Grammar Prepositions Dangling Modifiers

Which sentence is the proper way to use a dangling modifier? 

• Having finished the assignment, the TV was turned on.
• Without knowing his name, it was difficult to introduce him.
• Having finished the assignment, Jill turned on the TV.
• Rummaging in her giant handbag, the sunglasses escaped detection.

Which sentence is the proper way to use a dangling modifier? 

• After reading the great new book, Anna thought the movie based on it was sure to be exciting.
• After reading the the great new book, the movie based on it is sure to be exciting.

Which sentence is the proper way to use a dangling modifier? 

• Hoping to excuse my lateness, the note was written and given to my teacher. 
• Hoping to excuse my lateness, I wrote a note and gave it to my teacher. 

Which sentence is the proper way to use a dangling modifier? 

• To please the neighbors, some fireworks were set off a day early.
• Though only sixteen years old, the college accepted Martha's application.
  
• Climbing up the ladder carefully, the frightened cat was brought down from the tree.
• Having arrived late for practice, the team captain needed a written excuse.

Is this sentence correct or incorrect?

• Because Maria did not know hisname, it was difficult to introduce him.
• Without knowing his name, it was difficult to introduce him.

Is this sentence correct or incorrect?

• He improve his results, the experiment was done again.
• He improved his results by doing the experiment again

Is this sentence correct or incorrect?

• Reading the regulations, I did not take my dog into the park.
• Reading the regulations, the dog didn't go to the park.