Mary had five and one-half dollars. She spent tw wo and one-fourth dollars on a snack. How much money does Mary have left?
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Answer:
Explained below.
Step-by-step explanation:
The random variable <em>X</em> is defined as the number of stars in a given volume of space.
The probability mass function of <em>X</em> is:
(7)
Compute the probability of exactly two stars in 16 cubic light-years as follows:
(8)
Compute the probability of three or more stars in 16 cubic light-years as follows:
(9)
In 16 cubic light years there is only 1 star.
Then in 1 cubic light years there will be, (1/16) stars.
Then in 4 cubic light years there will be, 4 × (1/16) = (1/4) stars.
(10)
In 16 cubic light years there is only 1 star.
Then in 1 cubic light years there will be, (1/16) stars.
Then in <em>t</em> cubic light years there will be, [<em>t</em> × (1/16)] stars.
No, we do not multiply the first equation by 2 and then add it to the second equation. We have to multiply the first equation by 4.
To illustrate this point, consider system A:
If we multiply the first equation by 2, we get
Now, if we replace the second equation with the sum of the second equation and , we get
which simplifies to
This is not an equivalent system to System B. We can see that we ended up with a 2y = 4 equation.
In order to end up with a 2x = 10 second equation, we have to multiply the first equation of system A by 4 to get
If we replace the second equation with the sum of the second equation and , we get
which simplifies to
Otherwise, you are correct. The solution to system B is the solution to system A. Adding an equation to another does not change the system.