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3 years ago

Determine if the rates $168 rasied for washing 24 cars and $280 rasied for washing 40 cars are equivalent

Mathematics

1 answer:

Mariana [72]3 years ago

3 0

We are given : $168 raised for washing 24 cars and $280 raised for washing 40 cars.

We know the rate formula.

Rate = Total amount ÷ Total numbers.

Let us find value of each rate for the given problem.

Rate 1: Total amount ÷ Total numbers = $168 ÷ 24 = $7.

Rate 2: Total amount ÷ Total numbers = $280 ÷ 40 = $7.

We can clearly see that Rate 1 is equal to Rate 2, that is $7.

So, we can say rates are equivalent.

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$\large\boxed{\dfrac{5^2\cdot57}{2^{26}}=\dfrac{1425}{67108864}}$

Step-by-step explanation:

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$=\dfrac{(2^8)^{-2}}{(5^5)^{-2}}\cdot\dfrac{1^4}{(2^3)^4(5^2)^4}\cdot228=\dfrac{2^{-16}}{5^{-10}}\cdot\dfrac{1}{2^{12}5^8}\cdot228\\\\\text{use}\ a^n=\dfrac{1}{a^{-n}}\to\dfrac{1}{a^n}=a^{-n}\\\\=2^{-16}\cdot5^{10}\cdot2^{-12}\cdot5^{-8}\cdot228\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=2^{-16+(-12)}\cdot5^{10+(-8)}\cdot228=2^{-28}\cdot5^2\cdot228\\\\=2^{-28}\cdot5^2\cdot4\cdot57=2^{-28}\cdot5^2\cdot2^2\cdot57=2^{-28+2}\cdot5^2\cdot57\\\\=2^{-26}\cdot5^2\cdot57=\dfrac{5^2\cdot57}{2^{26}}$

$\large\boxed{\dfrac{5^2\cdot57}{2^{26}}=\dfrac{1425}{67108864}}$

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