Answer:
Step-by-step explanation:

The set is linearly dependent.
To explicitly prove this, we need to show there is at least one choice of constants
such that

or equivalently,

which is the same as solving the system of equations

From the first and last equations, we have
and
. Substituting these into the second equation leaves us with
, and so the overall solution set is

for which there are infinitely many not-all-zero solutions.
Answer:
We have been given confidence interval 95%, mean 20 , data set 30 and standard deviation 3.
We will use the formula: 
Here,
Z-score value at 95% confidence interval is 1.96
On substituting the values in the formula to plug the values:

Now, we have a formula for marginal error:
Marginal error means your answer will be within that percentage only.
Say you have 3% marginal means your value will be within 3% real population 95% of the time.
Using a calculator, inserting the values of x and y, the correlation coefficient for the given data-set is of -0.9422.
<h3>How to find the correlation coefficient of a data-set?</h3>
Using a calculator, the correlation coefficient is found inserting the ordered pairs (x,y) in the calculator.
In this problem, we have that:
- The values of x are: 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5.
- The values of y are: 112.5, 110.875, 106.8, 100.275, 91.3, 79.875, 70.083, 59.83, 30.65, 0.
Hence, using a calculator, the correlation coefficient is of -0.9422.
More can be learned about correlation coefficients at brainly.com/question/25815006
#SPJ1