Answer:
Step-by-step explanation:
A) corresponding angle theorem
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
Answer:
A
Step-by-step explanation:
This is a Bernoulli trial problem.
Since the probability that the seed will germinate is 80% or 0.8, the probability that they won’t germinate is 0.2
Now let’s say the probability to germinate is p and the probability not to is a, we can now set up the Bernoulli equation in this regard. Since we are proposing that exactly 14 will germinate, it means 6 are not expected to germinate
P(14) = 20C14 (0.8)^14 (0.2)^6 = 0.109099700973
Option A is the right answer
Answer:
465
Step-by-step explanation:
Since we are looking for the the number of combinations to have 2 different flavors in the ice cream, we can use the formula for combination.
Our variables are:
n = 31
k = 2
The number of possible combinations of having 2 different flavors out of 31 different flavors is 465.
