We have to find the potential solutions to
from least to greatest.
Using the properties of ln function.

Therefore, we get


taking antilog on both the sides, we get

So, 
Therefore, the potential solutions to 2 ln x = 4 ln 2 from least to greatest is -4 and 4.
Answer:
The sample consisting of 64 data values would give a greater precision.
Step-by-step explanation:
The width of a (1 - <em>α</em>)% confidence interval for population mean μ is:

So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (<em>n</em>).
That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.
Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.
The two sample sizes are:
<em>n</em>₁ = 25
<em>n</em>₂ = 64
The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.
Width for n = 25:
Width for n = 64:
![\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{64}}=\frac{1}{8}\cdot [2\cdot z_{\alpha/2}\cdot \sigma]](https://tex.z-dn.net/?f=%5Ctext%7BWidth%7D%3D2%5Ccdot%20z_%7B%5Calpha%2F2%7D%5Ccdot%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7B64%7D%7D%3D%5Cfrac%7B1%7D%7B8%7D%5Ccdot%20%5B2%5Ccdot%20z_%7B%5Calpha%2F2%7D%5Ccdot%20%5Csigma%5D)
Thus, the sample consisting of 64 data values would give a greater precision
For this case, the parent function is given by:

Applying the following transformation we have:
Vertical displacement
Assume k> 0,
To graph y = f (x) + k, move the graph k units up.
We have then:
Answer:
the equation of F (x) is given by:
Dependent and independent variables. ... The dependent variables represent the output or outcome whose variation is being studied. The independent variables, also known in a statistical context as regressors, represent inputs or causes, that is, potential reasons for variation.
An independent variable is a variable that is manipulated to determine the value of a dependent variable s. The dependent variable is what is being measured in an experiment or evaluated in a mathematical equation and the independent variables are the inputs to that measurement.
I hope this helps you out
Using the given formula T = LS
And given the time is 3 minutes (3 x 60 = 180 seconds)and the speed is 4-1/2 inches per second:
180 = L x 4-1/2
Solve for L by dividing both sides by 4-1/2:
L = 180 / 4-1/2
L = 40
The length should be 40 inches.