Answer:
b) H0:μ=90, H1:μ≠90
Step-by-step explanation:
The corporation wants to know if the mean number of days is different from the 90 days claimed.
This means that at the null hypothesis, we test if the mean number is the claimed value of 90, and so:
The corporations wants to know if the mean number is different, and thus, at the alternate hypothesis, we test if the mean number is different from 90, that is:
This means that the correct answer is given by option b.
This means x = 2, y = 3 and z = 1
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Work Shown:
Double everything in the second equation to get 4x-2y+4z=6
Add this result to the first equation
The first two lines of that expression above shows us adding x+2y-4z=4 to the equation 4x-2y+4z = 6
The x terms add to x+4x = 5x
The y terms add to 2y+(-2y) = 0y
The z terms add to -4z+4z = 0z
The terms on the right hand side add to 4+6 = 10
That's how we end up with the new equation 5x+0y+0z = 10
That becomes 5x = 10 which solves to x = 2 when we divide both sides by 5.
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Use this x value in the third original equation to find z
3x-8z = -2
3(2)-8z = -2
6-8z = -2
-8z = -2-6
-8z = -8
z = -8/(-8)
z = 1
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Use the x and z values we found to find y
x+2y-4z = 4
2+2y-4(1) = 4
2+2y-4 = 4
2y-2 = 4
2y = 4+2
2y = 6
y = 6/2
y = 3
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Overall we get the solutions to be x = 2, y = 3 and z = 1
We can say the solution as an ordered triple is (x,y,z) = (2,3,1)