Use a truth table to determine whether the symbolic form of the argument is valid or invalid.p ? qq ? p
A. Valid
B. Invalid
Answer: B
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Draw an appropriate Venn diagram and use the given information to fill in the number of elements in each region.n(A) = 48, n(B') = 60, n(C) = 51, n(A ? B) = 20, n(B ? C) = 19, n(A ? C) = 18, 
A. 
B. 
C. 
D. 
Solve the problem.The profit function for a product is given by 
dollars, where x is the number of units produced and sold. If break-even occurs when 60 units are produced and sold, use synthetic division to find a quadratic factor of P(x) and then find a number of units other than 60 that gives break-even for the product.
A. 250 units B. 10 units C. 100 units D. 200 units
Find the circumference and area of a circle having the given diameter or radius. Use 3.14 for ?. Round your results to the nearest tenth.r = 1.8 ft
A. C ? 11.3 ft, A ? 10.2 ft2 B. C ? 5.7 ft, A ? 40.7 ft2 C. C ? 5.7 ft, A ? 22.6 ft2 D. C ? 11.3 ft, A ? 11.3 ft2
Given the perimeter of the regular polygon, find the length of each side. Write any improper fractions as mixed numbers.A regular heptagon; P = 57
yd
A. side = 8
yd
B. side = 3
yd
C. side = 6
yd
D. side = 1
yd