Place these values in order, from smallest to largest length. show your work.

10 feet
9 feet
145 inches
12 feet
130 inches

Explanation:

9 feet10 feet (10 ft = 10·12 in = 120 in)130 inches12 feet (12 ft = 12·12 in = 144 in)145 inches

Obviously, 9 < 10 < 12, so ordering by feet is easy. Then we need to figure out where the inch measurements belong.

1 foot = 12 inches, so we can figure some references to use to compare to the inch measurements.

  10 feet = 10·12 in = 120 in, so 130 in is longer, by less than 1 ft.

  12 feet = 12·12 in = 144 in, so 145 in is longer.

Justification:

As told in the statement, n stands for the number of bits, and  is the highest number of ways n bits can be arranged in the system.

Now, Antonio wants to show that the character can collect one less key than that. So, that number is less 1, which is what the formula - 1 states.