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Chapter 5: Problem 142

The mad Dr. Frankenstein has gathered enough bits and pieces (so to speak) for \(2^{-1}+2^{-2}\) of his creature-to-be. Write a fraction that represents the amount of his creature that must still be obtained.

Short Answer

Expert verified
The amount of Dr. Frankenstein's creature that must still be obtained is \(1/4\) or 25%.

Step by step solution

01

Calculate the Gathered Portion

First, calculate the total gathered portion of the creature using the given fractional quantities. Let's calculate \(2^{-1}+2^{-2}\) which is \(0.5 + 0.25 = 0.75\) or 75% of the creature.
02

Calculate the Remaining Portion

We know that the full creature is represented by '1'. So, to find out how much of the creature still needs to be obtained, subtract the total gathered portion from 1. That's \(1 - 0.75 = 0.25\) or 25% of the creature.
03

Convert the Remaining Portion as Fraction

This step involves converting the remaining decimal portion into a proper fraction. The way to do this is to write down the decimal portion under 1 and simplify. The decimal number 0.25 when converted into fraction form becomes \(1/4\). Therefore, \(1/4\) of the creature still needs to be obtained by Dr. Frankenstein.

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Most popular questions from this chapter

The sum, \(S_{n}\), of the first n terms of an arithmetic sequence is given by $$ S_{n}=\frac{n}{2}\left(a_{1}+a_{n}\right), $$ in which \(a_{1}\) is the first term and \(a_{n}\) is the nth term. The sum, \(S_{n}\), of the first \(n\) terms of a geometric sequence is given by $$ S_{n}=\frac{a_{1}\left(1-r^{n}\right)}{1-r}, $$ in which \(a_{1}\) is the first term and \(r\) is the common ratio \((r \neq 1)\). Determine whether each sequence is arithmetic or geometric. Then use the appropriate formula to find \(S_{10}\), the sum of the first ten terms. \(3,-6,12,-24, \ldots\)

The sum, \(S_{n}\), of the first n terms of an arithmetic sequence is given by $$ S_{n}=\frac{n}{2}\left(a_{1}+a_{n}\right), $$ in which \(a_{1}\) is the first term and \(a_{n}\) is the nth term. The sum, \(S_{n}\), of the first \(n\) terms of a geometric sequence is given by $$ S_{n}=\frac{a_{1}\left(1-r^{n}\right)}{1-r}, $$ in which \(a_{1}\) is the first term and \(r\) is the common ratio \((r \neq 1)\). Determine whether each sequence is arithmetic or geometric. Then use the appropriate formula to find \(S_{10}\), the sum of the first ten terms. \(4,10,16,22, \ldots\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The sequence for the number of seats per row in our movie theater as the rows move toward the back is arithmetic with \(d=1\) so people don't block the view of those in the row behind them.

Enough curiosities involving the Fibonacci sequence exist to warrant a flourishing Fibonacci Association. It publishes a quarterly journal. Do some research on the Fibonacci sequence by consulting the research department of your library or the Internet, and find one property that interests you. After doing this research, get together with your group to share these intriguing properties.

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(\frac{1}{2}, 1, \frac{3}{2}, 2, \ldots\)
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