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A soccer field is rectangular in shape and measures 100 meters in length and 75 meters in width. The hectare is a metric unit of area often used to measure large areas. Given that 1 hectare = 10,000 square meters, what is the soccer field's area in hectares?
- A. 7,500 hectares
- B. 7.5 hectares
- C. 75,000,000 hectares
- D. 0.75 hectares
Correct Answer: D
Rationale: To find the area of the soccer field in square meters, multiply its length by its width: 100 meters * 75 meters = 7500 square meters. To convert square meters to hectares, divide the area in square meters by 10,000 (since 1 hectare = 10,000 square meters): 7500 square meters / 10,000 = 0.75 hectares. Therefore, the soccer field's area in hectares is 0.75 hectares.
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A consumer makes a $400 down payment on a television that costs $1,570. How many months will it take to pay off the television with monthly payments of $100? (Assume no interest)
- A. 16
- B. 12
- C. 11
- D. 15
Correct Answer: B
Rationale: To determine the number of months needed to pay off the television, subtract the down payment from the total cost: $1,570 - $400 = $1,170. Next, divide the remaining amount ($1,170) by the monthly payment of $100 to find the number of months: $1,170 · $100 = 11.7 months. Since you cannot make a fraction of a monthly payment, the consumer will need to make 12 monthly payments to fully pay off the television.
If a force of 132 Newtons stretched a coil by 0.007 meters, what force would be needed to stretch the coil by 0.1 meter? Round to the nearest tenth.
- A. 92.4N
- B. 136.0N
- C. 188.6N
- D. 1885.7N
Correct Answer: D
Rationale: To find the force needed to stretch the coil by 0.1 meters, we can use the concept of direct proportionality where the force to stretch remains constant. Setting up a proportion: (132N / 0.007m) = (x / 0.1m). Solving for x, we get x = (132N / 0.007m) * 0.1m = 1885.7N. Therefore, the force required to stretch the coil by 0.1 meters is 1885.7 Newtons.
Simplify the expression: [2(3 + 5 - 3)] / (12 + 2). What is the result of this expression?
- A. 12
- B. 1
- C. 8
- D. 2.57
Correct Answer: D
Rationale: To simplify the given expression [2(3 + 5 - 3)] / (12 + 2), follow the order of operations (PEMDAS/BODMAS). First, calculate the operations within the parentheses: 3 + 5 - 3 = 5. Substitute the result back into the expression to get [2(5)] / (12 + 2). Next, calculate within the brackets: 2(5) = 10. Now, the expression becomes 10 / 14. Simplifying further, 10 / 14 = 5 / 7 = 0.7142 (rounded to two decimal places). Therefore, the result of the expression is approximately 0.71, which corresponds to choice D.
A circle has an area of 49Ï€ square inches. What is the circumference of the circle in terms of pi?
- A. 7Ï€ inches
- B. 28Ï€ inches
- C. 14Ï€ inches
- D. 3.5Ï€ inches
Correct Answer: C
Rationale: To find the circumference of a circle with an area of 49π square inches, you first need to find the radius using the area formula A = πr^2. Given the area is 49π, then 49π = πr^2, which simplifies to r^2 = 49, resulting in r = 7. The circumference formula is C = 2πr. Substituting r = 7 gives C = 2π(7) = 14π. Therefore, the correct circumference of the circle in terms of pi is 14π inches.
How many feet are in 6 yards?
- A. 2 feet
- B. 9 feet
- C. 36 feet
- D. 18 feet
Correct Answer: D
Rationale: To convert yards to feet, remember that 1 yard is equal to 3 feet. To find how many feet are in 6 yards, you multiply 6 by 3, which equals 18 feet. Therefore, the correct answer is 18 feet. Understanding this conversion is essential for accurate measurements in various situations such as construction, crafting, or any activity involving distance calculations.