Write an argument using the Law of Detachment and the Law of Syllogism that has as its contrapositive the statement “If you did not do well on your exam then you did not study effectively.” Identify your use of the both Law of Detachment and the Law of Syllogism.
What will be an ideal response?
Answers will vary. One possible solution is:
If you get enough sleep then you can study effectively (p ? q)
If you study effectively then you will do well on your exam (q ? r)
Using the Law of Syllogism, we have p ? r, which is the statement:
If you get enough sleep then you will do well on your exam
Using the Law of Detachment, we have, if p then r; p, therefore r. The contrapositive of this is
If not r then not p, which is the statement:
If you did not do well on your exam then you did not study effectively
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Solve the problem.The concentration of a certain drug in the bloodstream x hr after being administered is approximately 
Use the differential to approximate the change in concentration as x changes from 1 to 1.52.
A. 0.42 B. 0.14 C. 0.18 D. 0.20
A drug is carried into an organ of volume 
cm3 by a liquid that enters the organ at the rate of a cm3/sec and leaves it at the rate of b cm3/sec. The concentration of the drug in the liquid entering the organ is c g/cm3. If the concentration of the drug in the organ at time 
is increasing at the rate of
?
?g/cm3/sec, and the concentration of the drug in the organ initially is 
g/cm3, show that the concentration of the drug in the organ at time 
is given by
?
What will be an ideal response?
Solve the problem using the quadratic formula.The cumulative number (in thousands) of deaths from a certain disease from 2000 to 2010 may be modeled by 
where x = 0 corresponds to 2000, x = 1 to 2001, etc. Use the formula for f(x) to estimate symbolically the year when the total number of deaths reached 120 thousand.
A. 2008 B. 2009 C. 2006 D. 2007
Multiply.0.2(3)(-0.008)(60)
A. 2.88 B. -2.88 C. -0.288 D. 0.288