3+2+1/2+1/7
5+1/2+1/7
5+7/14+2/14
5+9/14
5 9/14
Considering the area of the hole, it is found that there is a 4.9% probability of hitting a ball into the circular hole.
<h3>What is the area of a circle?</h3>
The area of a circle of radius r is given by:

In this problem, the hole has a diameter of 1 ft, hence it is radius is of r = 1 ft/2 = 0.5 ft, and it's area is given by:

Hence the probability is given by:
p = 0.7854/16 = 0.049 = 4.9%
More can be learned about probabilities at brainly.com/question/14398287
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Answer:
B
Step-by-step explanation:
45 grams of popcorn/15 grams of cheese = 3 grams of popcorn per 1 gram of cheese
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
To find out if the triangle is a right triangle, we must check if the following equation is true:

on the left side, we have:

and on the right side, we have:

since on both sides we get 625, we have that the brace forms a right triangle.