Answer:
The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches
Step-by-step explanation:
We have that:
Let the dimension of the paper be x and y;
Such that:
So:
Substitute 128 for Area
Make x the subject
When 1 inch margin is at top and bottom
The length becomes:
When 2 inch margin is at both sides
The width becomes:
The New Area (A) is then calculated as:
Substitute 
for x
Open Brackets
Collect Like Terms
To calculate the smallest possible value of y, we have to apply calculus.
Different A with respect to y
Set
This gives:
Collect Like Terms
Multiply through by 
Divide through by 2
Take square roots of both sides
Recall that:
Recall that the new dimensions are:
So:
To double-check;
Differentiate A'
The above value is:
This means that the calculated values are at minimum.
<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>
Answer:
They represent the rise and run of the graph.
Step-by-step explanation:
<em>The difference between the x-axis of the points represents the "run" of the graph (or how much you should run along x-axis to get to the next point.)</em>
<em>The difference between the y-axis of of the points represents the "rise" of the graph (or how much you should rise up the y-xis to get to the next point).</em>
The ratio of rise to run is the slope of the graph, which tells us how many steps should we take on the y-axis for every step we move forward on the x-axis.
Answer:
The correlation coeffcient for this case was provided:
r =0.934
And this coefficient is very near to 1 the maximum possible value, so then we can interpret that the relationship between the entrace exam score and the grade point average are strongly linearly correlated .
We can also find the 
who represent the determination coefficient and we got:
And the interpretation for this is that a linear model explains appproximately 87.2% of the variability between the two variables
Step-by-step explanation:
Previous concepts
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.
And in order to calculate the correlation coefficient we can use this formula:
![r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bn%28%5Csum%20xy%29-%28%5Csum%20x%29%28%5Csum%20y%29%7D%7B%5Csqrt%7B%5Bn%5Csum%20x%5E2%20-%28%5Csum%20x%29%5E2%5D%5Bn%5Csum%20y%5E2%20-%28%5Csum%20y%29%5E2%5D%7D%7D)
The correlation coeffcient for this case was provided:
r =0.934
And this coefficient is very near to 1 the maximum possible value, so then we can interpret that the relationship between the entrace exam score and the grade point average are strongly linearly correlated .
We can also find the who represent the determination coefficient and we got:
And the interpretation for this is that a linear model explains appproximately 87.2% of the variability between the two variables
First we need to find out what kind
of logarithm rule is given, the given is logarithm product rule which states
that a log of a product is equal to the sum of the log of the first base and
the log of the second base.
By:
= log (1.37 x 10⁹) =
log (1.37) + log (10⁹)
= log (1.37) + 9
= 9 + log (1.37)
In the meantime, 1.37 is between
1 and 10 its logarithm will be between 0 and 1. Thus, the value of log (1.37 x 10⁹)
falls between 9 and 10 because when you compose a scientific notation you will
always have a number among 1 and 10 by 10 to some power. That power tells you
the integer part of the logarithm.
<span> </span>
Let x be the earnings/hour at the movie theater.
y be the earnings/hour at the pet store
Systems of equations:
$152.50 = 10x + 8y
$171 = 8x + 10y
Solving for x and y:
x = $4.36/ hour in the movie theater
y = $13.61/ hour in the pet store.<span />
