Answer: h = 9
Step-by-step explanation: A system of linear equations is consistent when it has at least one solution.
The matrix given is:
![\left[\begin{array}{ccc}-15&21&h\\5&-7&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-15%2621%26h%5C%5C5%26-7%26-3%5Cend%7Barray%7D%5Cright%5D)
Transform this matrix in a row-echelon form:
![\left[\begin{array}{ccc}-15&21&h\\0&0&-9+h\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-15%2621%26h%5C%5C0%260%26-9%2Bh%5Cend%7Barray%7D%5Cright%5D)
For this row-echelon form to have solutions:
-9 + h = 0
h = 9
For this system to be consistent: h = 9.
Answer:
C. (36337.32, 48968.68)
Step-by-step explanation:
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of
.
So it is z with a pvalue of
, so 
Now, find M as such

In which
is the standard deviation of the population and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 42653 - 6315.68 = 36337.32.
The upper end of the interval is the sample mean added to M. So it is 42653 + 6315.68 = 48968.68.
So the correct answer is:
C. (36337.32, 48968.68)
Answer:
h. 36
Step-by-step explanation:
For a 68.26% confidence, z = 1.0.
Standard deviation (s) = 30 minutes
The sample size needed to assure that the sample mean does not differ from the true mean by more than 5 minutes is given by:
The sample size needed is 36.
Answer:
f(3) = 4
f(-7) = -26
Step-by-step explanation:
Hi there!

To find f(3), replace every x with 3:

Therefore, f(3)=4.

To find f(-7), replace every x with -7:

Therefore, f(-7)=-26.
I hope this helps!