Answer:
The population of the city in 2002 is 469,280 while the population of the suburb is 730,720.
Step-by-step explanation:
- 6% of the city's population moves to the suburbs (and 94% stays in the city).
- 2% of the suburban population moves to the city (and 98% remains in the suburbs).
The migration matrix is given as:
![A= \left \begin{array}{cc} \\ C \\S \end{array} \right\left[ \begin{array}{cc} C&S\\ 0.94&0.06 \\0.02&0.98 \end{array} \right]](https://tex.z-dn.net/?f=A%3D%20%5Cleft%20%5Cbegin%7Barray%7D%7Bcc%7D%20%20%5C%5C%20C%20%5C%5CS%20%5Cend%7Barray%7D%20%5Cright%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bcc%7D%20%20C%26S%5C%5C%200.94%260.06%20%5C%5C0.02%260.98%20%5Cend%7Barray%7D%20%5Cright%5D)
The population in the year 2000 (initial state) is given as:
![\left[ \begin{array}{cc} C&S\\ 500,000&700,000 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bcc%7D%20%20C%26S%5C%5C%20500%2C000%26700%2C000%20%20%5Cend%7Barray%7D%20%5Cright%5D)
Therefore, the population of the city and the suburb in 2002 (two years after) is:
![S_0A^2=\left \begin{array}{cc} [500,000&700,000]\\& \end{array} \right\left \begin{array}{cc} \end{array} \right\left[ \begin{array}{cc} 0.94&0.06 \\0.02&0.98 \end{array} \right]^2](https://tex.z-dn.net/?f=S_0A%5E2%3D%5Cleft%20%5Cbegin%7Barray%7D%7Bcc%7D%20%5B500%2C000%26700%2C000%5D%5C%5C%26%20%20%5Cend%7Barray%7D%20%5Cright%5Cleft%20%5Cbegin%7Barray%7D%7Bcc%7D%20%5Cend%7Barray%7D%20%5Cright%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bcc%7D%200.94%260.06%20%5C%5C0.02%260.98%20%5Cend%7Barray%7D%20%5Cright%5D%5E2)
![A^{2} = \left[ \begin{array}{cc} 0.8848 & 0.1152 \\\\ 0.0384 & 0.9616 \end{array} \right]](https://tex.z-dn.net/?f=A%5E%7B2%7D%20%3D%20%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bcc%7D%200.8848%20%26%200.1152%20%5C%5C%5C%5C%200.0384%20%26%200.9616%20%5Cend%7Barray%7D%20%5Cright%5D)
Therefore:
![S_0A^2=\left \begin{array}{cc} [500,000&700,000]\\& \end{array} \right\left \begin{array}{cc} \end{array} \right \left[ \begin{array}{cc} 0.8848 & 0.1152 \\ 0.0384 & 0.9616 \end{array} \right]\\\\=\left[ \begin{array}{cc} 500,000*0.8848+700,000*0.0384& 500,000*0.1152 +700,000*0.9616 \end{array} \right]\\\\=\left[ \begin{array}{cc} 469280& 730720 \end{array} \right]](https://tex.z-dn.net/?f=S_0A%5E2%3D%5Cleft%20%5Cbegin%7Barray%7D%7Bcc%7D%20%5B500%2C000%26700%2C000%5D%5C%5C%26%20%20%5Cend%7Barray%7D%20%5Cright%5Cleft%20%5Cbegin%7Barray%7D%7Bcc%7D%20%5Cend%7Barray%7D%20%5Cright%20%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bcc%7D%200.8848%20%26%200.1152%20%5C%5C%200.0384%20%26%200.9616%20%5Cend%7Barray%7D%20%5Cright%5D%5C%5C%5C%5C%3D%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bcc%7D%20500%2C000%2A0.8848%2B700%2C000%2A0.0384%26%20500%2C000%2A0.1152%20%2B700%2C000%2A0.9616%20%5Cend%7Barray%7D%20%5Cright%5D%5C%5C%5C%5C%3D%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bcc%7D%20469280%26%20730720%20%5Cend%7Barray%7D%20%5Cright%5D)
Therefore, the population of the city in 2002 is 469,280 while the population of the suburb is 730,720.
<span>Divide by 3 get a remainder of 2
5, 8, 11, 14, 17, 20, ...
Divide by 5 get a remainder of 2
7 , 12, 17, 23, ...
Divide by 7 get a reminder of 5
12, 19, 26, 33, ...
And find a number in all three lists
</span>
<span>Not the most convenient way for sure, but since 47 works it will not take too long</span><span>
</span>
7) Certainly there is a typo in the statement, just see that the expression of item (ii) is different from that of item (i). Probably the correct expression is:
. With this consideration, we can continue.
(i) Let E the expression that we are analyzing:
Since (x-1)² is a perfect square, it is a positive number. So, E is a result of a sum of two positive numbers, 2(x-1)² and 3. Hence, E is a positive number, too.
(ii) Manipulating the expression:
So, it's the case when E=0. However, E is always a positive number. Then, there is no real number x that satisfies the expression.
8) Let E the expression that we want to calculate:
Multiplying by (2-1) in the both sides:
Repeating the process, we obtain:
Answer:
{A and B are independent events}, P(A|B)=P(A)=0.16
Step-by-step explanation:
First of all we need to know when does two events become independent:
For the two events to be independent, P(A|B)=P(A) that is if condition on one does not effect the probability of other event.
Here, in our case the only option that satisfies the condition for the events to be independent is P(A|B)=P(A)=0.16.. Rest are not in accordance with the definition of independent events.
Answer:
25
Step-by-step explanation:
15/6.0=2.5
2.5x4=10
2.5x6=15
10+15=25
10 boys and 15 girls
