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klasskru [66]
3 years ago
11

Professor henry knows from past experience that 30% of all homework papers handed in will be missing the name of the person who

handed it in. In a class of 200, that is a problem. What is the probability that out of 200 homework papers,
a) between 50 and 70 papers will be missing the name
b) at least 75 papers will be missing the name
c) at most 45 papers will be missing the name
d) exactly 65 papers will be missing the name
Mathematics
1 answer:
Savatey [412]3 years ago
4 0
If you would like to know how many papers will be missing the name, you can calculate this using the following steps:

30% of 200 homework papers = 30% * 200 = 30/100 * 200 = 60 homework papers

The correct result would be a) between 50 and 70 papers will be missing the name.
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Charlie is watching hot air balloons. balloon a has risen at a 50° angle. balloon b has risen at a 78° angle. if the distance fr
AfilCa [17]

The distance from Balloon A to Balloon B, d ≈ 1,052 feet

What is distance ?

  • Distance is defined to be the magnitude or size of displacement between two positions.
  • Note that the distance between two positions is not the same as the distance traveled between them.
  • Distance traveled is the total length of the path traveled between two positions. Distance traveled is not a vector.

The given parameters are;

The angle at which Balloon A rises, x° = 50° above horizontal

The angle at which Balloon B rises, y° = 78° above horizontal

The (vertical) distance of Balloon A to the ground, h = 1,000 ft.

The required parameter;

The distance from Balloon A to Balloon B, d

We find the distances of the balloons from Charlie and the angle between the balloon strings, θ, then apply cosine rule

Let,

The height of the balloon strings are equal

The distance of Balloon A to the ground, h₁ = The distance of Balloon B to the ground, h₂ = 1,000 ft.

The distance of the Balloon A  from Charlie, l₁, is given as follows;

l₁ × sin(x°) = h₁

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Which gives;

l₁ = 1,000 ft./(sin(50°)) ≈ 1,305.41 ft.

l₁ ≈ 1,305.41 ft.

For Balloon B, we get;

h₁ = h₂ = 1,000 ft.

∴ l₂ = 1,000 ft./(sin(78°)) ≈ 1,022.34 ft.

l₂ ≈ 1,022.34 ft

The angle between the balloon strings, θ = 180° - (x° + y°)

∴ θ = 180° - (50° + 78°) = 52°

The angle between the balloon strings, θ = 52°

By cosine rule, we have;

d = √(l₁² + l₂² - 2 × l₁ × l₂ × cos(θ))

∴ d = √(1,305.41² + 1,022.34² - 2 × 1,305.41×1,022.34 × cos(52°)) ≈ 1,052 feet

Therefore, the distance from Balloon A to Balloon B, d ≈ 1,052 feet

Learn more about distance

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