Why is the annunciation to mary important to catholics? give as many reasons as you can.

As a Catholic I can say that in a moment the salvation depended on the words of Our Lady when she accepted the will of the Lord by saying: "Behold, I am the handmaid of the Lord. May it be done to me according to your word."

We, as Catholic, believe that God created humans with freedom (free will) and that God respects human freedom. Jesus Christ is the greatest proof that God respects our freedom. Jesus is "the image of the invisible God" (Col 1:15), and therefore is the one to whom we turn when we want to discover how God relates to people. Jesus did not force people to follow him or to do what was right. He chose Apostles, but he only invited them to follow, and when Judas turned against him, Jesus did not force him to choose the right thing. He allowed Judas to say no. When Jesus invited the rich young man to follow him, and the rich young man turned away, Jesus did not force him to change his mind (Mk 10:17-22). When Jesus said, "I am the bread of life," and many of his disciples refused to believe him, Jesus did not force them to accept his word; he let them walk away (John 6:60-71). Therefore, Jesus, the image of the invisible God, teaches us that God respects human freedom.

Now, is it possible that, in the most important event in human history, God would disregard human freedom and simply make Mary the Mother of God's Son without her consent? We read in Luke 1 that the angel announced God's will to Mary. The angel waits until Mary says, "Behold, I am the handmaid of the Lord. May it be done to me according to your word." Only then does the angel leave. This indicates that Mary consented to God's will.

The only other possibility is that Mary did not consent. In that case, she became pregnant by a miracle to which she did not freely consent! This would mean that the Son of God became a human being in the womb of a woman who did not want to become his Mother! This would mean that God completely disregarded human freedom and human choice in the one event which would begin the process of our salvation. This is clearly an impossibility. To summarize, there are two possibilities: God either invited Mary to become the Mother of God's Son and accepted her consent, or God simply made Mary the Mother of God's Son without her consent. The first choice, it seems to me, is consonant with the Bible and with our understanding of God as given us through Jesus Christ. The second presents an image of God which is pagan in its implications (for pagans, the gods simply used human beings) and which contradicts Scripture and the nature of God.  

marginal cost is a microeconomic measure that us to evaluate the extent to which the level of production of a good is sustainable in accounting, that is, to how many quantities the company plans to profit from the production of the good.

the concept of marginal cost is simple, it means the cost of producing one more item. for example, in the case of pies, the marginal cost is the cost of producing one more pie than those that have already been produced.

it is important to understand that productive activity influences marginal cost. the marginal cost of some goods can be very high, while others may be insignificant. for example, the marginal cost of producing an extra plane is very high. already the marginal cost of a water company to provide 1l more water is derisory.

in the case of pies, the cost involves the inputs, the labor and the fixed cost, which involves the fixed space of the bakery. the level of production initially has the marginal cost decreasing because there is space and manpower available. however, to produce more you have to hire more workers and buy more inputs. if physical space is limited, workers will conflict with places, inputs and their productivity will decrease, meaning there is an optimum point of production for each level of space and manpower. from this point on, the productivity of the workers will be getting smaller because of lack of space, so that the marginal cost of producing one more pie will be increasing. so, although you have not posted the chart, but if you have the answer, you can see that my explanation goes according to the marginal cost curve that will increase from the 4th pie, answer (c).