Answer:
In the first quadrant are solutions of the form ![x=\dfrac{\pi}{6}+2\pi k,\ k\in Z.](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B%5Cpi%7D%7B6%7D%2B2%5Cpi%20k%2C%5C%20k%5Cin%20Z.)
In the second quadrant are solutions of the form ![x=\dfrac{5\pi}{6}+2\pi k,\ k\in Z.](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B5%5Cpi%7D%7B6%7D%2B2%5Cpi%20k%2C%5C%20k%5Cin%20Z.)
Step-by-step explanation:
First, solve the equation
This equation is equivalent to equation
![\tan^2 x=\dfrac{1}{3},\\ \\\tan x=\dfrac{1}{\sqrt{3} }\ \text{or }\tan x=-\dfrac{1}{\sqrt{3} }.](https://tex.z-dn.net/?f=%5Ctan%5E2%20x%3D%5Cdfrac%7B1%7D%7B3%7D%2C%5C%5C%20%5C%5C%5Ctan%20x%3D%5Cdfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D%5C%20%5Ctext%7Bor%20%7D%5Ctan%20x%3D-%5Cdfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D.)
The equation
has the solution
![x=\arctan \dfrac{1}{\sqrt{3} }+\pi k,\ k\in Z,\\ \\x=\dfrac{\pi}{6}+\pi k,\ k\in Z.](https://tex.z-dn.net/?f=x%3D%5Carctan%20%5Cdfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D%2B%5Cpi%20k%2C%5C%20k%5Cin%20Z%2C%5C%5C%20%5C%5Cx%3D%5Cdfrac%7B%5Cpi%7D%7B6%7D%2B%5Cpi%20k%2C%5C%20k%5Cin%20Z.)
The equation
has the solution
![x=\arctan \left(-\dfrac{1}{\sqrt{3} }\right)+\pi k,\ k\in Z,\\ \\x=-\dfrac{\pi}{6}+\pi k,\ k\in Z.](https://tex.z-dn.net/?f=x%3D%5Carctan%20%5Cleft%28-%5Cdfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D%5Cright%29%2B%5Cpi%20k%2C%5C%20k%5Cin%20Z%2C%5C%5C%20%5C%5Cx%3D-%5Cdfrac%7B%5Cpi%7D%7B6%7D%2B%5Cpi%20k%2C%5C%20k%5Cin%20Z.)
In the first quadrant are solutions of the form ![x=\dfrac{\pi}{6}+2\pi k,\ k\in Z.](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B%5Cpi%7D%7B6%7D%2B2%5Cpi%20k%2C%5C%20k%5Cin%20Z.)
In the second quadrant are solutions of the form ![x=\dfrac{5\pi}{6}+2\pi k,\ k\in Z.](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B5%5Cpi%7D%7B6%7D%2B2%5Cpi%20k%2C%5C%20k%5Cin%20Z.)
The probability of it happening once is 1/5, since 10/50 simplifies to 1/5. Because the ticket goes back in the bag, the probability stays constant at 1/5.
For it to happen twice, you multiply the probability of it happening once, twice.
1/5 • 1/5 = 1/25 probability of it being Gary's name twice in a row.
Answer:
36,960 feet
Step-by-step explanation:
5280×7=36,960
Answer: I think it’s 40.4%
Step-by-step explanation:
Answer: 4/7
Step-by-step explanation:
The probability of would be 4/7. In total there are 7 bowls of ice cream in total so that will be the denominator. 4 of them are chocolate so it'll be the numerator.