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Helen [10]
3 years ago
13

María is making fruto punch for her family reunión. She uses 6 quarts of ginger ale, 8 quarts of lemonade, and 10 quarts of rasp

berry juice. How many gallons of punch does her recipe make?
Mathematics
2 answers:
bixtya [17]3 years ago
6 0

Answer:

6 gallons of punch makes her recipe.

24 quarts = 24 × 0.25 = 6 gallons of punch

6 gallons of punch makes her recipe.

expeople1 [14]3 years ago
3 0

Answer:

6 gallons of punch makes her recipe.

Step-by-step explanation:

Given:

Quarts of ginger ale (g) = 6

Quarts of lemonade (l) = 8

Quarts of raspberry (r) = 10

Therefore, the total volume of fruto punch is equal to the sum of the volume of each of its ingredients.

So, Total volume = g+l+r

Total volume = 6 + 8 + 10 = 24 quarts

Now, we know that,

1 quart = 0.25 gallons

Therefore, from unitary method,

24 quarts = 24 × 0.25 = 6 gallons of punch

Therefore, 6 gallons of punch makes her recipe.

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Linear equation is equation in which each term has at max one degree. The function that can represent the given graph is y=2.0769x + 1.5.

<h3>What is linear equation?</h3>

Linear equation is equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c

Linear equation with two variables, when graphed on Cartesian plane with axes of those variables, give a straight line.

For the given graph the equation can be written as, y = mx+c, this is because the graph is a line which means the relationship is linear. Therefore, the equation can be written as,

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Now, there are two points that are on the line and the coordinates of this points are,

A = (4, 9.5)

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Since c is the y-intercept of the graph, therefore, the value of c is 1.5.

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Step-by-step explanation:

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y = -3(x - 1)

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You're trying to find constants a_0,a_1,a_2 such that \hat y=a_0+a_1\hat x+a_2{\hat x}^2. Equivalently, you're looking for the least-square solution to the following matrix equation.


\underbrace{\begin{bmatrix}1&6&6^2\\1&3&3^2\\\vdots&\vdots&\vdots\\1&9&9^2\end{bmatrix}}_{\mathbf A}\underbrace{\begin{bmatrix}a_0\\a_1\\a_2\end{bmatrix}}_{\mathbf x}=\underbrace{\begin{bmatrix}100\\110\\\vdots\\70\end{bmatrix}}_{\mathbf b}

To solve \mathbf{Ax}=\mathbf b, multiply both sides by the transpose of \mathbf A, which introduces an invertible square matrix on the LHS.

\mathbf{Ax}=\mathbf b\implies\mathbf A^\top\mathbf{Ax}=\mathbf A^\top\mathbf b\implies\mathbf x=(\mathbf A^\top\mathbf A)^{-1}\mathbf A^\top\mathbf b

Computing this, you'd find that

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