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KATRIN_1 [288]
2 years ago
13

Melanie is making lemonade and finds a recipe that calls for 1 part lemon juice, 2 parts sugar, and 8 parts water. She juices 2

lemons to obtain 6 tablespoons of lemon juice. How much sugar and water will she need to make lemonade with the same ratio of ingredients as the recipe? Express your answers as decimals if necessary. (1 cup equals 16 tablespoons) With
Mathematics
2 answers:
Brums [2.3K]2 years ago
7 0

Answer:

Amount of lemon juice, sugar and water required will be = 0.375 cups, 0.75 cups and 3 cups.

Step-by-step explanation:

Malanie is making lemonade and finds a recipe that requires lemon juice, sugar and water in the ratio of 1 : 2 : 8.

She juices 2 lemons to obtain 6 tablespoons of lemon juice.

∵ 16 tablespoons = 1 cup

∴ 1 tablespoon = \frac{1}{16} cup

∴ 6 tablespoon =  \frac{6}{16} cup =  0.375 cups

Since ratio between lemon and sugar is 1 : 2

So amount of sugar required = 0.375×2 = 0.75 cups

Ratio between lemon and water is 1 : 8

So amount of water required = 0.375×8 = 3 cups

Therefore, amount of lemon juice, sugar and water required = 0.375 cups, 0.75 cups sugar and 3 cups respectively.

MakcuM [25]2 years ago
3 0
12 tablespoons of sugar and 3 cups of water (48 tablespoons)
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Given a circle described by the equation:
y^2+x^2=100
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The function g(x) describes a straight line with the equation:
\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}  \\  \\  \frac{y-(-22)}{x-(-1)} = \frac{-20-(-22)}{0-(-1)}  \\  \\ \frac{y+22}{x+1} = \frac{-20+22}{0+1} = \frac{2}{1}  \\  \\ y+22=2(x+1)=2x+2 \\  \\ y=2x-20

To check if the circle and the line intersects, we substitute the equation of the line into the equation of the circle to see if we have a real solution.
i.e.
y^2+x^2=100 \\  \\ (2x-20)^2+x^2=100 \\  \\ 4x^2-80x+400+x^2=100 \\  \\ 5x^2-80x+300=0 \\  \\ x^2-16x+60=0 \\  \\ (x-6)(x-10)=0 \\  \\ x-6=0 \ or \ x-10=0 \\  \\ x=6 \ or \ x=10

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Step-by-step explanation:

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AysviL [449]

Answer:

The percent decrease in the number of cheese sticks you can buy for $1 is 80%.

Step-by-step explanation:

Given : Cheese sticks that were previously priced at "10 for $1" are now "2 for $1".

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The formula used to find percent decrease is given by,

\%\text{ change}=\frac{\text{Amount of change}}{\text{Original amount }}\times 100

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Answer:

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The possible ways of getting a total of 7,

{ (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) }

Number of favorable outcomes = 7

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Therefore the expected payoff for this game is -$1.22.

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2 years ago
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