A store sells small notebooks

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

How do I prove that a quadrilateral is a rectangle? (in a Column chart with statement and reason)

klasskru [66]

By definition, we have to:

In plane geometry, a rectangle is a parallelogram whose four sides are at right angles to each other. Opposite sides have the same length.

There is a proof that a quadrilateral is a rectangle:

1) Its parallel sides are the same.

2) Its two diagonals are the same, and they bisect each other at the common midpoint

3) Any rectangle can be inscribed in a circle, two of whose diameters coincide with the diagonals of the rectangle.

4) If all the angles of a quadrilateral are right angles, then it is a rectangle

7 0

3 years ago

Adam currently runs about 20 miles per week,aND he wants to increase his weekly mileage by 40% How many miles will Adam run per

Afina-wow [57]

28 miles

increasing by 40% = original + increase = 100 + 40 = 140% = 1.4

multiplying 20 by 1.4 gives total he will run

miles run = 1.4 × 20 = 28

3 0

3 years ago

Read 2 more answers

If x^2 +2xy -8 = 0, then when x = 4, dy/dx =

Katena32 [7]

For simplicity, dy/dx means f'(x);
We have y = ( 8 - x^2 ) / 2x;
Then, y = 4/x - x/2;
So, f'(x) = (4/x - x/2)' = (4/x)' - (x/2)' = -4/(x^2) -1/2 because we use differentiation formulas, such as : (f+g)' = f' + g'; (cf)' = cf'; x'=1; (1/x)' = -1/(x^2);
Finally, f'(4) = -4/16 -1/2 = -4/16 - 8/16 = -12/16 = -3/4.
The correct answer is E.

3 0

3 years ago

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Please show me 3+2 (2x - 4) and can you please show the work?

Julli [10]

Answer:

4x -5

Step-by-step explanation:

3+2 (2x - 4)

Distribute

3 + 2*2x - 2*4

3+4x - 8

Combine like terms

4x +3-8

4x -5

7 0

3 years ago

Read 2 more answers