Which of the following correctly describes the bus distance constraint?

Question

BlackTom AI · Accepted Answer

2 ≤ B ≤ 10 because the bus distance variable B is bounded below by 2 and above by 10 (inclusive). This statement captures the allowable range for B exactly.

1) Relevant knowledge points and concepts
- A constraint of the form a ≤ B ≤ b means B can take any value between a and b inclusive.
- When comparing multiple-choice range statements, check both the lower bound and the upper bound for consistency with the given constraint.
- Inclusive inequalities (≤) include the endpoints a and b.

2) Step-by-step reasoning
- The correct constraint is specified as B having a minimum value of 2 and a maximum value of 10. That is written algebraically as 2 ≤ B ≤ 10.
- Evaluate each option by comparing its lower and upper bounds to the authoritative constraint (2 to 10).

3) Intermediate checks/calculations
- Option a: 2 ≤ B ≤ 10 — lower bound = 2 (matches), upper bound = 10 (matches). Exact match.
- Option b: 1 ≤ B ≤ 25 — lower bound 1 is less than required 2 (permits B = 1 which is invalid); upper bound 25 is greater than 10 (permits B > 10 which is invalid).
- Option c: B ≥ 0 — allows values less than 2 (e.g., 0 or 1) and values greater than 10; does not enforce the upper bound.
- Option d: 0 ≤ B ≤ 10 — allows B = 0 or B = 1 (below required minimum 2), although the upper bound matches 10.

4) Why the correct answer is correct
- Option (a) precisely enforces both the minimum and maximum limits for B. It does not permit values below 2 or above 10, and it includes the endpoints (if endpoints are allowed), so it fully matches the stated bus distance constraint.

5) Why the other options are incorrect (brief)
- (b) Permits values below 2 and above 10 (1 and up to 25), so it’s too wide.
- (c) Only enforces a nonnegative lower bound and no upper bound, so it’s too permissive.
- (d) Allows values 0 and 1 (below 2), so it violates the minimum requirement.

Conclusion: Option a (2 ≤ B ≤ 10) is the correct choice, matching the provided answer.

Which of the following correctly describes the bus distance constraint?单项选择题

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