Answer: F
Step-by-step explanation:
For a 30-60-90 triangle, we know that the hypotenuse is 2x. Since we know the hypotenuse is 10, we can solve for x.
2x=10
x=5
Now that we know x is 5, we can use this to solve for s and q. The side across from 30° is just x. Since we know x, s is 5.
The side across from 60° is x√3. Since we know what x is, we can just plug in. q is 5√3.
Letter C is correct.
When the function is even, (all powers are even) both ends will go in the same direction.
In this case since the leading coefficient is negative, both ends will go down.
Answer: 0.9730
Step-by-step explanation:
Let A be the event of the answer being correct and B be the event of the knew the answer.
Given: ![P(A)=0.9](https://tex.z-dn.net/?f=P%28A%29%3D0.9)
![P(A^c)=0.1](https://tex.z-dn.net/?f=P%28A%5Ec%29%3D0.1)
![P(B|A^{C})=0.25](https://tex.z-dn.net/?f=P%28B%7CA%5E%7BC%7D%29%3D0.25)
If it is given that the answer is correct , then the probability that he guess the answer ![P(B|A)= 1](https://tex.z-dn.net/?f=P%28B%7CA%29%3D%201)
By Bayes theorem , we have
![P(A|B)=\dfrac{P(B|A)P(A)}{P(B|A)P(A)+P(C|A^c)P(A^c)}](https://tex.z-dn.net/?f=P%28A%7CB%29%3D%5Cdfrac%7BP%28B%7CA%29P%28A%29%7D%7BP%28B%7CA%29P%28A%29%2BP%28C%7CA%5Ec%29P%28A%5Ec%29%7D)
![=\dfrac{(1)(0.9)}{(1))(0.9)+(0.25)(0.1)}\\\\=0.972972972973\approx0.9730](https://tex.z-dn.net/?f=%20%3D%5Cdfrac%7B%281%29%280.9%29%7D%7B%281%29%29%280.9%29%2B%280.25%29%280.1%29%7D%5C%5C%5C%5C%3D0.972972972973%5Capprox0.9730)
Hence, the student correctly answers a question, the probability that the student really knew the correct answer is 0.9730.