Answer:
The constant of variation for the given quadratic equation is, 30
Step-by-step explanation:
One of the form of a quadratic equation is written as:
....[1]
where k is the coefficient and for this case the constant of variation.
In order to obtain the answer for the given equation, we write the given equation to the form above.
or
or
Comparing this equation with equation [1], to get the value of k;
k=30.
therefore, the constant of variation is, 30.
Answer:
a)
And for this case if we use this formula we got:
b) Since we have n =16 values for the sample the median can be calculated as the average between position 8th anf 9th and we got:
c) (a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 90% of data from the top 10% is 1.8024.
d)
The variance for this estimator is given by:
We can assume the obervations independent so then we have:
And replacing we got:
And the standard error would be given by:
Step-by-step explanation:
Data given:
0.86 0.88 0.88 1.07 1.09 1.17 1.29 1.31 1.46 1.49 1.59 1.62 1.65 1.71 1.76 1.83
Part a
We can calculate the mean with the following formula:
And for this case if we use this formula we got:
Part b
For this case in order to calculate the median we need to put the data on increasing way like this:
0.86 0.88 0.88 1.07 1.09 1.17 1.29 1.31 1.46 1.49 1.59 1.62 1.65 1.71 1.76 1.83
Since we have n =16 values for the sample the median can be calculated as the average between position 8th anf 9th and we got:
Part c
For this case we can assume that the mean is
And we can calculate the population deviation with the following formula:
And if we replace we got:
And assuming normal distribution we have this:
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 90% of data from the top 10% is 1.8024.
Part d
The median is defined as :
The variance for this estimator is given by:
We can assume the obervations independent so then we have:
And replacing we got:
And the standard error would be given by:
Answer:
The area of rectangle C is 2
Step-by-step explanation:
Using a scale factor of yields the side lengths of 1 and 2
For a better understanding of the solution provided please go through the diagram in the file attached.
Let ABCD be the rectangular yard. The diagonal d=17 meters. AD=8 meters. Therefore, the length of DC can be found by applying the Pythagorean theorem in the right triangle as:
meters.
