Answer:
Step-by-step explanation:
For mixture problems, it is convenient to define a variable to represent the amount of the greatest contributor. Let x represent the amount of 22% solution in the mix. Then 4.8-x is the amount of 10% solution.
The amount of alcohol in the mix is ...
0.22x +0.10(4.8-x) = 0.12(4.8)
Eliminating parentheses, we have ...
0.22x -0.10x +0.10(4.8) = 0.12(4.8)
Subtracting (0.10)(4.8) and combining x-terms gives ...
0.12x = 0.02(4.8)
x = (0.02/0.12)(4.8) = 0.8 . . . . . divide by the x-coefficient
The scientist needs 0.8 L of 22% solution and 4.0 L of 10% solution.
Intersection of the first two lines:

Multiply the first equation by 4 and the second by 5:

Subtract the two equations:

Plug this value for y in one of the equation, for example the first:

So, the first point of intersection is 
We can find the intersection of the other two lines in the same way: we start with

Use the fact that x and y are the same to rewrite the second equation as

And since x and y are the same, the second point is 
So, we're looking for a line passing through
and
. We may use the formula to find the equation of a line knowing two of its points, but in this case it is very clear that both points have the same coordinates, so the line must be 
In the attached figure, line
is light green, line
is dark green, and their intersection is point A.
Simiarly, line
is red, line
is orange, and their intersection is B.
As you can see, the line connecting A and B is the red line itself.
4, 8, 10, 7, 3, 4... Those r in order from top to bottom! it's all about the simplification!
Answer:
A sample size of 128 is needed.
Step-by-step explanation:
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of
.
So it is z with a pvalue of
, so 
Now, find the margin of error M as such

In which
is the standard deviation of the population(square root of the variance) and n is the size of the sample.
How large should a sample be if the margin of error is 1 minute for a 93% confidence interval
We need a sample size of n, which is found when
. We have that
. So





Rounding up
A sample size of 128 is needed.