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NARA [144]
2 years ago
10

324 ft

Mathematics
1 answer:
kotegsom [21]2 years ago
7 0

The distance between the flagpole and the building is the number of feet between them

The building is 162 feet from the flagpole

<h3>How to determine the distance</h3>

The given parameters are:

  • Flagpole = 40 feet
  • Building Shadow = 324 feet

The flagpole's shadow is 50% longer than the flagpole.

So, the length (l) of the flagpole's shadow is:

l = 40 * (1 + 50\%)

l = 60

The length of the building's shadow (d) is then calculated as:

60 : 40 =d :  324

Express as fraction

\frac{60}{40}= \frac{d}{324}

1.50 = \frac{d}{324}

Solve for d

d = 1.50 * 324

d = 486

The distance (x) of the building from the flagpole is then calculated as:

x = 486 - 324

x = 162

Hence, the building is 162 feet from the flagpole

Read more about distance and bearing at:

brainly.com/question/11744248

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95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 75

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We also have that since the normal distribution is symmetric, 50% of the measures are below the mean and 50% are above.

a. The relative frequency of rates less than 85 using the 68-95-99.7 rule is

85 is two standard deviations above the mean.

So all the 50% below the mean is below 85

And of the 50% above the mean, 95% is less than 85. So

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80 is one standard deviations above the mean.

Of the 50% above the mean, 68% is less than 80. So 100-68 = 32% is more than 80.

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Answer:

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A. \dfrac{h}{12} = \dfrac{6}{5}

Step-by-step explanation:

The given parameters in the question are;

The medium through which the person looks at the top of the tree = A mirror

The angle formed by the person and the tree with the ground = Right angles = 90°

The distance of the person from the mirror, d₁ = 5 ft.

The height of the person, h₁ = 6 ft.

The distance of the tree from the mirror, d₂ = 12 ft.

The angle formed by the incident light from the tree on the mirror, θ₁ = The angle of the reflected light from the mirror to the person, θ₂

Let 'A', 'B', 'M', 'T', and 'R' represent the location of the point at the top of the person's head, the location of the point at the person's feet, the location of the mirror, the location of the top of the tree and the location of the root collar of the tree, we have;

TR in ΔMRT = The height of the tree = h, and right triangles ΔABM and ΔMRT are similar

The corresponding legs are;

The height of the person and the height of the tree, which are AB = 6 ft. and TR = h, respectively

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Given that θ₁ = θ₂, we have;

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tan\angle X = \dfrac{Opposite \ leg \ length \ to \ reference \ angle}{Adjacent \ leg \ length \ to \ reference \ angle}

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\dfrac{h}{12} = \dfrac{6}{5}

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