Answer:
![41^{\circ}](https://tex.z-dn.net/?f=41%5E%7B%5Ccirc%7D)
Step-by-step explanation:
![~~~~~~\cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}\\\\\\\implies \cos \theta = \dfrac{9}{12}\\\\\\\implies \theta = \cos^{-1} \left( \dfrac 9{12} \right)\\\\\\\implies \theta \approx 41^{\circ}](https://tex.z-dn.net/?f=~~~~~~%5Ccos%20%20%5Ctheta%20%3D%20%5Cdfrac%7B%5Ctext%7BBase%7D%7D%7B%5Ctext%7BHypotenuse%7D%7D%5C%5C%5C%5C%5C%5C%5Cimplies%20%5Ccos%20%5Ctheta%20%3D%20%5Cdfrac%7B9%7D%7B12%7D%5C%5C%5C%5C%5C%5C%5Cimplies%20%5Ctheta%20%3D%20%5Ccos%5E%7B-1%7D%20%5Cleft%28%20%5Cdfrac%209%7B12%7D%20%5Cright%29%5C%5C%5C%5C%5C%5C%5Cimplies%20%5Ctheta%20%5Capprox%2041%5E%7B%5Ccirc%7D)
Answer:
![P(A) = 0.21](https://tex.z-dn.net/?f=%20P%28A%29%20%3D%200.21)
We want to find the probability that a randomly selected freshman from this college does not take an introductory statistics class, so then we can use the complement rule given by:
![P(A') = 1-P(A)](https://tex.z-dn.net/?f=%20P%28A%27%29%20%3D%201-P%28A%29)
Where A is the event of interest (a freshman at a certain college takes an introductory statistics class) and A' the complement (a freshman at a certain college NOT takes an introductory statistics class) and then replacing we got:
![P(A')=1-0.21= 0.79](https://tex.z-dn.net/?f=%20P%28A%27%29%3D1-0.21%3D%200.79)
Step-by-step explanation:
For this problem we know that the probability that a freshman at a certain college takes an introductory statistics class is 0.21, let's define of interest as A and we can set the probability like this:
![P(A) = 0.21](https://tex.z-dn.net/?f=%20P%28A%29%20%3D%200.21)
We want to find the probability that a randomly selected freshman from this college does not take an introductory statistics class, so then we can use the complement rule given by:
![P(A') = 1-P(A)](https://tex.z-dn.net/?f=%20P%28A%27%29%20%3D%201-P%28A%29)
Where A is the event of interest (a freshman at a certain college takes an introductory statistics class) and A' the complement (a freshman at a certain college NOT takes an introductory statistics class) and then replacing we got:
![P(A')=1-0.21= 0.79](https://tex.z-dn.net/?f=%20P%28A%27%29%3D1-0.21%3D%200.79)
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