Let's first denote:
F - a favorable response
F' - an unfavorable response
S - successful
We know that:

So, from the conditional probability, we can calculate:

Answer E.
We will turn the left side into the right side.

Use the identity:



Now use the identity
solved for sin^2 x and for cos^2 x.




Answer: <CDB corresponds to <ECD
Step-by-step explanation:
The angles in similar triangles correspond to each other.
For two angles in similar triangles to correspond to each other, then they have to be in the same position in the triangle. (EX: a 90 degree angle corresponds to another 90 degree angle or an angle across from the shortest side corresponds to another angle in the other triangle across from the shortest side)
In this case, <CDB is to the right of the 90 degree angle, so the angle it will correspond to is the angle in the other triangle which is opposite to the 90 degree angle, which is <CED.
<CED is not <ECD, so that answer is wrong.
Tell me if I need to clarify anything - this topic is kind of hard to explain :/
I don’t know the answer but I hope someone else doesnt
Answer: Right (Last option)
Step-by-step explanation:
As you can see in the figure, the parallel lines AD and GJ are intersected by two lines.
The line EL intersects the parallel lines and there are two angles that are formed by this intersections which are located on the exterior of AD and GJ, but on opposite sides of EL, (these angles are called "Alternate exterior angles" and they are congruent), which are:
∠LHJ and ∠EBA
You can observe that the angle ∠EBA is indicated with a square. This means that the measure of that angle is 90° (Right angle).
Therefore, if ∠EBA=90°, then ∠LHJ =90°