What is 19 and 20 you didn’t put anything
10/16 = 5/8
An equivalent fraction is:
20/32
Answer:
60 and 90
Step-by-step explanation:
![2 \cos(2 \beta + 30) = - \sqrt{3}](https://tex.z-dn.net/?f=2%20%5Ccos%282%20%5Cbeta%20%20%2B%2030%29%20%20%3D%20%20-%20%20%5Csqrt%7B3%7D%20)
![\cos(2 \beta + 30) = - \frac{ \sqrt{3} }{2}](https://tex.z-dn.net/?f=%20%5Ccos%282%20%5Cbeta%20%20%2B%2030%29%20%20%3D%20%20-%20%20%5Cfrac%7B%20%5Csqrt%7B3%7D%20%7D%7B2%7D%20)
![2 \beta + 30 = \cos {}^{ - 1} ( \frac{ - \sqrt{3} }{2} )](https://tex.z-dn.net/?f=2%20%5Cbeta%20%20%2B%2030%20%3D%20%20%5Ccos%20%7B%7D%5E%7B%20-%201%7D%20%28%20%5Cfrac%7B%20%20%20-%20%20%20%5Csqrt%7B3%7D%20%7D%7B2%7D%20%29%20)
First solution.
![2 \beta + 30 = 150](https://tex.z-dn.net/?f=2%20%5Cbeta%20%20%2B%2030%20%3D%20150)
![2 \beta = 120](https://tex.z-dn.net/?f=2%20%5Cbeta%20%20%3D%20120)
![\beta = 60](https://tex.z-dn.net/?f=%20%5Cbeta%20%20%3D%2060)
Second solution
![2 \beta + 30 = 210](https://tex.z-dn.net/?f=2%20%5Cbeta%20%20%2B%2030%20%3D%20210)
![2 \beta = 180](https://tex.z-dn.net/?f=2%20%5Cbeta%20%20%3D%20180)
![\beta = 90](https://tex.z-dn.net/?f=%20%5Cbeta%20%20%3D%2090)
![4^{x} = 64](https://tex.z-dn.net/?f=%204%5E%7Bx%7D%20%3D%2064)
By taking <span>logarithmic of base 10
∴ </span><span>
![log 4^{x} = log 64](https://tex.z-dn.net/?f=%20log%204%5E%7Bx%7D%20%3D%20log%2064)
∴ x log 4 = log 64
∴
![x = \frac{log \ 64}{log \ 4}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7Blog%20%5C%2064%7D%7Blog%20%5C%204%7D%20)
∴ The correct choice is
</span><span>x = log base 10 of 64, all over log base 10 of 4</span>
20% can be represented as 1/5.
Therefore you're expected to win 1 ticket out of every 5 you purchase. So if you purchase 50 you can expect to win 10 tickets. Therefore the answer is C.