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Blizzard [7]
3 years ago
5

The leaning tower of Pisa is approximately 179 ft in “height” and is approximately 16.5 ft out of plumb. Find the angle at which

it deviates from the vertical.
Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
7 0

Answer:

height of the leaning tower of pisa is 179 feet

it makes a 5.1 degrees from the vertical.

it's angle to the ground would be 90 - 5.1 = 84.9 degrees.

the height of the vertical would be one leg of a right triangle.

to find the vertical height of the tower, we would take the sine of 84.9 using the formula:

sine (84.9) = opposite divided by hypotenuse.

opposite i x

hypotenuse is 179

formula becomes:

sine (84.9) = x/179

multiply both sides of this equation by 179 to get:

x = 179 * sine (84.9)

this results in:

x = 178.2913507 feet

Step-by-step explanation:

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For each traveler who made a reservation, there are only two possible outcomes. Either they show up, or they do not. The probability of a traveler showing up is independent of other travelers. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

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This means that p = 0.1

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This means that n = 4

a) What is the probability that at least two of the four selected will turn to be no-shows?

This is P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

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P(X = 3) = C_{4,3}.(0.1)^{3}.(0.9)^{1} = 0.0036

P(X = 4) = C_{4,4}.(0.1)^{4}.(0.9)^{0} = 0.0001

P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.0486 + 0.0036 + 0.0001 = 0.0523

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b) What is the most likely value for X?

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{4,0}.(0.1)^{0}.(0.9)^{4} = 0.6561

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P(X = 2) = C_{4,2}.(0.1)^{2}.(0.9)^{2} = 0.0486

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P(X = 4) = C_{4,4}.(0.1)^{4}.(0.9)^{0} = 0.0001

X = 0 has the highest probability, which means that 0 is the most likely value for X.

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