Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.1 + 3 + 32 + ... + 3n - 1 = 
What will be an ideal response?
First, we show that the statement is true when n = 1.
For n = 1, we get 1 (or 3[(1) - 1]) = 
= 
= 1.
This is a true statement and Condition I is satisfied.
Next, we assume the statement holds for some k. That is,
is true for some positive integer k.
We need to show that the statement holds for 
. That is, we need to show that
So we assume that 
is true and add the next term, 3k, to both sides of the equation.
Condition II is satisfied. As a result, the statement is true for all natural numbers n.
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Solve the problem.A reservation clerk worked 12.15 hours one day. She spent twice as much time entering new reservations as she did verifying old ones and one and a half as much time calling to confirm reservations as verifying old ones. How much time did she spend entering new reservations?
A. 4.05 hours B. 10.8 hours C. 2.7 hours D. 5.4 hours
Find the center of mass of a thin plate covering the given region with the given density function.The region enclosed by the parabolas y = - x2 + 8 and y = x2, with density ?(x) = x2
A. 
= 0, 
= 4
B. 
= 0, 
= 8
C. 
= 0, 
= 
D. 
= 4, 
= 0
Place the correct symbol, >, <, or =, in the blank in the given pair of fractions.
A. = B. > C. <
Solve.The formula 
represents the number of households N, in thousands, in a certain city that have a computer x years after 1990. According to the formula, in what year were there 89 thousand households with computers in this city?
A. 1993 B. 1994 C. 1995 D. 1992