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A genetic modification specialist modifies a gene in 150 bacterial cultures. After treatment, 30% show successful expression. Of the unsuccessful ones, 20% are retested and two-thirds show success. How many cultures failed initially but succeeded on retest?
Initially successful: 150 × 0.30 = <<150*0.30=45>>45 cultures.
Initially unsuccessful: 150 – 45 = <<150-45=105>>105 cultures.
Retested: 20% of 105 = 105 × 0.20 = <<105*0.20=21>>21 cultures.
Of these, 2/3 succeed: 21 × (2/3) = <<21*(2/3)=14>>14 cultures.
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A drone flying over a wheat field captures images every 30 seconds across a 5.4-kilometer transect. If the drone flies at 18 km/h, how many images does it capture during the full transect, including the start?
First, convert speed to km per second: 18 km/h = 18 ÷ 3600 = <<18/3600=0.005>>0.005 km/s.
Time to cross 5.4 km: 5.4 ÷ 0.005 = <<5.4/0.005=1080>>1080 seconds.
Images captured every 30 seconds: 1080 ÷ 30 = <<1080/30=36>>36, and including the first image, total is 36 + 1 = <<36+1=37>>37 images.