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3241004551 [841]
3 years ago
12

The ratio of cups of orange juice concentrate to water in a punch recipe is 1 : 4. If Gordon used 32 cups of water, how many cup

s of orange juice concentrate did he use?
Mathematics
1 answer:
Natasha_Volkova [10]3 years ago
4 0

Answer: 8 cups of orange juice concentrate

Step-by-step explanation:

Since the ratio of cups of orange juice concentrate to water in a punch recipe is 1 : 4. It simply means that for 1 cup of orange juice, there are 4 cups of water.

Therefore, if Gordon used 32 cups of water, the number of cups of orange juice concentrate that he used will be one quarter of 32. This will be:

= 1/4 × 32

= 8 cups of orange juice concentrate

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How to solve this equation 2√4
guapka [62]

Answer:

4

Step-by-step explanation:

First things first we will need to solve the square root.

\sqrt{4} = 2

We can check this by squaring 2.

2^{2} = 2 x 2 = 4

Now that we have solved the square root, we are left with 2(2). 2 x 2.

2(2) = 4

2\sqrt{4} = ?

2(2) = ?

4

6 0
3 years ago
Compute the product AB by the definition of the product of​ matrices, where A and A are computed​ separately, and by the​ row-co
chubhunter [2.5K]

Complete Question

The complete question is shown on the first uploaded image

Answer:

First question

   Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}5\\-2\\\end{array}\right]

Second question

 Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}5\\-2\\\end{array}\right] = \left[\begin{array}{ccc}{(-1 * 5 )+ (3* -2)}\\{(1 * 5)+ (4 * -2)}\\{(5 * 5) + (8*-2)}\end{array}\right]  = \left[\begin{array}{ccc}{-11}\\{-3}\\{29}\end{array}\right]

 Third question

  Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}-3\\4\\\end{array}\right]

 Fourth question

  Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}-3\\4\\\end{array}\right] = \left[\begin{array}{ccc}{(-1 * -3 )+ (3* 4)}\\{(1 * -3)+ (4 * 4)}\\{(5 * -3) + (8*4)}\end{array}\right]  = \left[\begin{array}{ccc}{15}\\{13}\\{-23}\end{array}\right]

Fifth question

  The correct option is A

Step-by-step explanation:

From the question we are told that

  The matrix  A  is  A = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]

   The matrix B is   B = \left[\begin{array}{ccc}5&{-3}\\{-2}&4\end{array}\right]

The first question is to set up the product Ab_1  , where b_1 is the first column of matrix B, this shown as

          Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}5\\-2\\\end{array}\right]

The second question is to calculate Ab_1 , this is evaluated as

          Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}5\\-2\\\end{array}\right] = \left[\begin{array}{ccc}{(-1 * 5 )+ (3* -2)}\\{(1 * 5)+ (4 * -2)}\\{(5 * 5) + (8*-2)}\end{array}\right]  = \left[\begin{array}{ccc}{-11}\\{-3}\\{29}\end{array}\right]

The third question is to set up the product Ab_2  , where b_2 is the second column of matrix B, this shown as

          Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}-3\\4\\\end{array}\right]

The fourth question is to calculate Ab_2 , this is evaluated as

          Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}-3\\4\\\end{array}\right] = \left[\begin{array}{ccc}{(-1 * -3 )+ (3* 4)}\\{(1 * -3)+ (4 * 4)}\\{(5 * -3) + (8*4)}\end{array}\right]  = \left[\begin{array}{ccc}{15}\\{13}\\{-23}\end{array}\right]

The fifth question is to determine the numerical expression for the first entry in the first column of AB using the row-column rule and from the calculation of Ab_1 we see that it is

      {(-1 * 5 )+ (3* -2)}

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To answer the question, combine the terms having the same nature of variables in the given above,
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Answer:

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The answer is 4

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