Answer: x = 0
y = 2
z = -1
Step-by-step explanation:
The system of equations are
x+y+z=1 - - - - - - - - - - 1
-2x+4y+6z=2 - - - - - - - - - 2
-x+3y-5z=11 - - - - - - - - - 3
Step 1
We would eliminate x by adding equation 1 to equation 3. It becomes
4y -4z = 12 - - - - - - - - - 4
Step 2
We would multiply equation 1 by 2. It becomes
2x + 2y + 2z = 2 - - - - - - - - - 5
We would add equation 2 and equation 5. It becomes
6y + 8z = 4 - - - - - - - - - 6
Step 3
We would multiply equation 4 by 6 and equation 6 by 4. It becomes
24y - 24z = 72 - - - - - - - - 7
24y + 32z = 16 - - - - - - - - 8
We would subtract equation 8 from equation 7. It becomes
-56z = 56
z = -56/56 = -1
Substituting z = -1 into 7, it becomes
24y - 24×-1 = 72
24y + 24 = 72
24y = 72 - 24 = 48
y = 48/24 = 2
Substituting y = 2 and z = -1 into equation 1, it becomes
x + 2 - 1 = 1
x = 1 - 1 = 0
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 25235
For the alternative hypothesis,
µ > 25235
This is a right tailed test.
Since the population standard deviation is not given, the distribution is a student's t.
Since n = 100,
Degrees of freedom, df = n - 1 = 100 - 1 = 99
t = (x - µ)/(s/√n)
Where
x = sample mean = 27524
µ = population mean = 25235
s = samples standard deviation = 6000
t = (27524 - 25235)/(6000/√100) = 3.815
We would determine the p value using the t test calculator. It becomes
p = 0.000119
Since alpha, 0.05 > than the p value, 0.000119, then we would reject the null hypothesis. There is sufficient evidence to support the claim that student-loan debt is higher than $25,235 in her area.
When a series of events takes place, each with a fixed
number of possible values, the total number of possible outcomes is the product
of the number of values of each event. I am hoping that this
answer has satisfied your query and it will be able to help you in your
endeavor, and if you would like, feel free to ask another question.
