Determine whether the slope line is positive or negative and then find the slope of each line?
1 answer:
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Isolate the root expression:
![\sqrt[3]{x+1}+2=0\implies\sqrt[3]{x+1}=-2](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%2B1%7D%2B2%3D0%5Cimplies%5Csqrt%5B3%5D%7Bx%2B1%7D%3D-2)
Take the third power of both sides:
![\sqrt[3]{x+1}=-2\implies(\sqrt[3]{x+1})^3=(-2)^3](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%2B1%7D%3D-2%5Cimplies%28%5Csqrt%5B3%5D%7Bx%2B1%7D%29%5E3%3D%28-2%29%5E3)
Simplify:
![(\sqrt[3]{x+1})^3=(-2)^3\implies x+1=-8](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7Bx%2B1%7D%29%5E3%3D%28-2%29%5E3%5Cimplies%20x%2B1%3D-8)
Isolate and solve for
:
Since the cube root function is bijective, we know this won't be an extraneous solution, but it doesn't hurt to verify that this is correct. When, we have
![\sqrt[3]{-9+1}=\sqrt[3]{-8}=\sqrt[3]{(-2)^3}=-2](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-9%2B1%7D%3D%5Csqrt%5B3%5D%7B-8%7D%3D%5Csqrt%5B3%5D%7B%28-2%29%5E3%7D%3D-2)
as required.
Take the third power of both sides:
Simplify:
Isolate and solve for
Since the cube root function is bijective, we know this won't be an extraneous solution, but it doesn't hurt to verify that this is correct. When
as required.
Answer:
The upper limit for the 95% confidence interval for the population proportion of defective gaming systems is 0.022
Step-by-step explanation:
Upper Limit for 95% Confidence Interval can be calculated using p+ME where
- p is the sample proportion of defective gaming systems (
)
- ME is the margin of error from the mean
and margin of error (ME) around the mean can be found using the formula
ME= where
- z is the statistic of 95% confidence level (1.96)
- p is the sample proportion (
- N is the sample size (1200)
Using the numbers we get:
ME= ≈ 0.007
Then upper limit for the population proportion is 0.015+0.007 =0.022