Y=2x+6, 3y=x-2 solve for unknown variables
2 answers:
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I: x-2y>=8
II:2x+y<=3
start by isolating y on a side
with I:
x-2y>=8
-2y>=8-x
2y<=x-8
y<=x/2-4
with II:
2x+y<=3
y<=-2x+3
now you can draw I' and II' and read of the solutions with the graph.
transform the inequalities into lines in slope intercept form by replacing the inequality with equality:
y<=x/2-4
->
y=x/2-4
y<=-2x+3
->
y=-2x+3
look at the inequalities to figure out if the area above or below is valid for each line (y<=... -> area below is valid->colored in the attached image)
the area in which all areas overlap is the solution space.
II:2x+y<=3
start by isolating y on a side
with I:
x-2y>=8
-2y>=8-x
2y<=x-8
y<=x/2-4
with II:
2x+y<=3
y<=-2x+3
now you can draw I' and II' and read of the solutions with the graph.
transform the inequalities into lines in slope intercept form by replacing the inequality with equality:
y<=x/2-4
->
y=x/2-4
y<=-2x+3
->
y=-2x+3
look at the inequalities to figure out if the area above or below is valid for each line (y<=... -> area below is valid->colored in the attached image)
the area in which all areas overlap is the solution space.
Answer:
And the deviation is given by this formula:
And as we can see the population proportion expected for the number of heads 0.5 is very close to the mean of the sampling distribution, the error is :
Step-by-step explanation:
Assuming the data on the figure attached. We ar assuming that this is a sampling distribution of sample proportions of heads in 40 flips of a coin.
As we can see we have the following values:
0.25, 0.35, 0.375,0.375, 0.40,0.40,0.40, 0.425,0.425,0.425, 0.45,0.45,0.45,0.45, 0.475,0.475,0.475, 0.475,0.475, 0.50,0.50,0.50, 0.525,0.525,0.525,0.525, 0.55,0.55,0.55,0.55,0.55, 0.575,0.575,0.575 0.575, 0.575, 0.60,0.60, 0.65,0.65
And we can calculate the sample proportion with the following formula:
And the deviation is given by this formula:
And as we can see the population proportion expected for the number of heads 0.5 is very close to the mean of the sampling distribution, the error is :
