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skelet666 [1.2K]
2 years ago
15

NO LINKS!!! Find the probability that a randomly chosen point in the figure lies in the shaded region area.​

Mathematics
2 answers:
Marysya12 [62]2 years ago
8 0

#36

Area of rectangle

  • 12(8)
  • 96

Area of 6 circles.

  • 6(π)(8/4)²
  • 6π(4)
  • 24π
  • 75.4

Probability

  • 75.4/96
  • 0.78

#2

Area of whole

  • (2+6)(6+10)
  • 8(16)
  • 144

Area of two rectangles

  • 2(10)(2)
  • 40

So

Probability

  • 144-40/144
  • 104/144
  • 0.7

#3

Area of whole circle

  • π(4+4+2)²
  • 100π

Area of inner circle(not shaded)

  • π(2)²
  • 4π

Area of shaded circle

  • π(4+2)²
  • 36π

Probability

  • 16π-4π/96π
  • 12π/96π
  • 3/8
mezya [45]2 years ago
5 0

Answer:

To find the probability that a randomly chosen point in the figure lies in the <u>shaded region</u>, we need to divide the area of shaded region by the total area of the figure.

<h3><u>Question 36</u></h3>

<u>Total Area</u>

Area of a rectangle = width × length = 8 × 12 = 96 units²

<u>Shaded Region Area</u>

This is made up of 6 congruent circles.

The radius of each circle is 1/6 of the length of the rectangle (or 1/4 of the width).

⇒ radius = 12/6 = 2 units

Area of a circle = πr² = π(2)² = 4π units²

⇒ Shaded region area = 6 circles = 6 × 4π = 24π units²

<u>Probability</u>

= Shaded region area ÷ total area

= 24π ÷ 96

= 0.7853981634...

= 78.5% (3 s.f.)

<h3><u>Question 37</u></h3>

<u>Total Area</u>

Area of a rectangle = width × length = 16 × 8 = 128 units²

<u>Shaded Region Area</u>

The easiest way to calculate this is to subtract the un-shaded areas from the total area:

⇒ Shaded region area = 128 - 2(2 · 10) = 88 units²

<u>Probability</u>

= Shaded region area ÷ total area

= 88 ÷ 128

= 0.6875

= 68.8% (3 s.f.)

<h3><u>Question 38</u></h3>

<u>Total Area</u>

The radius of the largest circle is the sum of the individual given radii.

⇒ Area of a circle = πr² = π(4 + 4 + 2)² = 100π units²

<u>Shaded Region Area</u>

= Area of a circle with radius (4 + 2) - area of circle with radius 2

= π(6)² - π(2)²

= 32π units²

<u>Probability</u>

= Shaded region area ÷ total area

= 32π ÷ 100π

= 0.32

= 32%

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