Does the Bible say we have to repent AND be baptized to be saved?


Peter replied, “Repent and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of your sins. And you will receive the gift of the Holy Spirit. Acts 2:38
            This verse seems to suggest that someone must believe AND be baptized to be saved.  It doesn’t.  Peter implored the people to repent and be baptized.  Salvation occurs at repentance.  Baptism is the outward sign of the salvation.  There are other verses in Acts that talk about salvation resulting from belief and repentance only.
Repent, then, and turn to God, so that your sins may be wiped out, that times of refreshing may come from the Lord… Acts 3:19
Then Peter said, “Surely no one can stand in the way of their being baptized with water. They have received the Holy Spirit just as we have.” So he ordered that they be baptized in the name of Jesus Christ. Then they asked Peter to stay with them for a few days. Acts 10:47-48
The jailer called for lights, rushed in and fell trembling before Paul and Silas. He then brought them out and asked, “Sirs, what must I do to be saved?”
They replied, “Believe in the Lord Jesus, and you will be saved—you and your household.” Then they spoke the word of the Lord to him and to all the others in his house. At that hour of the night the jailer took them and washed their wounds; then immediately he and all his household were baptized. The jailer brought them into his house and set a meal before them; he was filled with joy because he had come to believe in God—he and his whole household.  Acts 16:29-34
Then Paul left the synagogue and went next door to the house of Titius Justus, a worshiper of God. Crispus, the synagogue leader, and his entire household believed in the Lord; and many of the Corinthians who heard Paul believed and were baptized. Acts 18:7-8
            Belief and baptism are important – representing inward and outward transformation.  However, the thief on the cross received the kingdom of God but had no opportunity to be baptized.  Jesus said he would be in heaven.