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miss Akunina [59]
4 years ago
7

A small, test batch of lemonade used 1/4 cup of sugar added to 1 cup of water and 1/4 cup of lemon juice. After confirming it ta

sted 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:
Levart [38]4 years ago
4 0

Hi there!

In order to answer your question, you'll need to use the cross product method:

1 cup water → 1/4 cup sugar

10 cups water → X cup sugar


(<u>(1/4) × 10)</u> ÷ 1 = X cups sugar

<u>2.5 ÷ 1</u> = X cups sugar

2.5 = X cups sugar


Your answer is : Using 10 cups of water, you should add 2 and a half cups of sugar so that the large batch tastes the same as the test batch.


There you go! I really hope this helped, if there's anything just let me know! :)

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Two number cubes are rolled sequentially. What is the probability that the first number cube shows a five and the other number c
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The probability of first number cube shows a five and the other number cube shows an even number is \frac{1}{12}.

Solution:

Two cubes are rolled sequentially.

Sample space when two dies are rolled

                   =\left\{\begin{array}{l}{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)} \\{(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)} \\{(3,1), 3(, 2),(3,3),(3,4),(3,5),(3,6)} \\{(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)} \\{(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)} \\{(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}\end{array}\right\}

Number of sample space = 36

Even numbers getting when two cubes rolled are 2, 4, 6.

First number cube shows a five and the other number cube shows an even number = {(5, 2), (5, 4), (5 6)}

Number of first number cube shows a five and the other number cube shows an even number = 3

Probability of first number cube shows a five and the other number cube shows an even number

                 $=\frac{\text{Number of outcomes}}{\text{Total number of sample space}} $

                $=\frac{3}{36}

                $=\frac{1}{12}

Hence, the probability of first number cube shows a five and the other number cube shows an even number is \frac{1}{12}.

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Answer:

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