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What is the length of the unknown leg of a right triangle that has one leg measuring 8 feet and a hypotenuse of 12 feet? (Round to the nearest tenth)
- A. 40 feet
- B. 4 feet
- C. 14.4 feet
- D. 8.9 feet
Correct Answer: D
Rationale: To find the length of the unknown leg of a right triangle, you can use the Pythagorean theorem. The theorem states that the square of the length of the hypotenuse (12 feet) is equal to the sum of the squares of the other two sides. Let x be the length of the unknown leg. So, 12^2 = 8^2 + x^2. Solving for x gives x = √(12^2 - 8^2) = √(144 - 64) = √80 ≈ 8.9 feet. Therefore, the length of the unknown leg is approximately 8.9 feet.
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When the weights of newborn babies are graphed, the distribution of weights is symmetric with the majority of weights centered around a single peak. Which of the following describes the shape of this distribution?
- A. Skewed right
- B. Bimodal
- C. Uniform
- D. Bell-shaped
Correct Answer: D
Rationale: The described distribution, where the majority of weights are centered around a single peak and symmetric, is referred to as bell-shaped. In a bell-shaped distribution, the data is symmetric around the mean, with most values clustering near the peak and tapering off towards the extremes. This pattern is commonly seen in normal distributions, such as the distribution of birth weights in newborns. The bell-shaped curve represents a typical symmetric distribution, indicating that most newborn weights fall close to the average weight with fewer extreme values. Therefore, the correct answer is 'Bell-shaped'.
What is the value of x in the equation below? 18x - 4 = -10
- A. x = -2 or x = 1
- B. x = -1/3 or x = 2
- C. x = -1/2 or x = 3/2
- D. x = -3/2 or x = 1/2
Correct Answer: B
Rationale: To solve the equation 18x - 4 = -10, first, add 4 to both sides to get 18x = -6. Then, divide by 18 to isolate x, which gives x = -1/3. Therefore, the correct answer is x = -1/3 or x = 2. It's crucial to double-check the solutions in relation to the original equation to ensure accuracy. The error in the original solution is the incorrect value provided for x = -1 which should have been x = -1/3 instead. Hence, the correct solution is x = -1/3 or x = 2.
A person weighed 180 lb. Three months later, they weighed 160 lb. What is the percentage of weight the person lost over 3 months? (Round to the nearest percent.)
- A. 13%
- B. 20%
- C. 10%
- D. 5%
Correct Answer: B
Rationale: To calculate the percentage of weight lost, subtract the final weight from the initial weight, divide by the initial weight, and multiply by 100. In this case: (180 - 160) / 180 * 100 = 20%, which rounds to the nearest percent as 20%. Therefore, the person lost 20% of their initial weight over the three months. This calculation represents the relative decrease in weight from the initial weight to the final weight, indicating that the person lost 20% of their initial weight during the three-month period.
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.
Four friends are sharing a pizza. One friend eats half of the pizza. The other three friends equally divide the rest among themselves. What portion of the pizza did each of the other three friends receive?
- A. 1/6
- B. 1/4
- C. 1/3
- D. 1/6
Correct Answer: D
Rationale: After one friend eats half of the pizza, half of the pizza remains to be divided among the other three friends. Dividing this remaining half equally among three friends means each friend receives 1/6 of the pizza (1/2 · 3 = 1/6). Therefore, each of the other three friends receives 1/6 of the pizza.