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Difficulty:
55%
(hard)
Question Stats:
45%
(01:27)
correct 55%
(02:21)
wrong
based on 11
sessions
History
Date
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A science lab is conducting an experiment monitoring the appearance of genetic traits in laboratory rats. Of the three traits being monitored, one third of the rats were obese, three fourths of the rats had white fur, and one half of the rats had an elongated mandible. How many had all three of these traits?
(1) Of the 120 rats in the experiment, 40 had white fur and an elongated mandible. (2) Of the 120 rats in the experiment, 40 had exactly two of the traits.
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A science lab is conducting an experiment monitoring the appearance of genetic traits in laboratory rats. Of the three traits being monitored, one third of the rats were obese, three fourths of the rats had white fur, and one half of the rats had an elongated mandible. How many had all three of these traits?
(1) Of the 120 rats in the experiment, 40 had white fur and an elongated mandible. (2) Of the 120 rats in the experiment, 40 had exactly two of the traits.
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A science lab is conducting an experiment monitoring the appearance of genetic traits in laboratory rats. Of the three traits being monitored, one third of the rats were obese--- a+b+d+e=T/3, three fourths of the rats had white fur---b+c+e+f=3T/4, and one half of the rats had an elongated mandible----d+e+f+g=T/2. How many had all three of these traits?----- e??
(1) Of the 120 rats in the experiment, 40 had white fur and an elongated mandible. So, T=120, and e+f=40
(2) Of the 120 rats in the experiment, 40 had exactly two of the traits So, T=120, and b+d+f=40
Combined.. e+f=b+d+f=40....(i) a+b+d+e=120/3=40=b+d+f........a+e=f,....(ii) From (i) and (ii), we get e+f=40 and a+e=f.......e+(a+e)=40.....a+2e=40...(iii) three fourths of the rats had white fur---b+c+e+f=3T/4=90.....b+c+40=90...b+c=50.....(iv), and one half of the rats had an elongated mandible----d+e+f+g=T/2=60.....d+40+g=60.....d+g=20....(v). Now a+b+c+d+e+f+g=120 .. Substitute (i) (iv) and (v) in it....a+50+40+20=120...a=10 Substitute a=10 in a+2e=40...10+2e=40.....2e=30...e=15
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