Since the problem states only the 12 are common to all, and the rest are unique to each site, total distinct = 160 - 4×12 + 12 = 160 - 48 + 12 = <<160-48+12=124>>124.

Apr 21, 2026

Alternatively, simpler: add all counts, subtract duplicates not in sum—since 12 are shared in all 5, they are counted 5 times but should be once. So subtract 4×12 = 48 from total sum.

Apr 21, 2026

Total distinct = 160 - 48 = <<160-48=112>>112? Wait—this is incorrect because the 12 are shared, so they are counted once in total, but appear 5 times in sum. So subtract 4×12 = 48 → 160 - 48 = 112.

Apr 21, 2026

But data shows 32, 28, 36, 30, 34 — if these include the 12 common species, then total distinct = sum of all unique local species minus overlaps. However, the phrasing 12 species common across all suggests they are included in each count, so total distinct = (32–12) + (28–12) + (36–12) + (30–12) + (34–12) + 12 = 20 + 16 + 24 + 18 + 22 + 12 = <<20+16+24+18+22+12=112>>112.

Apr 21, 2026

#### 112

Apr 21, 2026

A science fiction writer imagines a space station rotating to simulate gravity. If the station has a radius of 500 meters and simulates Earth’s gravity (9.8 m/s²) via centripetal acceleration, use the formula \( a = v^2/r \) to find the required linear velocity \( v \) in meters per second.

Apr 21, 2026

Given: \( a = 9.8 \), \( r = 500 \), so \( v^2 = a \times r = 9.8 \times 500 = <<9.8*500=4900>>4900 \).

Apr 21, 2026

Then \( v = \sqrt{4900} = <<sqrt(4900)=70>>70 \) m/s.

Apr 21, 2026

A clean tech startup reduces carbon emissions by 12,000 tons in its first year. Each year, improvements increase efficiency by 15%, compounding the reduction effect. What is the total carbon reduction over the first three years?

Apr 21, 2026

Year 1: 12,000 tons.

Apr 21, 2026