Answer:
so what are we trying to figure out?
Step-by-step explanation:
7,15,19,34 are not multiples of four. to find this answer out just divide four into them.
We'll use the following properties of sine and cosine to prove this:
![sin(a)\cdot sin(b) = \frac12(cos(a-b) - cos(a+b))](https://tex.z-dn.net/?f=sin%28a%29%5Ccdot%20sin%28b%29%20%3D%20%5Cfrac12%28cos%28a-b%29%20-%20cos%28a%2Bb%29%29)
![cos(a)\cdot cos(b) = \frac12(cos(a+b) + cos(a-b))](https://tex.z-dn.net/?f=cos%28a%29%5Ccdot%20cos%28b%29%20%3D%20%5Cfrac12%28cos%28a%2Bb%29%20%2B%20cos%28a-b%29%29)
![cos(180+a) = cos(180-a)](https://tex.z-dn.net/?f=cos%28180%2Ba%29%20%3D%20cos%28180-a%29)
Then it's just a matter of filling it in...
sin20sin40 * sin60sin80 = 1/2(cos20 - cos60) * 1/2 (cos20 - cos140) =
1/8( cos40 + 1 - cos160 - cos120 - cos40 - cos80 + cos80 + cos200) =
1/8(1 - cos160 - cos120 + cos200) =
1/8(1 - cos160 - cos120 + cos160) =
1/8(1 - cos120 ) = 1/8( 1 + 1/2 ) = 3/16
Answer:
7/12 of a chance
Step-by-step explanation:
If you have 12 batteries and 5 are dead, 12 - 5 is 7, so there's going to be 7/12 of a chance.