Find the surface area of the pyramid: A. 88 in. B. 118 in. C. 64 in. D. 56 in.

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 can you analyze the numerator and/or the denominator in a rational expression to locate the x-intercepts?

andre [41]

Answer:

$x=0$ for $f(x)=\frac{P(x)}{Q(x)}$ , with $Q(x) \neq 0$ .

Step-by-step explanation:

To obtain x-intercepts, we need to give certain value, specifically $x=0$ .

However, in case of a rational function, we must make sure that $x=0$ doesn't makes the denominator null, beacuse in that case the function is undefined.

Therefore, for x-intercepts we must say

$x=0$ for $f(x)=\frac{P(x)}{Q(x)}$ , with $Q(x) \neq 0$ .

7 0

2 years ago

the British Thermal Unit(BTU) is a unit of energy used globally in air conditioning industries. the number of BTUs needed to coo

7nadin3 [17]

Answer:

32.5 m^2

Step-by-step explanation:

B = 377lw

I will use L for length instead of l.

B = 12,252.5 BTU

w = 5 m

First, we find the length.

12,252.5 = 377(L)(5)

12,252.5 = 1885L

L = 6.5

The length is 6.5 m. The width is 5 m.

A = LW = (6.5 m)(5 m) = 32.5 m^2

4 0

3 years ago

Jack,sally, and joe all work in a bookstore.jack sold 126 books.joe 1/2 as many books as jack,and sally sold 1/3 as many books a

Darina [25.2K]

Sally sold 2302323 books!

7 0

3 years ago

Solve the inequalities x2 < 3 - 2x

ddd [48]

Inequality Form:

−3 < x < 1

3 0

2 years ago