Three hundred trillion, two hundred seventy-two million, seven hundred fifteen

In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than on

Kazeer [188]

Answer:

In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.

In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.

In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.

Step-by-step explanation:

We have to write the transition matrix M for the population.

We have three states (nonsmokers, smokers of one pack and smokers of more than one pack), so we will have a 3x3 transition matrix.

We can write the transition matrix, in which the rows are the actual state and the columns are the future state.

- There is an 8% probability that a nonsmoker will begin smoking a pack or less per day, and a 2% probability that a nonsmoker will begin smoking more than a pack per day. Then, the probability of staying in the same state is 90%.

- For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. Then, the probability of staying in the same state is 80%.

- For smokers who smoke more than a pack per day, there is an 8% probability of quitting and a 10% probability of dropping to a pack or less per day. Then, the probability of staying in the same state is 82%.

The transition matrix becomes:

$\begin{vmatrix} &NS&P1&PM\\NS& 0.90&0.08&0.02 \\ P1&0.10&0.80 &0.10 \\ PM& 0.08 &0.10&0.82 \end{vmatrix}$

The actual state matrix is

$\left[\begin{array}{ccc}5,000&2,500&2,500\end{array}\right]$

We can calculate the next month state by multupling the actual state matrix and the transition matrix:

$\left[\begin{array}{ccc}5000&2500&2500\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] =\left[\begin{array}{ccc}4950&2650&2400\end{array}\right]$

In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.

To calculate the the state for the second month, we us the state of the first of the month and multiply it one time by the transition matrix:

$\left[\begin{array}{ccc}4950&2650&2400\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] =\left[\begin{array}{ccc}4912&2756&2332\end{array}\right]$

In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.

If we repeat this multiplication 12 times from the actual state (or 10 times from the two-months state), we will get the state a year from now:

$\left( \left[\begin{array}{ccc}5000&2500&2500\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] \right)^{12} =\left[\begin{array}{ccc}4792.63&3005.44&2201.93\end{array}\right]$

In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.

3 0

3 years ago

PLEASE HELPPPPPP!!

Sergeeva-Olga [200]

This transformation is called a rotation.

6 0

3 years ago

Read 2 more answers

Question 3

Yuliya22 [10]

Answer:

Median and Mode.

Step-by-step explanation:

The data could be represented in table form in ascending order as:

Number of meals Frequency

2 2

3 3

4 2

19 1`

On the basis of the data now we find the mean, median and mode:

Mean= average of the data

Mean=\dfrac{2\times 2+3\times 3+4\times 2+19\times 1}{2+3+2+1}=\dfrac{40}{8}=5

Hence mean is 5.

Median is the central tendency of the data

on looking at our data we see that the Median=3.

also the mode of the data is the entry corresponding to the highest entry.

Hence the highest frequency is 3 and the corresponding value is 3.

Hence, Mode=3

Hence, the most appropriate measure of center for this situation is :

Median and Mode.

4 0

3 years ago

How do I find the midpoint of the segment with the given points

Leokris [45]

9 + (-4) = 5/2= 2.5
10 + 7 = 17/2 = 8.5

4 0

3 years ago

PLEASE HELP! I will mark brainliest!

Nitella [24]

Answer:

D

Step-by-step explanation:

Instead of going through each of the table, let's create one ourselves.

So, we have the piecewise function:

$f(x)=-x+8,\text{ if } x$

So, let's create a table of values starting with 2 and skipping the odd numbers until 12.

2:

For 2, since 2 is less than one, plug it into the first equation. Thus:

$f(2)=-(2)+8=6$

So, the first value is (2,6).

For 4, since 4 is not less than 4 but rather equal to 4, use the second equation. Thus:

$f(4)=(4)=4$

The second value is (4,4).

For 6, the same thing. 6 is greater than 4 so use the second equation:

$f(6)=(6)=6$

So the third value is (6,6).

And this pattern will repeat. Therefore, our table of equations is:

x | y

2 | 6

4 | 4

6 | 6

8 | 8

10 | 10

12 | 12

The choice that represents this is D. D is the correct answer.

5 0

3 years ago