3 years ago

Amanda has 15 coins in her pocket. Of these, 8 are quarter. What is ratio of quarters to coins in Amanda's pocket?i

Mathematics

2 answers:

MakcuM [25]3 years ago

8 0

The answer will be 8:15

deff fn [24]3 years ago

5 0

8:15 or 8 to 15 would be the ratio because you compare 8 quarters to 15 coins.

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√180 can be expressed in the form p√q. where p and q are integers. Find the smallest value of p + q.

frutty [35]

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The smallest value of p+q is 11

It happens when p = 6 and q = 5.

=======================================================

Explanation:

Let's factor 180 in such a way that exactly one factor is a perfect square.

I'll ignore the trivial factor of 1.

Here are the possible factorizations we could go with:

180 = 4*45

180 = 9*20

180 = 36*5

Those factorizations then lead to the following

$\sqrt{180} = \sqrt{4*45} = \sqrt{4}*\sqrt{45}= 2\sqrt{45}\\\\\sqrt{180} = \sqrt{9*20} = \sqrt{9}*\sqrt{20}= 3\sqrt{20}\\\\\sqrt{180} = \sqrt{36*5} = \sqrt{36}*\sqrt{5}= 6\sqrt{5}\\\\$

Then we have

p+q = 2+45 = 47

p+q = 3+20 = 23

p+q = 6+5 = 11

The smallest value of p+q is 11 and it happens when p = 6 and q = 5.

Side note: p+q is smallest when we go with the largest perfect square factor.

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