Answer:
Domain:- All real numbers
Range:-[3,infinite)
Step-by-step explanation:
In the function there's no value of x for which it is not defined thus domain is R.
Now a modulus will have always it's minimum value 0 thus minimum value of function is 0+3=3. And Max value of a modulus is infinite so infinite+3=infinite.
Answer: the first one :x=y+
−19
/8
the second one: x=y−2
Step-by-step explanation:
The answer is 16
Refer image for working :-
Drop comments if any doubt arises.
When dividing exponents you subtract the exponents. When multiplying you add them. When raising an exponent by an exponent you multiply them.<span />
Part A:
Significant level:
<span>α = 0.05
Null and alternative hypothesis:
</span><span>h0 : μ = 3 vs h1: μ ≠ 3
Test statistics:

P-value:
P(-0.9467) = 0.1719
Since the test is a two-tailed test, p-value = 2(0.1719) = 0.3438
Conclusion:
Since the p-value is greater than the significant level, we fail to reject the null hypothesis and conclude that there is no sufficient evidence that the true mean is different from 3.
Part B:
The power of the test is given by:

Therefore, the power of the test if </span><span>μ = 3.25 is 0.8105.
Part C:
</span>The <span>sample size that would be required to detect a true mean of 3.75 if we wanted the power to be at least 0.9 is obtained as follows:


Therefore, the </span>s<span>ample size that would be required to detect a true mean of 3.75 if we wanted the power to be at least 0.9 is 16.</span>