Solve the problem.The resistance of a wire varies directly as the length of the wire and inversely as the square of the diameter of the wire. A 20 foot length of wire with a diameter of  has a resistance of  What would the resistance be for a  length, with diameter  of the same kind of wire ?

A. 687 ohms
B. 668 ohms
C. 675 ohms
D. 672.5 ohms


Answer: C

Mathematics

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Solve the problem.The amount of money in an account is given by  where P is the principal invested, r is the interest rate (as a decimal), and t is the time of the investment. Find the amount at the end of 2 years if $600 is invested at 5%. Round to the nearest cent.

A. $1,350.00 B. $630.00 C. $900.00 D. $661.50

Mathematics

Write the indicated event in set notation.The event that Betty and Emily are selected as board members when three board members are selected at random from the following group: Allison, Betty, Charlie, Dave, and Emily.  [The possible outcomes can be represented as follows.ABCABDABEACDACEADEBCDBCEBDECDE]

A.
B.
C.
D.

Mathematics

Find the product. Assume all variable exponents represent whole numbers.(x + y)(x2 - 6xy - y2)

A. x3 - 6x2y - 6xy2 - y3 B. x3y - 6x2y - xy3 C. x3 - 6x2y - xy2 D. x3 - 5x2y - 7xy2 - y3

Mathematics

Provide an appropriate response.List all positive integer pairs that have a product of 30.

A.  3, 10; 5, 6 B. 1, 30 C. 1, 30; 2, 15;  3, 10; 5, 6 D.  2, 15;  3, 10; 5, 6

Mathematics