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shusha [124]
4 years ago
14

Otto used 6 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the

value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y?
Mathematics
1 answer:
nadezda [96]4 years ago
5 0
Y = 6 + x

We can use this equation to find the total amount of flour that Otto used in the recipe.

The constraints on 'x' and 'y' are that they must both be positive, because we cannot have a negative amount of flour.

<span>And a restraint something like 50 cups of flour total because one person making a recipe won't use that many cups of flour.</span>
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The regression lines 3x+2y=26 and 6x+y=31 are linear regressions

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<h3>The mean value and the correlation</h3>

We have the equations to be:

3x+2y=26 and 6x+y=31

Make y the subject in the second equation

y = 31 - 6x

Substitute y = 31 - 6x in the first equation

3x+2[31 - 6x] = 26

Expand

3x+ 62 - 12x = 26

Collect like terms

3x - 12x = 26 - 62

Evaluate

-9x = -36

Divide by - 9

x = 4

Substitute x = 4 in y = 31 - 6x

y = 31 - 6 * 4

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This means that the mean values are 4 and 7

To determine the correlation coefficient, we make y the subject in 3x+2y=26 and x the subject in 6x+y=31.

So, we have:

y = 13 - 3x/2 and x = 31/6 - 1/6y

The above means that:

Bxy = -1/6 and Byx = -3/2

The correlation coefficient is then calculated as:

r^2 = Bxy * Byx

r = -1/6 * -3/2

r = 0.25

Hence, the correlation coefficient between x and y is 0.25

<h3>The standard deviation of x</h3>

We have:

Var(y) = 4

In (a), we have:

y = 13 - 3x/2

To solve further, we make use of:

Var(y) = Var(ax + b) = a^2Var(x)

This gives

Var(y) = Var(13 - 3x/2) = 13^2 * Var(x)

So, we have:

Var(y) = 13^2 * Var(x)

Substitute 4 for Var(y)

4 = 13^2 * Var(x)

Divide both sides by 13^2

4/13^2 = Var(x)

Express 4 as 2^2

(2/13)^2 = Var(x)

So, we have:

Var(x) = (2/13)^2

Take the square root of both sides

SD(x) = 2/13

Hence, the standard deviation of x is 2/13

Read more about regression lines at:

brainly.com/question/4341286

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