Answer:
Step-by-step explanation:
We'll take this step by step. The equation is
![8-3\sqrt[5]{x^3}=-7](https://tex.z-dn.net/?f=8-3%5Csqrt%5B5%5D%7Bx%5E3%7D%3D-7)
Looks like a hard mess to solve but it's actually quite simple, just do one thing at a time. First thing is to subtract 8 from both sides:
![-3\sqrt[5]{x^3}=-15](https://tex.z-dn.net/?f=-3%5Csqrt%5B5%5D%7Bx%5E3%7D%3D-15)
The goal is to isolate the term with the x in it, so that means that the -3 has to go. Divide it away on both sides:
![\sqrt[5]{x^3}=5](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7Bx%5E3%7D%3D5)
Let's rewrite that radical into exponential form:
![x^{\frac{3}{5}}=5](https://tex.z-dn.net/?f=x%5E%7B%5Cfrac%7B3%7D%7B5%7D%7D%3D5)
If we are going to solve for x, we need to multiply both sides by the reciprocal of the power:
![(x^{\frac{3}{5}})^{\frac{5}{3}}=5^{\frac{5}{3}}](https://tex.z-dn.net/?f=%28x%5E%7B%5Cfrac%7B3%7D%7B5%7D%7D%29%5E%7B%5Cfrac%7B5%7D%7B3%7D%7D%3D5%5E%7B%5Cfrac%7B5%7D%7B3%7D%7D)
On the left, multiplying the rational exponent by its reciprocal gets rid of the power completely. On the right, let's rewrite that back in radical form to solve it easier:
![x=\sqrt[3]{5^5}](https://tex.z-dn.net/?f=x%3D%5Csqrt%5B3%5D%7B5%5E5%7D)
Let's group that radicad into groups of 3's now to make the simplifying easier:
because the cubed root of 5 cubed is just 5, so we can pull it out, leaving us with:
which is the same as:
![x=5\sqrt[3]{25}](https://tex.z-dn.net/?f=x%3D5%5Csqrt%5B3%5D%7B25%7D)
Control = group with no music / maybe no variable?
Manipulated/independent variable = Number of tomatoes being grown
Dependent/responding = Number of tomatoes produced by each plant
Conclusion = Use four parts... Was your hypothesis correct or not and why...Cite numbers/evidence from experiment.... Were the results reliable?.... any improvements to be made
Can you re-phrase the question
Answer: ![p-value \approx 0.01](https://tex.z-dn.net/?f=p-value%20%5Capprox%200.01)
Step-by-step explanation:
Hypothesis testing
![\\\left\{\begin{matrix}H_0 : \mu_0 =0\\ H_1: \mu_0 \neq 0\end{matrix}\right.\\](https://tex.z-dn.net/?f=%5C%5C%5Cleft%5C%7B%5Cbegin%7Bmatrix%7DH_0%20%3A%20%5Cmu_0%20%3D0%5C%5C%20H_1%3A%20%5Cmu_0%20%5Cneq%200%5Cend%7Bmatrix%7D%5Cright.%5C%5C)
For this problem, we need to use the t-student distribution to make inference about the data. We calculate the t-statistics as below:
![\bar{X} = 20\:\mu m\\S.E. = 60\:\mu m\\n=82\\t_{stat} = \frac{\bar{X}-\mu_0}{S.E/\sqrt{n}}=\frac{20-0}{60/\sqrt{82}}=3.0185](https://tex.z-dn.net/?f=%5Cbar%7BX%7D%20%3D%2020%5C%3A%5Cmu%20m%5C%5CS.E.%20%3D%2060%5C%3A%5Cmu%20m%5C%5Cn%3D82%5C%5Ct_%7Bstat%7D%20%3D%20%5Cfrac%7B%5Cbar%7BX%7D-%5Cmu_0%7D%7BS.E%2F%5Csqrt%7Bn%7D%7D%3D%5Cfrac%7B20-0%7D%7B60%2F%5Csqrt%7B82%7D%7D%3D3.0185%20)
Using a t-statistics table, or using the function TDIST in Microsoft Excel with
with two-tailed distribution, we obtain
.
Answer:
This variation is a source of
response error.
Step-by-step explanation:
A response error shows the lack of accuracy in the customer responses to the survey questions. A response error can be caused by a questionnaire that requires framing improvements, misinterpretation of questions by interviewers or respondents, and errors in respondents' statements. Some responses are influenced by the answers provided to previous questions, which introduces response bias.