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Vaselesa [24]
3 years ago
11

The local library has a children's section with picture books and chapter books. The ratio is 2:3. If there are a total of 500 b

ooks in the children's section then how many chapter books are in the section?
Mathematics
2 answers:
Ivenika [448]3 years ago
7 0

Answer:

300 chapter books

Step-by-step explanation:

Given that:

Total books = 500

Ratio given = 2:3

So they are divided into 5 parts

Each part contains = 500/5 books = 100 books

So The chapter books have 3 parts

Chapters books = 3 * 100 = 300 books

i hope it will help you!

Nataly_w [17]3 years ago
7 0

Answer:

Step-by-step explanation:

Let k be the constant of proportionality.  Then we use it as follows:

2k + 3k = 500, or 5k = 500, or k = 100.

Thus, the number of picture books is 2(100) = 200, and the number of chapter books is 3(100) = 300.

As checks:  200 + 300 = 500 (books), and

200

-------- = 2/3, as specified in the problem.

300

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Answer:

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2) 2^{-1}.2^{-4} = \frac{1}{32}

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Step-by-step explanation:

1) \frac{(-2)^{-5}}{(-2)^{-10}}

Solving using exponent rule: a^{-m}=\frac{1}{a^m}

\frac{(-2)^{-5}}{(-2)^{-10}}\\=(-2)^{-5+10}\\=(-2)^{5}\\=-32

So, \frac{(-2)^{-5}}{(-2)^{-10}}=-32

2) 2^{-1}.2^{-4}

Using the exponent rule: a^m.a^n=a^{m+n}

We have:

2^{-1}.2^{-4}\\=2^{-1-4}\\=2^{-5}

We also know that: a^{-m}=\frac{1}{a^m}

Using this rule:

2^{-5}\\=\frac{1}{2^5}\\=\frac{1}{32}

So, 2^{-1}.2^{-4} = \frac{1}{32}

3) (-\frac{1}{2} )^3.(-\frac{1}{2} )^2

Solving:

(-\frac{1}{2} )^3.(-\frac{1}{2} )^2\\=(-\frac{1}{8} ).(\frac{1}{4} )\\=-\frac{1}{32}

So, (-\frac{1}{2} )^3.(-\frac{1}{2} )^2=-\frac{1}{32}

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We know that: a^{-m}=\frac{1}{a^m}

\frac{2}{2^{-4}}\\=2\times 2^4\\=2(16)\\=32

So, \frac{2}{2^{-4}} = 32

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