We are asked to determine the correlation factor "r" of the given table. To do that we will first label the column for "Quality" as "x" and the column for "Easiness" as "y". Like this:
Now, we create another column with the product of "x" and "y". Like this:
Now, we will add another column with the squares of the values of "x". Like this:
Now, we add another column with the squares of the values of "y":
Now, we sum the values on each of the columns:
Now, to get the correlation factor we use the following formula:
Where:
Now we substitute the values, we get:
Solving the operations:
Therefore, the correlation factor is 0.858. If the correlation factor approaches the values of +1, this means that there is a strong linear correlation between the variables "x" and "y" and this correlation tends to be with a positive slope.
Answer:
The system of inequalities is
y\geq 3x-2
y<-(1/5)x+2
Step-by-step explanation:
step 1
Find the equation of the solid blue line
Let
A(0,-2), B(1,1)
Find the slope of AB
m=(1+2)/(1-0)=3
The equation of the line into slope intercept form is equal to
y=mx+b
we have
m=3
b=-2 - ----> the point A is the y-intercept
substitute
y=3x-2 - -----> equation of the solid blue line
The solution of the inequality is the shaded area above the solid line
therefore
The first inequality is
y\geq 3x-2
C(0,2), D(5,1)
step 2
Find the equation of the dashed red line
Let
Find the slope of CD
m=(1-2)/(5-0)=-1/5
The equation of the line into slope intercept form is equal to
y=mx+b
we have
m=-1/5
b=2 ----> the point C is the y-intercept
substitute
y=-(1/5)x+2 -----> equation of the dashed red line
The solution of the inequality is the shaded area below the dashed line
therefore
The second inequality is
y<-(1/5)x+2
The system of inequalities is
y\geq 3x-2
y<-(1/5)x+2
Answer: A
Step-by-step explanation: true true true
The equation of a line can be written in the form y=mx+b, where m is the slope and b is the y-intercept.
Since you are looking for a line with a slope (m) of -3/4 and a y-intercept (b) of 5... the equation you want is y = -3/4 x + 5
Answer:
σ should be adjusted at 0.5.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean 12.
Assuming we can precisely adjust σ, what should we set σtobe so that the actual amount dispensed is between 11 and 13 ounces, 95% of the time?
13 should be 2 standard deviations above the mean of 12, and 11 should be two standard deviations below the mean.
So 1 should be worth two standard deviations. Then
σ should be adjusted at 0.5.
