Answer:
identify property
commutative property
associative property
Step-by-step explanation:
I took the assignment:)
Answer: 1.460
Step-by-step explanation:
Given : Researchers report that on average freshman who live on campus gain 15 pounds during their first year in college.
Let
represents the population mean .
Then, the set of hypothesis will be:-
![H_0: \mu=15](https://tex.z-dn.net/?f=H_0%3A%20%5Cmu%3D15)
![H_a:\mu\neq15](https://tex.z-dn.net/?f=H_a%3A%5Cmu%5Cneq15)
We assume that this is normal distribution.
Sample size : n = 10, which is a small sample (n<30) ,s o we use t-test.
Sample mean : ![\overliene{x}=16.2\ lbs](https://tex.z-dn.net/?f=%5Coverliene%7Bx%7D%3D16.2%5C%20lbs)
Standard deviation : ![\sigma=2.6](https://tex.z-dn.net/?f=%5Csigma%3D2.6)
The test statistic for population mean for small sample is given by :-
![t=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7B%5Coverline%7Bx%7D-%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
![t=\dfrac{16.2-15}{\dfrac{2.6}{\sqrt{10}}}=1.45951276623\approx1.460](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7B16.2-15%7D%7B%5Cdfrac%7B2.6%7D%7B%5Csqrt%7B10%7D%7D%7D%3D1.45951276623%5Capprox1.460)
Hence , the value of test statistic = 1.460
The definition of the piece-wise function is:
.
<h3>What is a piece-wise function?</h3>
A piece-wise function is a function that has different definitions, depending on the input.
In this problem, for inputs between -2 and 2, the function is a line that goes through (-2,-4) and (2,6). The slope is:
m = (6 - (-4))/(2 - (-2)) = 2.5.
The y-intercept is of b = 1, hence the rule is:
![f(x) = 2.5x + 1, -2 \leq x \leq 2](https://tex.z-dn.net/?f=f%28x%29%20%3D%202.5x%20%2B%201%2C%20-2%20%5Cleq%20x%20%5Cleq%202)
For x greater than 2 and less than 6, the function is constant at -3, hence the rule is:
.
More can be learned about piece-wise functions at brainly.com/question/27262465
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