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Lee and Mia share profits 4:3. Interest on drawings was omitted: Lee $90, Mia $50. By how much will Lee's current account balance decrease when corrected?
Option A ($10) is correct.
Total interest on drawings = $90 + $50 = $140 added to profit available.
Lee's extra profit share = $140 × 4/7 = $80
Net change to Lee's account = −$90 (interest charged) + $80 (extra profit) = −$10
Bi Sheng invented movable clay type in China around 1041 AD — nearly four centuries before Gutenberg. However, the Chinese writing system contains thousands of characters (Mandarin has over 50,000, with several thousand in common use), compared to the 26-letter Latin alphabet used in European languages. Setting up movable type for Chinese therefore required an enormous number of individual pieces, making it cumbersome and time-consuming — often slower than traditional block printing for short or medium runs. By contrast, a European printer needed only a small set of metal type for the entire alphabet, making Gutenberg's press extraordinarily efficient for European languages. This alphabetic advantage is a key reason the printing press became a revolutionary mass communication tool in Europe but remained a marginal improvement in China. Interestingly, Gutenberg also used durable oil-based ink and rag paper introduced to Europe via Muslim trade routes, further improving output quality.
A satellite orbits at height $h$ from Earth's surface where $h \ll R$ ($R$ = Earth's radius). The minimum increase in speed for the satellite to escape Earth's gravitational field is:
For $h \ll R$, orbital radius $\approx R$:
Orbital speed: $v_o = \sqrt{gR}$
Escape speed from surface (approximately same radius): $v_e = \sqrt{2gR}$
Minimum increase: $\Delta v = v_e - v_o = \sqrt{2gR} - \sqrt{gR} = \sqrt{gR}(\sqrt{2}-1)$
Fill in the blank: He has been working ______ this project for two weeks.
The correct preposition is 'on' when referring to working on a task or project. 'Working on a project' is the standard phrase.
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