Several logs are stored in a pile with 30 logs on the bottom layer, 29 on the second layer, 28 on the third layer, and so on. If the top layer has one log, how many logs are in the pile?
?
A. 464
B. 465
C. 450
D. 435
E. none of the above
Answer: B
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Use the rules for exponents to rewrite the expression and then evaluate the new expression. 
A. 
B. -4
C. 2
D. - 
Simplify the complex fraction.
A. 
B. 
C. 
D. 
The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product can be calculated.A is 1 × 4; B is 1 × 4.
A. AB is 4 × 1; BA is 1 × 4. B. AB is 1 × 4; BA is 4 × 1. C. AB is 1 × 1; BA is 4 × 4. D. AB cannot be calculated; BA cannot be calculated.
Provide an appropriate response.In certain situations, a matrix game can be reduced to a smaller game by deleting certain rows and/or columns from the payoff matrix. The optimal strategy for the reduced game will then determine the optimal strategy for the original game. In what circumstances may a row or column be deleted from the payoff matrix?
A. A row may be deleted if it is recessive to some other row and a column may be deleted if it is dominant to some other column. B. A row may be deleted if it is dominant to some other row and a column may be deleted if it is recessive to some other column. C. A row may be deleted if it is dominant to some other row and a column may be deleted if it is dominant to some other column. D. A row may be deleted if it is recessive to some other row and a column may be deleted if it is recessive to some other column.