I used the app SnapCalc Just so u know
Answer:
![M=\log{(100S)}](https://tex.z-dn.net/?f=M%3D%5Clog%7B%28100S%29%7D)
Step-by-step explanation:
The <em>Richter scale</em>, the standard measure of earthquake intensity, is a <em>logarithmic scale</em>, specifically logarithmic <em>base 10</em>. This means that every time you go up 1 on the Richter scale, you get an earthquake that's 10 times as powerful (a 2.0 is 10x stronger than a 1.0, a 3.0 is 10x stronger than a 2.0, etc.).
How do we compare two earthquake's intensities then? As a measure of raw intensity, let's call a "standard earthquake" S. What's the magnitude of this earthquake? The magnitude is whatever <em>power of 10</em> S corresponds to; to write this relationship as an equation, we can say
, which we can rewrite in logarithmic form as
.
We're looking for the magnitude M of an earthquake 100 times larger than S, so reflect this, we can simply replace S with 100S, giving us the equation
.
To check to see if this equation is right, let's say we have an earthquake measuring a 3.0 on the Richter scale, so
. Since taking 100 times some intensity is the same as taking 10 times that intensity twice, we'd expect that more intense earthquake to be a 5.0. We can expand the equation
using the product rule for logarithms to get the equation
![M=\log{(100S)}=\log{100}+\log{S}](https://tex.z-dn.net/?f=M%3D%5Clog%7B%28100S%29%7D%3D%5Clog%7B100%7D%2B%5Clog%7BS%7D)
And using the fact that
and our assumption that
, we see that
as we wanted.
Answer:
Yes the conclusion in the question is a reasonable conclusion
Step-by-step explanation:
From the question we are told that
The sample size is
The sample mean for USA is ![\= x_1 = 391 \ minutes](https://tex.z-dn.net/?f=%5C%3D%20x_1%20%3D%20%20391%20%5C%20minutes)
The sample mean for Mexico is ![\= x_2 = 426 \ minutes](https://tex.z-dn.net/?f=%5C%3D%20x_2%20%3D%20426%20%5C%20minutes)
The sample standard deviation for USA is ![s_1 = 25 \ minutes](https://tex.z-dn.net/?f=s_1%20%3D%20%2025%20%5C%20minutes)
The sample standard deviation for Mexico is ![s_2 = 49 \ minutes](https://tex.z-dn.net/?f=s_2%20%3D%20%2049%20%5C%20%20minutes)
The null hypothesis is ![H_o : \mu_1 = \mu_2](https://tex.z-dn.net/?f=H_o%20%20%3A%20%20%5Cmu_1%20%3D%20%5Cmu_2)
The alternative hypothesis is ![H_a : \mu_1 < \mu_2](https://tex.z-dn.net/?f=H_a%20%20%3A%20%20%5Cmu_1%20%20%3C%20%5Cmu_2)
Generally the test statistics is mathematically represented as
![z = \frac{\= x_1 - \= x_2 }{ \sqrt{ \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2 } } }](https://tex.z-dn.net/?f=z%20%3D%20%20%5Cfrac%7B%5C%3D%20x_1%20-%20%5C%3D%20x_2%20%7D%7B%20%5Csqrt%7B%20%5Cfrac%7Bs_1%5E2%7D%7Bn_1%7D%20%2B%20%5Cfrac%7Bs_2%5E2%7D%7Bn_2%20%7D%20%7D%20%7D)
=> ![z = \frac{ 391 - 426 }{ \sqrt{ \frac{25^2}{250} + \frac{49^2}{250} } }](https://tex.z-dn.net/?f=z%20%3D%20%20%5Cfrac%7B%20391%20%20-%20426%20%20%7D%7B%20%5Csqrt%7B%20%5Cfrac%7B25%5E2%7D%7B250%7D%20%2B%20%5Cfrac%7B49%5E2%7D%7B250%7D%20%7D%20%7D)
=> ![z = -10](https://tex.z-dn.net/?f=z%20%3D%20%20-10)
From the z table the area under the normal curve to the left corresponding to -10 is
![p-value = P(Z < -10 ) = 0.00](https://tex.z-dn.net/?f=p-value%20%3D%20%20P%28Z%20%3C%20%20-10%20%29%20%3D%20%200.00)
Generally from the value obtained we see that
The p-value is <
hence
The decision rule is
Reject the null hypothesis
The conclusion is
The is sufficient evidence to conclude that adults in the United States get less sleep on work nights than adults in Mexico
Hence the conclusion in the question is a reasonable conclusion
Answer:
7m-3
Step-by-step explanation:
first, distribute
m+3m+3m-3
then, combine all like terms
m+6m-3
7m-3
i hope this helps! have a nice day!