Nokea
If X represents the width of a rectangle and the length is four less than three times the width, which of the following expressions represents the length of the rectangle in terms of X?
- A. 3x - 4
- B. 4x - 3
- C. 4 - 3x
- D. 3 - 4x
Correct Answer: A
Rationale: To determine the expression for the length of the rectangle in terms of X, we need to consider that the length is four less than three times the width. This can be mathematically represented as 3 times X minus 4, which simplifies to 3x - 4 (choice A). Therefore, choice A correctly represents the length of the rectangle in terms of X, making it the correct answer.
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A couple dining at a restaurant receives a bill for $38.40. They wish to leave a 15% gratuity. What is the estimated gratuity amount?
- A. $6.00
- B. $5.00
- C. $4.00
- D. $7.00
Correct Answer: A
Rationale: To calculate the 15% gratuity on a $38.40 bill, you multiply the bill amount by 0.15 (15%): $38.40 x 0.15 = $5.76. Since gratuity amounts are typically rounded up, the estimated gratuity would be $6.00, making choice A the correct answer. In this case, rounding up to the nearest whole dollar is common practice in gratuity calculations to simplify tipping and ensure a fair amount for the service provided.
An employer wants to purchase one cup of coffee for each of their 214 employees. A cup of coffee costs $3.95. To estimate the total cost, the employer plans to round the number of employees to the nearest ten and round the cost of the coffee to the nearest dollar. Which of the following prices represents the estimated total cost for the coffee?
- A. $845.30
- B. $840.00
- C. $829.50
- D. $850.00
Correct Answer: B
Rationale: Rounding 214 employees to the nearest ten gives 210. Rounding the cost of coffee ($3.95) to the nearest dollar gives $4. The estimated total cost is 210 x $4 = $840.00.
The length of a person's shadow is proportional to their height. If a person's shadow is 120 cm long and their height is 180 cm, how long is the shadow of a person who is 135 cm tall at the same time of day?
- A. 202.5 cm
- B. 75 cm
- C. 160 cm
- D. 90 cm
Correct Answer: D
Rationale: To find the shadow length of a 135 cm tall person, set up the proportion: 120 cm / 180 cm = x / 135 cm. Cross multiply to get 180x = 120 * 135, then solve for x by dividing both sides by 180. Therefore, x = 120 * 135 / 180 = 90 cm. Hence, the shadow length of a 135 cm tall person at the same time of day would be 90 cm.
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.
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.