Answer:
So the ratio is 5:4:3
As there are 60 clown fish, divide 60 by 5. =12
12 x 4 = 48 (amount of angel fish)
12 x 3 = 36 (amount of goldfish)
Answer:
![\sin(105) = \frac{\sqrt 2 + \sqrt 6}{4}](https://tex.z-dn.net/?f=%5Csin%28105%29%20%3D%20%5Cfrac%7B%5Csqrt%202%20%2B%20%5Csqrt%206%7D%7B4%7D)
Step-by-step explanation:
Given
![\sin(105^o)](https://tex.z-dn.net/?f=%5Csin%28105%5Eo%29)
Required
Solve
Using sine rule, we have:
![\sin(A + B) = \sin(A)\cos(B) + \sin(B)\cos(A)](https://tex.z-dn.net/?f=%5Csin%28A%20%2B%20B%29%20%3D%20%5Csin%28A%29%5Ccos%28B%29%20%2B%20%5Csin%28B%29%5Ccos%28A%29)
This gives:
![\sin(105^o) = \sin(60 + 45)](https://tex.z-dn.net/?f=%5Csin%28105%5Eo%29%20%3D%20%5Csin%2860%20%2B%2045%29)
So, we have:
![\sin(60 + 45) = \sin(60)\cos(45) + \sin(45)\cos(60)](https://tex.z-dn.net/?f=%5Csin%2860%20%2B%2045%29%20%3D%20%5Csin%2860%29%5Ccos%2845%29%20%2B%20%5Csin%2845%29%5Ccos%2860%29)
In radical forms, we have:
![\sin(60 + 45) = \frac{\sqrt 3}{2} * \frac{\sqrt 2}{2} + \frac{\sqrt 2}{2} * \frac{1}{2}](https://tex.z-dn.net/?f=%5Csin%2860%20%2B%2045%29%20%3D%20%5Cfrac%7B%5Csqrt%203%7D%7B2%7D%20%2A%20%5Cfrac%7B%5Csqrt%202%7D%7B2%7D%20%2B%20%5Cfrac%7B%5Csqrt%202%7D%7B2%7D%20%2A%20%5Cfrac%7B1%7D%7B2%7D)
![\sin(60 + 45) = \frac{\sqrt 6}{4} + \frac{\sqrt 2}{4}](https://tex.z-dn.net/?f=%5Csin%2860%20%2B%2045%29%20%3D%20%5Cfrac%7B%5Csqrt%206%7D%7B4%7D%20%2B%20%5Cfrac%7B%5Csqrt%202%7D%7B4%7D)
Take LCM
![\sin(60 + 45) = \frac{\sqrt 6 + \sqrt 2}{4}](https://tex.z-dn.net/?f=%5Csin%2860%20%2B%2045%29%20%3D%20%5Cfrac%7B%5Csqrt%206%20%2B%20%5Csqrt%202%7D%7B4%7D)
Rewrite as:
![\sin(60 + 45) = \frac{\sqrt 2 + \sqrt 6}{4}](https://tex.z-dn.net/?f=%5Csin%2860%20%2B%2045%29%20%3D%20%5Cfrac%7B%5Csqrt%202%20%2B%20%5Csqrt%206%7D%7B4%7D)
Hence:
![\sin(105) = \frac{\sqrt 2 + \sqrt 6}{4}](https://tex.z-dn.net/?f=%5Csin%28105%29%20%3D%20%5Cfrac%7B%5Csqrt%202%20%2B%20%5Csqrt%206%7D%7B4%7D)
Answer:
1) Event A = 2/3
Event B = 1/2
2) 1/2
Step-by-step explanation:
1)
Event A :
No. we need on dice = 4
Total numbers on dice = 6
Hence sample space of the event = 6
P( getting 4) = 4/6 = 2/3
Event B :
A coin has a head & a tail.
Hence sample space of the event = 2
But as we need tail only ,
P ( getting Tail ) = 1/2 [ if only tossed once ]
2)
Total numbers on a die = 6
Total no. of odd numbers on die = 3 (∵ 1 , 3 & 5 are odd )
Sample space of this event = 6
P (getting an odd number) = 3/6 = 1/2
Answer:
C (reflection across the x access)
Step-by-step explanation:
I got it right on edge
Answer is -5.
Explanation- Since t equals 0. You put 0 in place of every t.
0(2)- 2(0)- 5 =
0-0-5= -5