Solve the linear system of equations 8x−4y=20 5x−8y=62 x= y=
1 answer:
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<h2><u>Answer with explanation</u>:</h2>
Let be the average life of light bulbs.
As per given , we have
Null hypothesis :
Alternative hypothesis :
Since is right-tailed and population standard deviation is also known, so we perform right-tailed z-test.
Formula for Test statistic :
where, n= sample size
= sample mean
= Population mean
=population standard deviation
For , we have
Using z-value table , Critical one-tailed test value for 0.06 significance level :
Decision : Since critical z value (1.5548) < test statistic (1.6180), so we reject the null hypothesis .
[We reject the null hypothesis when critical value is less than the test statistic value .]
Conclusion : We have enough evidence at 0.06 significance level to support the claim that the new filament yields a longer bulb life
The Solution for the given system of equations is (-2) and .
The given are linear equations as follow:
y = + 3 .. ... ...(1)
and x = -2. .. .... ...(2)
We already know the first part of the solution (x) which is -2. We can find the other part (y) by putting the value of equation (2) in equation (1).
By putting the values of x in equation (1), we get
y = + 3
y = + 3
Taking the L. C. M of denominators which will be '3', we get:
y =
y =
So the second part (y) of the solution of the given equation is .
Hence, the overall solution to the given system of equation is .
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