Answer: ![\bold{b)\quad \dfrac{2\pi}{3},\dfrac{4\pi}{3},0}](https://tex.z-dn.net/?f=%5Cbold%7Bb%29%5Cquad%20%5Cdfrac%7B2%5Cpi%7D%7B3%7D%2C%5Cdfrac%7B4%5Cpi%7D%7B3%7D%2C0%7D)
<u>Step-by-step explanation:</u>
Note the following identities: tan² x = sec²x - 1
![\sec x=\dfrac{1}{\cos}](https://tex.z-dn.net/?f=%5Csec%20x%3D%5Cdfrac%7B1%7D%7B%5Ccos%7D)
tan² x + sec x = 1
(sec² x -1) + sec x = 1
sec² x + sec x - 2 = 0
(sec x + 2)(sec x - 1) = 0
sec x + 2 = 0 sec x - 1 = 0
sec x = -2 sec x = 1
![\dfrac{1}{\cos x}=-2\qquad \dfrac{1}{\cos x}=1\\\\\cos x=-\dfrac{1}{2}\qquad \cos x=1\\\\x=\dfrac{2\pi}{3}, \dfrac{4\pi}{3}\qquad x=0](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B%5Ccos%20x%7D%3D-2%5Cqquad%20%5Cdfrac%7B1%7D%7B%5Ccos%20x%7D%3D1%5C%5C%5C%5C%5Ccos%20x%3D-%5Cdfrac%7B1%7D%7B2%7D%5Cqquad%20%5Ccos%20x%3D1%5C%5C%5C%5Cx%3D%5Cdfrac%7B2%5Cpi%7D%7B3%7D%2C%20%5Cdfrac%7B4%5Cpi%7D%7B3%7D%5Cqquad%20x%3D0)
Answer:
A lurking variable is a variable that has an important effect on the relationship among the variables in the study, but is not one of the explanatory variables studied. Two variables are confounded when their effects on a response variable cannot be distinguished from each other.
Answer: A
Step-by-step explanation:
For this problem, we need to understand how translations work.
As you can see, the triangles only slide to the right side, along the x axis. Therefore, we can eliminate B and C.
Now, we can see that the triangle has shifted by +8 units. Therefore, A is the correct answer.
False, A person would not want a bank where they could not depend on the staff and be able to come to them if they were having problems with the bank account
Answer:
0.000064 = 0.0064% probability that the box will contain less than the advertised weight of 466 g.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
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 p-value, we get the probability that the value of the measure is greater than X.
N(489,6)
This means that ![\mu = 489, \sigma = 6](https://tex.z-dn.net/?f=%5Cmu%20%3D%20489%2C%20%5Csigma%20%3D%206)
What is the probability that the box will contain less than the advertised weight of 466 g?
This is the p-value of Z when X = 466. So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{466 - 489}{6}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B466%20-%20489%7D%7B6%7D)
![Z = -3.83](https://tex.z-dn.net/?f=Z%20%3D%20-3.83)
has a p-value of 0.000064
0.000064 = 0.0064% probability that the box will contain less than the advertised weight of 466 g.