the probablity of getting 6 in a dice if rolled once.
Probablity=
We know, dice have six side, therefore, total number of event will be 6.
∴ Probablity of getting six in one roll=
As given, Dice is rolled at most 3 times.
Now, finding the probablity of getting 6 in a dice if rolled 3 times.
∴ Probablity of getting six in three roll=
⇒ Probablity of getting six in three roll=
Taking LCD 216
⇒Probablity of getting six in three roll=
⇒Probablity of getting six in three roll=
∴Probablity of getting six in three roll=0.199
Answer:
15.15% probability that the sample mean will be $192,000 or more.
Step-by-step explanation:
To solve this problem, we need to understand 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:
The probability that the sample mean will be $192,000 or more is
This is 1 subtracted by the pvalue of z when X = 192000. So
By the Central Limit Theorem
has a pvalue of 0.8485.
1-0.8485 = 0.1515
15.15% probability that the sample mean will be $192,000 or more.