1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ludmilkaskok [199]
3 years ago
12

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

e pack per day. During any month, 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. 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. 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. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.)
Mathematics
1 answer:
Kazeer [188]3 years ago
3 0

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. <em>Then, the probability of staying in the same state is 90%.</em>

-  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. <em>Then, the probability of staying in the same state is 80%.</em>

- 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. <em>Then, the probability of staying in the same state is 82%.</em>

<em />

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.

You might be interested in
PLEASE HELP ME ASAP!!
IrinaVladis [17]

Answer:

8. 5/6

9. 6.25, 6 and 1/4

10. 14.4

Step-by-step explanation:

Sorry that this is a little late. All of these problems end up with the same process to get to the answer. Since you want to find the rate, you would want to divide the amount of time taken by itself to find the unit rate. So basically, 8. would be 20 cm in 24 hours. You would divide both by 24 and you get 20/24 cm in 1 hour. and then you simplify the fraction and boom, there's your answer.

8 0
2 years ago
3. A recipe calls for 2 cups of sugar to make 2 dozen cookies. Use the proportion to calculate how much sugar is needed to make
vova2212 [387]

Answer:

c. 6 cups

Step-by-step explanation:

The proportion is 1 cup of sugar for 1 dozen cookies (1/1). So if you multiply the denominator by 6 you must multiply the numerator by 6, and 6*1=6. Therefore you need 6 cups of sugar to make 6 dozen cookies.

7 0
3 years ago
Read 2 more answers
The circumference of a coin is 18π cm. What is the​ radius? What is the​ diameter?
Hoochie [10]
6 I do believe so hope this helps!
4 0
2 years ago
Read 2 more answers
Find the volume of the solid to the nearest whole cubic unit. Use a calculator, if needed.
riadik2000 [5.3K]

Furstly, multiplying mixed fractions together is chaotic. Convert them into improper fractions first.

(22/3) * (20/3) * (27/10)

Secondly, don't start multiplying all out! Look for common factors. There are two 3's at the denominator, and 27 is 3^3 at the numerator. Cross them out!

22 * 20 * 3 / 10

Hey! There are multiples of 10 too!

22 * 2 * 3

= (11 * 2) * 2 * 3

= 11 * 12

= 132

That leads to option 3!

6 0
3 years ago
What is the prime factor of 32
ipn [44]
We factor out primes from 32 to find it's prime factorization.

32=2*16=2*2*8=2*2*2*4=2*2*2*2*2.  2 is a prime number, so this cannot be reduced further.  Since we have five twos and no other primes, the factorization is 2^5, and the only prime factor is 2.
5 0
2 years ago
Read 2 more answers
Other questions:
  • Can someone help with this questions please
    15·2 answers
  • The local drugstore is offering 15% off the normal price for a 16-pack of AAA batteries. If a 16-pack of AAA batteries is normal
    9·2 answers
  • G(t)= t-3 <br> h(x)= 3t-2 <br> find (g-h)(t)
    12·1 answer
  • !!!!!1ILL GIVE 26 POINTS AND BRAINLIEST JUST PLEASE B((((((((((((((!!!!!
    14·1 answer
  • Need help plz !!!!!!!!!!!
    10·2 answers
  • I need help with the top 3 plz
    7·1 answer
  • There is a spinner with 12 equal areas, numbered 1 through 12. If the spinner is spun
    12·1 answer
  • Y = -3x + 2 y = 4x - 5. *<br>can someone solve this for me please?​
    9·1 answer
  • What is the inverse of this function?<br> [Will give Brainliest]
    7·2 answers
  • Answer the question below, will give brainliest to first answer
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!