Franco played computer chess for 2 hours Lian played computer chess for 90 minutes compare the times spent playing computer ches
2 answers:
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Answer:
x = 0; y = -6; z = 1
Step-by-step explanation:
You want to find the solution to the system of equations ...
- 9x+y-3z=-9
- 10x-y+2z=8
- -10x-y+4z=10
This set of equations is conveniently solved using the matrix row-reduction features of a scientific or graphing calculator, spreadsheet, or any of a number of apps or on-line calculators.
The attachment shows the solution to be ...
(x, y, z) = (0, -6, 1)
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<em>Additional comment</em>
Solving a system of three or more equations "by hand" often can be done by an ad hoc process. It can be done in systematic fashion using Gauss-Jordan reduction techniques, but that often gets messy. Similarly, Cramer's Rule can be used, but that math tends to involve more arithmetic operations than are really necessary.
Adding the first equation to the other two eliminates the y-variable and reduces the system to two equations in two unknowns.
(9x +y -3z) +(10x -y +2z) = (-9) +(8) . . . . adding [1] and [2]
19x -z = -1 . . . . simplified
(9x +y -3z) +(-10x -y +4z) = (-9) +(10) . . . . adding [1] and [3]
-x +z = 1 . . . . simplified
At this point, we could graph the two equations, or we can proceed algebraically.
Adding these two equations gives ...
(19x -z) +(-x +z) = (-1) +(1)
18x = 0 ⇒ x = 0
Using the second of the reduced equations, we find ...
-x +z = 1
0 +z = 1 ⇒ z = 1
And using the second of the original equations, gives us ...
10(0) -y +2(1) = 8
-y = 6 . . . . . subtract 2
y = -6 . . . . multiply by -1
Then the solution is (x, y, z) = (0, -6, 1), as above.
Answer:
Null hypothesis:
Alternative hypothesis:
b) 2.70
b. 1.85
b. 0.03
a. We can reject H(0) in favor of H(a)
Step-by-step explanation:
Data given and notation
represent the mean for the sample 1
represent the mean for the sample 2
represent the population standard deviation for the sample 1
represent the population standard deviation for the sample B2
sample size selected 1
sample size selected 2
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the expenditure of households in City 1 is more than that of households in City 2, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We know the population deviations, so for this case is better apply a z test to compare means, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".
Standard error
The standard error on this case is given by:
Replacing the values that we have we got:
b. 2.70
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
Since is a one side right tailed test the p value would be:
b. 0.03
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis.
a. We can reject H(0) in favor of H(a)