Answer:
60
Step-by-step explanation:
Let the number of dog owners and cat owners be 4x and 5x
4x = 48
x = 48/4
x = 12
Therefore 5x = 5×12
= 60
Recall the sum identity for cosine:
cos(a + b) = cos(a) cos(b) - sin(a) sin(b)
so that
cos(a + b) = 12/13 cos(a) - 8/17 sin(b)
Since both a and b terminate in the first quadrant, we know that both cos(a) and sin(b) are positive. Then using the Pythagorean identity,
cos²(a) + sin²(a) = 1 ⇒ cos(a) = √(1 - sin²(a)) = 15/17
cos²(b) + sin²(b) = 1 ⇒ sin(b) = √(1 - cos²(b)) = 5/13
Then
cos(a + b) = 12/13 • 15/17 - 8/17 • 5/13 = 140/221
Ok pretty sure the probability of a 5 is 1/5
The probability of a # greater than 3 is 2/5
And the probability of a 2 or 5 is 2/5
(1/5 is 20% and 2/5 is 40% if you need those)
