Using the definition of vertical angles, the value of z is: 15.
<h3>Vertical Angles Pair</h3>
The two pairs of opposite angles formed when two straight lines intersect are called vertical angles, and are therefore congruent to each other.
Thus:
2z + 10 = 40
2z = 40 - 10
2z = 30
z = 30/2
z = 15
Therefore, using the definition of vertical angles, the value of z is: 15.
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Every confidence interval has associated z value. As confidence interval increases so do the z value associated with it.
The confidence interval can be calculated using following formula:

Where

is the mean value, z is the associated z value, s is the standard deviation and n is the number of samples.
We know that standard deviation is simply a square root of variance:

The confidence interval of 95% has associated z value of <span>1.960.
</span>Now we can calculate the confidence interval for our income:
Both servings of pancakes cost $8.50
One serving of pancakes cost $4.35
Equation: 1.15 (2x + 1.50) = 11.50
2.3x + 1.725 + 11.50
2.3x = 9.725
x = 4.25 for one serving of pancakes
2x = 8.50 for both servings of pancakes
5x-3=2.5x+x solve this equation that I just gave you for X then plug it in to 2.5x and that will equal MN
Given

To find a solution for the linear equation, the first step is to write the equation in slope-intercept form:
-Pass the x-term to the right side of the equation by applying the opposite operation to both sides of the equal sign:

-Divide both sides by -2:

Once you have expressed the equation of the line in slope-intercept form, replace it with any value for x and calculate the corresponding value of y, for example, x=2

One solution for the linear equation is x=2 and y=-6, you can check the solution by replacing the values on the original equation, with both values the result should be 8:

As you can see the values are a valid solution for the linear equation.
So the solution is: