Decide whether the argument is valid or invalid, and give the form (of valid or invalid argument) that applies.If the bough breaks, then the cradle will fall.
The cradle will fall.
A. Invalid; fallacy of the inverse
B. Invalid; fallacy of the converse
C. Valid; modus ponens
D. Valid; reasoning by transitivity
Answer: C
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Determine if the given function y = f(x) is a solution of the accompanying differential equation.y' + y = e2xy = 8e- x + e2x
A. Yes B. No
Perform the indicated operations. Assume that all variables represent nonnegative real numbers.3 
+ 3 
A. 24x
B. 8 
C. 24 
D. 3 
Solve.Can a quadrilateral be formed given two 10-cm sides and a 75° angle that is not a trapezoid, parallelogram, kite, or rhombus?
Fill in the blank(s) with the appropriate word(s).
Solve the problem.Recent research has shown that the population f(S) of cod in the North Sea next year as a function of this year's population S (measured in thousands of tons) can be described by the Shepherd model, f(S) = 
where a, b, and c are constants. The values of a, b, and c are 3.036, 250.04, and 3.29, respectively. Find the approximate value of this year's population that maximizes next year's population using this model.
A. 194 tons B. 194,000 tons C. 4000 tons D. 161,000 tons