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Two buildings in downtown Chicago stand across the river. The first building is 1,700 feet tall and casts a shadow of 525 feet. If the second building is 1,450 feet tall, how long will its shadow be?
- A. 478 feet
- B. 455 feet
- C. 448.5 feet
- D. 450 feet
Correct Answer: C
Rationale: To find the shadow of the second building, we use the ratio of heights to shadows: 1,700/525 = 1,450/x. Solving for x gives x = (525 1,450)/1,700 = 448.5. Therefore, the shadow of the second building will be approximately 448.5 feet long.
Choice A (478 feet) is incorrect because it is not the result of the correct calculation. Choice B (455 feet) is incorrect as it does not match the accurate answer obtained through the calculation. Choice D (450 feet) is incorrect as it does not reflect the correct length of the shadow of the second building.
You may also like to solve these questions
What is the perimeter of a square with a side length of 5 meters?
- A. 15 meters
- B. 20 meters
- C. 25 meters
- D. 30 meters
Correct Answer: B
Rationale: The formula to calculate the perimeter of a square is P = 4s, where P is the perimeter and s is the length of a side. Given that the side length is 5 meters, the perimeter is 4 * 5 = 20 meters. Therefore, the correct answer is B. Choices A (15 meters), C (25 meters), and D (30 meters) are incorrect as they do not correctly apply the formula to calculate the perimeter of a square.
Square: A garden bed has a side length of 8 meters. What is its perimeter?
- A. 16m
- B. 24m
- C. 32m
- D. 64m
Correct Answer: C
Rationale: The perimeter of a square is found by adding up all four sides. Since all sides of a square are equal in length, the perimeter is calculated by multiplying the side length by 4. In this case, the side length of the square garden bed is 8 meters. Therefore, the perimeter is 8m x 4 = 32m. Choice A (16m) is incorrect as it represents only half of the perimeter. Choice B (24m) is incorrect because it is the perimeter of a square with a side length of 6 meters, not 8 meters. Choice D (64m) is incorrect as it represents the area of the square, not the perimeter.
Which number is the highest among 0.077, 0.777, 0.08, and 0.87?
- A. 0.077
- B. 0.777
- C. 0.08
- D. 0.87
Correct Answer: D
Rationale: To determine the highest number among 0.077, 0.777, 0.08, and 0.87, we compare the numbers. 0.87 is greater than 0.777, 0.08, and 0.077, making it the highest number. Choice A (0.077), Choice B (0.777), and Choice C (0.08) are lower numbers compared to 0.87, so they are incorrect.
A water fountain has a spherical base with a diameter of 50cm and a cylindrical body with a diameter of 30cm and a height of 80cm. What is the total surface area of the fountain (excluding the water surface)?
- A. 3142 sq cm
- B. 4712 sq cm
- C. 5486 sq cm
- D. 7957 sq cm
Correct Answer: C
Rationale: To find the total surface area of the fountain, we first calculate the surface area of the sphere and the cylinder separately.
For the sphere:
- Radius = Diameter / 2 = 50 / 2 = 25 cm
- Surface area of a sphere = 4πr² = 4 x π x 25² = 500π cm²
For the cylinder:
- Radius = Diameter / 2 = 30 / 2 = 15 cm
- Surface area of a cylinder = 2πrh + 2πr² = 2 x π x 15 x 80 + 2 x π x 15² = 240π + 450π = 690π cm²
Total surface area = Surface area of sphere + Surface area of cylinder
= 500π + 690π = 1190π cm²
≈ 5486 sq cm. Therefore, the correct answer is C.
Choice A (3142 sq cm) is incorrect as it is much smaller than the correct answer. Choices B and D are also incorrect as they do not reflect the accurate calculation of the total surface area of the fountain.
In a bar graph showing the number of patients admitted to the ER each day for a week, how do you determine the day with the highest number of admissions?
- A. Find the tallest bar in the graph.
- B. Compare the heights of all bars.
- C. Calculate the average number of admissions per day.
- D. Subtract the lowest number of admissions from the highest.
Correct Answer: A
Rationale: The correct answer is A: 'Find the tallest bar in the graph.' In a bar graph, the height of each bar represents the quantity being measured. The tallest bar indicates the day with the highest number of admissions. Therefore, this is the most direct and accurate method to determine the day with the highest number of admissions. Choices B, C, and D are incorrect because comparing all bars, calculating the average, or subtracting the lowest from the highest does not directly identify the day with the highest number of admissions in a bar graph.