Find the value of cos(θ) for an angle θ in standard position with a terminal Ray that passes through the point (-5,-12)

D

Step-by-step explanation:

Let's draw a picture (see attachment).

We know that since our point is (-5, -12), it must pass in the third quadrant. Now, if we drop a perpendicular line from the point (-5, -12) to the x-axis, we have a right triangle. Notice that we already know the two leg lengths of this: -5 and -12.

Cosine is adjacent / hypotenuse. Here, the adjacent side to the angle θ is -5. We need to find the hypotenuse, which we can do so by using the Pythagorean Theorem:

c² = a² + b²

c² = (-5)² + (-12)²

c² = 25 + 144 = 169

c = 13

So, the hypotenuse is 13. Now, plug these values in:

cos(θ) = adjacent / hypotenuse = -5/13

The answer is D.

d. -5/13

Step-by-step explanation:

Hypotenuse = sqrt(5² + 12²) = 13

|cos(theta)| = 5/13

Since the angle is in quadrant 3, cos will be negative

Therefore, cos(theta) = -5/13

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560