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enot [183]
3 years ago
10

A small, test batch of lemonade used one fourth cup of sugar added to one cup of water and one fourth cup of lemon juice. After

confirming it tasted good, a larger batch is going to be made with the same ratios using 10 cups of water. How much sugar should be added so that the large batch tastes the same as the test batch
Mathematics
1 answer:
Elden [556K]3 years ago
5 0

Answer:

They need do add 2.5 or 5/2 cup of sugar so that large batch tastes the same.

Step-by-step explanation:

Consider the provided information.

A small, test batch of lemonade used one fourth cup of sugar added to one cup of water.

Therefore the ratio of sugar and water is \frac{1}{4} : 1

This can be written as:

\frac{suger}{water}=\frac{0.25}{1}

After confirming it tasted good, a larger batch is going to be made with the same ratios using 10 cups of water.

Now multiply both the sides by 10 in above expression.

\frac{suger}{water}=\frac{0.25\times 10}{1\times 10}

\frac{suger}{water}=\frac{2.5}{10}

Hence, they need do add 2.5 or 5/2 cup of sugar so that large batch tastes the same.

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An experiment involves 17 participants. From these, a group of 3 participants is to be tested under a special condition. How man
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Hey there! I'm happy to help!

When talking about possibilities of groups, outcomes, etc. we will either use permutations or combinations.

Permutations has to do with order.

Combinations does not have to do with order.

Our question says that the order in which the participants are chosen is irrelevant, so we will use combinations.

However, to get to combinations, you first have to find the permutation, which we will do below.

So, let's imagine that there are three seats you sit in to be in this group.

First, you have to pick someone to sit in the first chair. There are 17 choices to put in this chair.

For the second chair, you only have 16 choices because one of them is sitting in the first chair.

Following this, there are only 15 choices for the 3rd chair.

We multiply this number of choices together:

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Therefore, there are 4080 possible permutations here. This means ways you choose the people and how you order them.

Using our permutation, we will find the combination, where order does not matter.

To find the number of possible combinations, we have to divide our permutation by the number of possible ways you can arrange people in 3 seats. This will get rid of all of the extra possibilities with the same people but a different order.

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Well, there's 3 choices for the first seat, 2 for the second, and 1 for the third.

3×2×1=6

So, we divide 4080 by 6, giving us 680

Therefore, there are 680 groups of 3 participants that can be chosen assuming that the order in which the participants are chosen is irrelevant.

Have a wonderful day! :D

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