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Dmitrij [34]
3 years ago
5

An extremely simple (and surely unreliable) weather prediction model would be one where days are of two types: sunny or rainy. A

sunny day is 90% likely to be followed by another sunny day, and a rainy day is 50% likely to be followed by another rainy day. Model this as a Markov chain. If Sunday is sunny, what is the probability that Tuesday (two days later) is also sunny
Mathematics
1 answer:
andrezito [222]3 years ago
7 0

Answer:

The probability that if Sunday is sunny, then Tuesday is also sunny is 0.86.

Step-by-step explanation:

Let us denote the events as follows:

Event 1: a sunny day

Event 2: a rainy day

From the provided data we know that the transition probability matrix is:

                 \left\begin{array}{ccc}1&\ \ \ \ 2\end{array}\right

\text{P}=\left\begin{array}{c}1&2\end{array}\right  \left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right]

In this case we need to compute that if Sunday is sunny, what is the probability that Tuesday is also sunny.

This implies that we need to compute the value of P₁₁².

Compute the value of P² as follows:

P^{2}=P\cdot P

     =\left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right]\cdot \left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right]\\\\=\left[\begin{array}{cc}0.86&0.14\\0.70&0.30\end{array}\right]

The value of P₁₁² is 0.86.

Thus, the probability that if Sunday is sunny, then Tuesday is also sunny is 0.86.

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Answer: The equation is f(x) = 0.95^{x};

The piece of plastic has to have 10mm of thickness.

Step-by-step explanation: It is known that with 1 mm of thickness, 5% of the intensity is reduced. So, 95% of the light is transmitted.

For each milimetre added, "more" 95% of light is transmitted.

For example, if another milimetre of plastic is added, another 0.95 of light is transmitted:

0.95.0.95 = 0.9025 of light reach the visor

So, the model that relate thickness of plastic and intensity of light is:

f(x) = 0.95^{x}

in which:

f(x) is the intensity of light;

x is thickness in mm;

Using the equation, the thickness necessary to reduce intensity to 60% is:

f(x) = 0.95^{x}

0.6 = 0.95^{x}

log 0.6 = log 0.95^{x}

x. log (0.95) = log (0.6)

x = \frac{log 0.6}{log 0.95}

x = 9.95

x ≈ 10

The thickness necessary to reduce intensity of light to 60% is 10mm.

6 0
3 years ago
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The height of the rectangle and the triangle are the same. The base of the triangle is half the base of the rectangle.
Lina20 [59]
<h2>Answer: C 375 cm²</h2>

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Find the slope and y-intercept of 3y - 4x = 39
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<h2>Greetings!</h2><h3>Firstly, the slope is found by rearranging the formula:</h3>

3y = 4x + 39

y = \frac{4x}{3} + \frac{39}{3}

When x is 0, y = 0(x) +  \frac{39}{3}, so the y intercept is \frac{39}{3}

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3 years ago
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??? Anyone know how to answer this question
True [87]
Answer: 35 additional teachers are needed

-------------------------------------------------
-------------------------------------------------

Explanation:

We have 2470 students and the ratio of students to teachers is 26:1. This means that for every teacher, there are 26 students. Put another way, we can set up this ratio

2470/x = 26/1

where x is the number of teachers. Cross multiply and solve for x

2470/x = 26/1
2470*1 = 26*x
2470 = 26x
26x = 2470
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So we have 95 teachers currently

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Let y be the new number of teachers needed to bring the ratio down to 19:1

Using a similar idea as done above, we would have this ratio

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Let's solve for y
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So we'll need 130 teachers to have the ratio be 19:1

The difference of the values is y - x = 130 - 95 = 35, which is the final answer. This is the additional amount of teachers needed.
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Answer:

Each boxed lunch costs $11.20

Step-by-step explanation:

29 boxed lunches = $324.80

divide by 29 on each one

1 boxed lunch = $11.20

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