From the given options, select the pair of words which carries the same relationship to the given pair of words:

Resolute : Determined

Miniature : Small

The answer is Option 4: Miniature : Small

The relationship between "Resolute" and "Determined" is that they are synonyms. Both words describe someone who is firm in their purpose or decision.

Let's examine the options to find a pair with a similar synonymous relationship:

Option 1: Appease : Frighten - These words have opposite meanings. "Appease" means to pacify or soothe, while "frighten" means to cause fear.

Option 2: Hinder : Assist - These words also have opposite meanings. "Hinder" means to obstruct or delay, while "assist" means to help.

Option 3: Bustle : Motionless - These words are antonyms. "Bustle" refers to energetic and noisy activity, while "motionless" means without movement.

Option 4: Miniature : Small - These words are synonyms. "Miniature" means a thing that is much smaller than normal, and "small" refers to something of limited size.

Therefore, the pair of words that carries the same relationship as "Resolute : Determined" is "Miniature : Small".