Answer:
<h2><em><u>Option</u></em><em><u> </u></em><em><u>B</u></em><em><u>:</u></em></h2><h2>Step-by-step explanation:
<em><u>Given</u></em><em><u>,</u></em>
Number of numbers of each side of the cube
= 4, 5, 6, 7, 8 and 9
= 6 numbers
Number of sides of cube having the number 5
= 1
<em><u>Therefore</u></em><em><u>,</u></em><em><u> </u></em>
Probability of getting a side of the cube of no. 5 is
Answer:
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
And using the fact that and our assumption that
, we see that
as we wanted.
