Answer:
The first table; <em>the first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 16, 8, 4, 2.</em>
Step-by-step explanation:
Exponential decay means that the graph or table is exponentially decreasing. Meaning, if you went from point 4 to 1, you would see an exponential increase. Other tables show other forms of functions, such as quadratic, or linear. To find out which rate it is decaying by, ask yourself, at 0, what is the y output? You can then divide the output of 0 by 1, and so on. If it is decaying at a consistent rate, then you know it is exponential. If you do not need to divide, but know it is decaying at a rate of two, it is linear. If it does not divide the first time smoothly, it is quadratic. It could also be a number of things.
I hope this helps you. We studied this quite a while ago, and I do not remember the equation at the tip of my tongue, and I do not want to give you wrong information. Have a great rest of your day!
Given Information:
Population size = N = 210
Mean height of women population = μ = 64.4 in.
Standard deviation of height of women population = σ = 2.9 in.
Sample size = n = 36
Required Information:
Sample mean = μx = ?
Sample standard deviation = σx = ?
Answer:
Sample mean = μx = 64.4 in.
Sample standard deviation = σx = 0.44 in.
Step-by-step explanation:
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
The mean of the sample will be same as population mean that is
μ = μx = 64.4 in
Whereas the sample standard deviation is given by
![\sigma_{x} = \frac{\sigma}{\sqrt{n} } \cdot \sqrt{\frac{N-n}{N-1} }](https://tex.z-dn.net/?f=%5Csigma_%7Bx%7D%20%3D%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%20%7D%20%5Ccdot%20%5Csqrt%7B%5Cfrac%7BN-n%7D%7BN-1%7D%20%7D)
Where σ is the standard deviation of height of women population, N is the population size and n is the sample size.
The term
is known as finite population correction factor and is used since the sampling is done without replacement.
![\sigma_{x} = \frac{2.9}{\sqrt{36} } \cdot \sqrt{\frac{210-36}{210-1} }\\\sigma_{x} = 0.483 \cdot \sqrt{\frac{174}{209} }\\\sigma_{x} = 0.483 \cdot 0.912\\\sigma_{x} = 0.44](https://tex.z-dn.net/?f=%5Csigma_%7Bx%7D%20%3D%20%5Cfrac%7B2.9%7D%7B%5Csqrt%7B36%7D%20%7D%20%5Ccdot%20%5Csqrt%7B%5Cfrac%7B210-36%7D%7B210-1%7D%20%7D%5C%5C%5Csigma_%7Bx%7D%20%3D%200.483%20%5Ccdot%20%5Csqrt%7B%5Cfrac%7B174%7D%7B209%7D%20%7D%5C%5C%5Csigma_%7Bx%7D%20%3D%200.483%20%5Ccdot%200.912%5C%5C%5Csigma_%7Bx%7D%20%3D%200.44)
Therefore, the standard deviation of sample is 0.44 in.
![3(4x - 2) = 12x \\ 12x - 6 = 12x \\ 12x - 12x = 6 \\ 0 = 6](https://tex.z-dn.net/?f=3%284x%20-%202%29%20%3D%2012x%20%5C%5C%2012x%20-%206%20%3D%2012x%20%5C%5C%2012x%20-%2012x%20%3D%206%20%5C%5C%200%20%3D%206)
The answer is no solution
The answer would be 2 because 4-2=2