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
Viefleur [7K]
3 years ago
6

A certain town never has two sunny days in a row. Each day is classified as being either sunny, cloudy (but dry), or rainy. If i

t is sunny one day, then it is equally likely to be either cloudy or rainy the next day. If it is rainy or cloudy one day, then there is one chance in two that it will be the same the next day, and if it changes then it is equally likely to be either of the other two possibilities. In the long run, what proportion of days are sunny
Mathematics
1 answer:
11111nata11111 [884]3 years ago
8 0

Answer:

the proportion of days that are Sunny is 0.2

Step-by-step explanation:

Given the data in the question;

Using markov chain;

3 states; Sunny(1), Cloudy(2) and Rainy(3)

Now, based on given conditions, the transition matrix can be obtained in the following way;

\left[\begin{array}{ccc}0&0.5&0.5\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]

so let the proportion of sunny, cloudy and rainy days be S, C and R respectively.

such that, from column 1

S = 0.25C + 0.25R   -------------let this be equation 1

from column 2

0.5C = 0.5S + 0.25R

divided through by 0.5

C = S + 0.5R ---------------------- let this be equation 2

now putting equation 2 into equation;

S = 0.25(S + 0.5R) + 0.25R

S = 0.25S + 0.125R + 0.25R

S - 0.25S = 0.375R

0.75S = 0.375R

S = 0.375R / 0.75

S = 0.5R

Therefore,

from equation 2; C = S + 0.5R

input S = 0.5R

C = 0.5R + 0.5R

C = R

Now, we know that, the sum of the three proportion should be equal to one;

so

S + C + R = 1

since C = R and S = 0.5R

we substitute

0.5R + R + R = 1

2.5R = 1

R = 1/2.5

R = 0.4

Hence, the proportion of days that are Rainy is 0.4

C = R

C = 0.4

Hence, the proportion of days that are Cloudy is 0.4

S = 0.5R

S = 0.5(0.4)

S = 0.2

Hence, the proportion of days that are Sunny is 0.2

You might be interested in
What is 9/20-3/20 in the simplest
stepan [7]
\frac{9}{20}- \frac{3}{20} =  \frac{6}{20}÷\frac{2}{2} = \frac{3}{10}
4 0
3 years ago
Read 2 more answers
A local store buys used video games. For each game bought, they will pay $18 less than the original price paid for the game. Whi
LenKa [72]

Answer:

d

Step-by-step explanation:

I already did this before

4 0
2 years ago
If m angle 1 = 42 and m angle 2 = 27, then m angle APC =
Arada [10]
I think that it's 111
4 0
3 years ago
Suma cyfr szukanej liczby dwucyfrowej jest równa 12. Jeżeli cyfry tej liczby przestawimy, to
polet [3.4K]

Answer:

yes

Step-by-step explanation:

7 0
2 years ago
A car is moving with a velocity (3.0 m/s) x̂ + (1.0 m/s) ŷ and 3.0 seconds later its velocity is (6.0 m/s) x̂ - (3.0 m/s) ŷ. Wha
Mars2501 [29]

Here we know that the initial velocity of the car is given by:

V_i=(3.0\hat x+1.0\hat y)m/s

And the final velocity of the car is given by:

V_f=(6.0\hat x-3.0\hat y)m/s

It took 3 seconds to attain the final velocity, so we have t=3 s

Therefore, the acceleration can be obtained by:

V_f-V_i=a\times t

a=\frac{V_f-V_i}{t}

Plugging the values of the initial, final velocity and the time, we get:

a= \frac{(6\hat x-3\hat y)-(3 \hat x+1 \hat y)}{3} =\frac{6\hat x-3 \hat y -3 \hat x-1 \hat y}{3} =\frac{3 \hat x-4 \hat y}{3}

So the acceleration of the car is given by:

a=\frac{3 \hat x}{3} -\frac{4 \hat y}{3} =1 \hat x- \frac{4}{3} \hat y

Now we need to find the direction of the average acceleration of the car:

\theta=tan^{-1} \frac{y}{x}

Here, x and y are the coefficients of the 'x' and 'y' components of the vector:

\theta=tan^{-1}(\frac{-\frac{4}{3} }{1} )=tan^{-1}(\frac{-4}{3}) =-53.13^\circ

Therefore, the direction of the average acceleration of the car is -53.13^\circ.

8 0
3 years ago
Other questions:
  • What is the solution to the linear equation?
    12·1 answer
  • Please answer this question !! 20 points and brainliest !!
    8·2 answers
  • What is 216847.314 rounded by the nearest liter
    5·1 answer
  • Find the inverse of the function. f(x) = 7x + 8
    14·1 answer
  • 3/8+5/16 in lowest terms
    7·1 answer
  • The end points of wx are w (-5,-1) and x (2,6) What is the length of wx
    12·1 answer
  • 7/5 simplafied please help me
    13·1 answer
  • If Anna can run 2km in 8 min, how long will it take her to run 5 km if she maintains her speed​
    11·1 answer
  • 1<br> What is the slope of this table? <br> A 4<br> B 9<br> C 1 <br> D 8
    10·2 answers
  • The radius of a CD is 6cm which equation could be used to find the circumference of the CD in cm ?
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!