Prayer seems unanswered
In Acts 12 the church was being persecuted, and Peter was thrown in prison. His friends began praying for him, and they prayed for many hours. So, God answers their prayer. He sends an angel to rescue Peter out of prison, yet when he shows up at their door, at first they don't believe it's really him.
When Peter knocks, a damsel goes to the door, and because she is so excited, forgets to open the door. She runs into the other room to tell everyone that Peter is not only alive, but "he is here!" They don't believe her. Then they all go see what this is about, and are completely astonished when they see Peter. He goes on to tell them about his dramatic rescue by an angel, and now they believe.
There will always be doubters, but let's not be like them. Let's build our faith daily by getting the Word of God in our hearts. As we read and speak the Word, faith will come. Then we'll have faith to believe when we pray. We'll have faith to receive when we pray, and our prayers will be answered.
So then faith cometh by hearing, and hearing by the word of God. Romans 10:17
Peter's angel gets him out of jail Acts 12:4-17
And when he (Herod the King) had apprehended him (Peter), he put him in prison, and delivered him to four quaternions of soldiers to keep him; intending after Easter to bring him forth to the people. Peter therefore was kept in prison: but prayer was made without ceasing of the church unto God for him. And when Herod would have brought him forth, the same night Peter was sleeping between two soldiers, bound with two chains: and the keepers before the door kept the prison. And, behold, the angel of the Lord came upon him, and a light shined in the prison: and he smote Peter on the side, and raised him up, saying, Arise up quickly. And his chains fell off from his hands. And the angel said unto him, Gird thyself, and bind on thy sandals. And so he did. And he saith unto him, Cast thy garment about thee, and follow me. And he went out, and followed him; and wist not that it was true which was done by the angel; but thought he saw a vision. When they were past the first and the second ward, they came unto the iron gate that leadeth unto the city; which opened to them of his own accord: and they went out, and passed on through one street; and forthwith the angel departed from him. And when Peter was come to himself, he said, Now I know of a surety, that the Lord hath sent his angel, and hath delivered me out of the hand of Herod, and from all the expectation of the people of the Jews. And when he had considered the thing, he came to the house of Mary the mother of John, whose surname was Mark; where many were gathered together praying. And as Peter knocked at the door of the gate, a damsel came to hearken, named Rhoda. And when she knew Peter's voice, she opened not the gate for gladness, but ran in, and told how Peter stood before the gate. And they said unto her, Thou art mad. But she constantly affirmed that it was even so. Then said they, It is his angel. But Peter continued knocking: and when they had opened the door, and saw him, they were astonished. But he, beckoning unto them with the hand to hold their peace, declared unto them how the Lord had brought him out of the prison. And he said, Go shew these things unto James, and to the brethren. And he departed, and went into another place.