Answer:
The nearest option is -3 (negative 3)
So, Option B is correct.
Step-by-step explanation:
We need to solve the inequality
Solving:
Step 1: Switching sides of inequality and reversing the inequality
Step 2: Adding 4 on both sides
Step 3: Dividing both sides by -3 and reversing the inequality
The nearest option is -3 (negative 3)
So, Option B is correct.
Answer:
The sample size to obtain the desired margin of error is 160.
Step-by-step explanation:
The Margin of Error is given as
Rearranging this equation in terms of n gives
Now the Margin of Error is reduced by 2 so the new M_2 is given as M/2 so the value of n_2 is calculated as
As n is given as 40 so the new sample size is given as
So the sample size to obtain the desired margin of error is 160.
The vectors in form a basis of
if they are mutually linearly independent and span
.
To check for independence, we can compute the Wronskian determinant:
The determinant is non-zero, so the vectors are indeed independent.
To check if they span , you need to show that any vector in
can be expressed as a linear combination of the vectors in
. We can write an arbitrary vector in
as
Then we need to show that there is always some choice of scalars such that
This is equivalent to solving
or the system (in matrix form)
This has a solution if the coefficient matrix on the left is invertible. It is, because
(that is, the coefficient matrix is not singular, so an inverse exists)
Compute the inverse any way you like; you should get
Then
A solution exists for any choice of , so the vectors in
indeed span
.
The vectors in are independent and span
, so
forms a basis of
.