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Question 1

A)A circle with a radius of 2 inches and a square with a side length of 3 inches are both inscribed in a rectangle with a width of 7 inches and a length of 8 inches. The circle and square are beside each other in the rectangle. Determine the probability that a point placed randomly in the figure is inside the circle. Round your answer to the nearest hundredth.(1 point)
Responses

0.78
0.78

0.84
0.84

0.16
0.16

0.22
0.22
Question 2
A)A circle with a radius of 3 inches and a square with a side length of 4 inches are both inscribed in a rectangle with a width of 12 inches and a length of 8 inches. The circle and square are next to each other in the rectangle. Determine the probability that a point placed randomly in the figure is inside the square. Round your answer to the nearest hundredth.(1 point)
Responses

0.71
0.71

0.83
0.83

0.29
0.29

0.17
0.17
Question 3
A)A circle with a radius of 2 inches and a square with a side length of 12 inches are both inscribed in a rectangle with a width of 17 inches and a length of 22 inches. The circle and square inscribed in the rectangle are beside each other. Determine the probability that a point placed randomly in the figure is not inside the square. Round your answer to the nearest hundredth.(1 point)
Responses

0.03
0.03

0.39
0.39

0.97
0.97

0.61
0.61
Question 4
A)A circle with a radius of 6 inches and a square with a side length of 10 inches are both inscribed in a rectangle with a width of 24 inches and a length of 30 inches. The circle and square inscribed in the rectangle are beside each other. Determine the probability that a point placed randomly in the figure is not inside the circle. Round your answer to the nearest hundredth.(1 point)
Responses

0.86
0.86

0.14
0.14

0.16
0.16

0.84
0.84
Question 5
A) A circle with a radius of 4 inches and a square with a side length of 8 inches are both inscribed in a rectangle with a width of 19 inches and a length of 21 inches. The circle and square inscribed in the rectangle are beside each other. Determine the probability that a random point placed in the figure is not inside the circle or inside the square. Round your answer to the nearest hundredth.(1 point)
Responses

0.71
0.71

0.87
0.87

0.29

1 answer

To solve the questions, we first need to calculate the areas of the shapes (circle and square), their total areas, and then use these values to find the respective probabilities. Let’s go through each question one by one.

Question 1

  1. Circle Area: Area = π × r² = π × 2² = 4π square inches.
  2. Square Area: Area = side² = 3² = 9 square inches.
  3. Rectangle Area: Area = length × width = 8 × 7 = 56 square inches.
  4. Total Area: Total Area = Circle Area + Square Area = 4π + 9 ≈ 4(3.14) + 9 ≈ 12.56 + 9 ≈ 21.56 square inches.
  5. Probability (inside circle) = Circle Area / Rectangle Area = (4π) / 56 ≈ (12.56) / 56 ≈ 0.224 or rounded to 0.22.

Answer: 0.22

Question 2

  1. Circle Area: Area = π × r² = π × 3² = 9π square inches.
  2. Square Area: Area = side² = 4² = 16 square inches.
  3. Rectangle Area: Area = length × width = 12 × 8 = 96 square inches.
  4. Total Area: Total Area = Circle Area + Square Area = 9π + 16 ≈ 28.27 + 16 ≈ 44.27 square inches.
  5. Probability (inside square) = Square Area / Rectangle Area = 16 / 96 = 1/6 ≈ 0.1667 or rounded to 0.17.

Answer: 0.17

Question 3

  1. Circle Area: Area = π × r² = π × 2² = 4π square inches.
  2. Square Area: Area = side² = 12² = 144 square inches.
  3. Rectangle Area: Area = length × width = 22 × 17 = 374 square inches.
  4. Total Area: Total Area = Circle Area + Square Area = 4π + 144 ≈ 12.56 + 144 ≈ 156.56 square inches.
  5. Probability (not inside square) = 1 - (Square Area / Rectangle Area) = 1 - (144 / 374) ≈ 1 - 0.384 = 0.616 or rounded to 0.61.

Answer: 0.61

Question 4

  1. Circle Area: Area = π × r² = π × 6² = 36π square inches.
  2. Square Area: Area = side² = 10² = 100 square inches.
  3. Rectangle Area: Area = length × width = 30 × 24 = 720 square inches.
  4. Total Area: Total Area = Circle Area + Square Area = 36π + 100 ≈ 113.09 + 100 = 213.09 square inches.
  5. Probability (not inside circle) = 1 - (Circle Area / Rectangle Area) = 1 - (36π / 720) = 1 - (36×3.14 / 720) = 1 - (113.09 / 720) ≈ 1 - 0.157 = 0.843 or rounded to 0.84.

Answer: 0.84

Question 5

  1. Circle Area: Area = π × r² = π × 4² = 16π square inches.
  2. Square Area: Area = side² = 8² = 64 square inches.
  3. Rectangle Area: Area = length × width = 21 × 19 = 399 square inches.
  4. Total Area: Total Area = Circle Area + Square Area = 16π + 64 ≈ 50.27 + 64 ≈ 114.27 square inches.
  5. Probability (not inside circle or square) = 1 - ((Circle Area + Square Area) / Rectangle Area) = 1 - ((16π + 64) / 399) ≈ 1 - (114.27 / 399) ≈ 1 - 0.286 = 0.714 or rounded to 0.71.

Answer: 0.71