The amount of the radioactive substance is 374.6 g
<h3>How to determine the amount of
radioactive substance?</h3>
The given parameters are:
- Initial, a = 424 mg
- Rate, r = 6%
- Time, t = 2 hours
The amount of the radioactive substance is calculated as:
A(t) = a(1 - r)^t
This gives
A(t) = 424 * (1 - 6%)^t
At 2 hours, we have:
A(2) = 424 * (1 - 6%)^2
Evaluate
A(2) = 374.6
Hence, the amount of the radioactive substance is 374.6 g
Read more about exponential functions at:
brainly.com/question/2456547
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We define the probability of a particular event occurring as:

What are the total number of possible outcomes for the rolling of two dice? The rolls - though performed at the same time - are <em>independent</em>, which means one roll has no effect on the other. There are six possible outcomes for the first die, and for <em>each </em>of those, there are six possible outcomes for the second, for a total of 6 x 6 = 36 possible rolls.
Now that we've found the number of possible outcomes, we need to find the number of <em>desired</em> outcomes. What are our desired outcomes in this problem? They are asking for all outcomes where there is <em>at least one 5 rolled</em>. It turns out, there are only 3:
(1) D1 - 5, D2 - Anything else, (2), D1 - Anything else, D2 - 5, and (3) D1 - 5, D2 - 5
So, we have

probability of rolling at least one 5.
The <em>rigid</em> transformations used for each figure:
- Figure 5 - Reflection around x and y axes: (x, y) → (- x, - y)
- Figure 6 - Horizontal and vertical translations: (x, y) → (x + 1, y - 2)
<h3>What transformation rules do create the resulting images?</h3>
In this question we must determine what kind of <em>rigid</em> transformations generates each image. <em>Rigid</em> transformations are transformations applied on geometric loci such that <em>Euclidean</em> distance is conserved. Now we proceed to determine the transformation rule for each case:
Figure 5 - Reflection around the x-axis followed by reflection around the y-axis.
(x, y) → (- x, - y)
Figure 6 - Translation one unit in the +x direction and two units in the -y direction.
(x, y) → (x + 1, y - 2)
To learn more on transformation rules: brainly.com/question/9201867
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<h2>
Answer:</h2>
<em>Rounded to the nearest hundredth the volume of the composite figure is:</em>
<em>1308 33 cubic millimeters</em>
<h2>
Explanation:</h2>
Hello! I wrote the complete question in a comment above. The volume of a cylinder is defined as:

While the volume of half a sphere is:

Since we have 2 half spheres, then the volume of these is the same as the volume of a sphere:

Then, the composite figure is:

The radius of the cylinder is the same of the radius of each half sphere. So:

Answer:
The population will reach 34,200 in February of 2146.
Step-by-step explanation:
Population in t years after 2012 is given by:

In what month and year will the population reach 34,200?
We have to find t for which P(t) = 34200. So



Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
.
This polynomial has roots
such that
, given by the following formulas:



In this question:

So 
Then



We only take the positive value.
134 years after 2012.
.14 of an year is 0.14*365 = 51.1. The 51st day of a year happens in February.
So the population will reach 34,200 in February of 2146.