A forest consists of 1,000 trees forming a perfect 50Ã20 rectangle. The northwestern (top-left) corner tree catches fire. Wind blows from the west, therefore, the probability that any tree catches fire from its burning left neighbor is 0.8. The probabilities to catch fire from trees immediately to the right, above, or below are all equal 0.3. 1. Conduct a Monte Carlo study to estimate the probability that more than 30% of the forest will eventually be burning. With probability 0.95, your answer should differ from the true value by no more than 0.005.
2. Based on the same study, predict the total number of affected trees X.
3. Estimate Std(X) and comment on the accuracy of your estimator of X.
4. What is the probability that the actual number of affected trees differs from your estimator by more than 25 trees?
5. A wooden house is located in the northeastern corner of the forest. Would you advise the owner that her house is in real danger?

step-by-step explanation:

if you want to separate 54 into 6 individual tiers then you need to divide if you want to separate 54 into 6 individual tiers then you need to divide 6 and 54.

if you divide 9 by 6 you will get 54.

- hope i .

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west

25/6 hope it : )

step-by-step explanation: