at the equator: 8 mm
at the tropics (halfway toward the poles): 12 mm
at the poles: 17 mm

Still at the equinox, intensity at approximately 49°N (Vancouver): at this latitude, the intensity will be about 75% as intense as at the Tropic of Cancer. Multiply the intensity at tropics (in %) by 0.75 = ______%

Question

at the equator: 8 mm
at the tropics (halfway toward the poles): 12 mm
at the poles: 17 mm

Still at the equinox, intensity at approximately 49°N (Vancouver): at this latitude, the intensity will be about 75% as intense as at the Tropic of Cancer. Multiply the intensity at tropics (in %) by 0.75 = ______%

BlackTom AI · Accepted Answer

Question restatement: You are given a brightness/intensity progression at various latitudes, and an instruction to compute a reduced intensity at Vancouver (49°N) by multiplying the tropics’ intensity (expressed as a percentage) by 0.75. The answer choices are 100%, 47%, 67%, and 50%. Now, let’s analyze each option in turn.

Option 1: 100%
- If we took the Tropics’ intensity as a baseline of 100%, multiplying by 0.75 would yield 75%, not 100%. This option ignores the specified 0.75 factor and the instruction to scale the tropics’ intensity downward, so it is inconsistent with the given calculation.

Option 2: 47%
- This would correspond to multiplying 62.7% (approximately) by 0.75, or some other baseline, but there is no straightforward reading of the problem where the Tropics’ intensity in percent is 62.7% or where applying 0.75 yields exactly 47%. It seems to come from a misapplication of the 0.75 factor or an incorrect baseline conversion.

Option 3: 67%
- Interpreting the instruction literally, you would multiply the Tropics’ intensity (as a percentage) by 0.75. If the Tropics’ intensity were 89.3%, then 0.75 × 89.3% ≈ 67%, but the problem states the Tropics’ intensity (in %), not a specific 89.3% value. Without that intermediate conversion, 67% does not emerge cleanly from the given data, making this choice rely on an unstated intermediate step.

Option 4: 50%
- This option corresponds to multiplying a Tropics’ intensity of 66.7% by 0.75 (since 0.75 × 66.7% ≈ 50%), or, more straightforwardly, to choosing a Tropics’ intensity value that, when scaled by 0.75, results in exactly 50%. Given the provided instruction to multiply the Tropics’ intensity (in %), and the multiple-choice options offered, 50% is the only choice that cleanly aligns with a simple, exact 0.75 scaling of a Tropics’ percentage value that would reasonably be used in such a problem.

Summary of reasoning patterns: Each option represents a different way of applying the 0.75 scaling to a Tropics’ intensity stated as a percentage. The problem asks for a direct product of the Tropics’ intensity (as a percent) with 0.75, so only a Tropics’ intensity value that yields one of the listed options when multiplied by 0.75 will match that option. The options 100% and 47% require less natural alignment with a 0.75 factor given the tropics baseline; 67% would require a specific intermediate Tropics’ intensity value that isn’t stated, while 50% fits neatly with a reasonable Tropics’ intensity value and the exact 0.75 scaling.

Note on potential ambiguities: If the Tropics’ intensity were defined relative to some baseline (e.g., a Tropics baseline of 100%), 0.75 of that would be 75%, which is not among the choices. The given options suggest a straight % value after applying 0.75, so selecting the option that corresponds to a clean 0.75 scaling of a plausible Tropics’ percentage is consistent with the instruction and typical problem design.

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