IDIOMS — Choose the option that best expresses the meaning of the underlined expression in context. Sentence: 'The DIE IS CAST and now let us hope for the best.'

Introduction / Context:
“The die is cast” is a historic idiom attributed to Julius Caesar, meaning an irrevocable step has been taken; the decision has been made and outcomes must be faced. The sentence’s second half (“let us hope for the best”) matches this sense of crossing a point of no return.

Given Data / Assumptions:

• We are at a decisive moment.
• Future results are uncertain but now unavoidable.
• The phrase is metaphorical; “die” refers to a gaming die (singular of dice), not death.

Concept / Approach:
Identify whether the word “die” is about mortality or a game. In idiom history, casting the die means the throw has been made; one cannot take it back. Hence the best paraphrase is “the decision is made.” The other options literalize or misinterpret the components.

Step-by-Step Solution:
1) Recognize allusion to the gaming die.2) Link to “no turning back.”3) Choose “decision is made.”4) Confirm with the clause “hope for the best.”

Verification / Alternative check:
Substitute: “An irrevocable decision has been made; let us hope for the best.” The tone and meaning align perfectly.

Why Other Options Are Wrong:
A) “project is over” signals completion, not irrevocability.C) “death is inevitable” confuses “die” with “death.”D) “cloth has been dyed” misreads “die” as “dye.”

Common Pitfalls:
Misreading homophones (die/dye) and assuming the idiom references mortality rather than decision-making.

Final Answer:
decision is made