The production manager is going to present this information to the company's board of directors. which graph should the manager use to best emphasize that the number of defects has remained relatively consistent throughout the year?

Step-by-step explanation:

First of all, we have to consider that variables that represent time are always independent, because the time doesn't depend on anything. So, in this case the variable months have to be in the horizontal, which is the independent variable correct position, and the vertical axis must contain the dependent variable, which is number of defects. Considering these important details, there are only two possible correct choices, the third and fourth graph.

Among those two, the third one emphasize better the relation between the given variables, basically because the length of the vertical axis is shorter, which allow to observe better the behaviour of the data, that's the only characteristic that differentiate the third graph from the fourth graph.

Therefore, the third graph is the answer.

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.