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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.
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To determine the cost of a pizza, Polar considers the diameter of the pizza, the number of pizza toppings, and the amount of cheese. Which of the following is the dependent variable?
- A. Number of toppings
- B. Amount of cheese
- C. Diameter of the pizza
- D. Cost of the pizza
Correct Answer: D
Rationale: In this scenario, the cost of the pizza is the dependent variable. It is not fixed but varies based on the diameter of the pizza, the number of toppings, and the amount of cheese. The cost of the pizza is influenced by these independent variables. As the diameter, toppings, or cheese amount change, the cost changes accordingly. Therefore, the cost of the pizza is the dependent variable, as it depends on the values of the other variables. The diameter of the pizza, number of toppings, and amount of cheese are independent variables because they can be changed without the cost being fixed, showing that they affect the cost and are not dependent on it.
A circle has an area of 49π square inches. What is the circumference of the circle in terms of π?
- A. 7Ï€ in
- B. 14Ï€ in
- C. 28Ï€ in
- D. 3.5Ï€ in
Correct Answer: B
Rationale: To find the circumference of a circle in terms of π, we first determine the radius using the formula for the area of a circle, A = πr^2. Given that the area is 49π square inches, we have 49π = πr^2, which simplifies to r = 7. The circumference of a circle is calculated using the formula C = 2πr. Substituting r = 7, we get C = 2π(7) = 14π. Therefore, the circumference of the circle is 14π inches.
Which of the following expressions represents the sum of three times a number and eight times another number?
- A. 3x + 8x
- B. 3x + 8y
- C. 8x - 3y
- D. 3x - 8y
Correct Answer: B
Rationale: To find the sum of three times a number and eight times another number, you need to multiply each number by its respective factor. Three times a number is represented by 3x, and eight times another number is represented by 8y. When adding these two terms together, the correct expression is 3x + 8y. Therefore, choice B is the correct answer as it accurately represents the sum of three times a number and eight times another number.
Translate the phrase 'Five less than twice the number' into a mathematical expression.
- A. 5x-2
- B. 2x-5
- C. 2-5x
- D. 5-2x
Correct Answer: B
Rationale: To translate 'Five less than twice the number' into a mathematical expression, you first calculate twice the number (2x) and then subtract 5 from it. This gives you 2x-5. Therefore, choice B, 2x-5, accurately represents the mathematical expression for 'Five less than twice the number.' The phrase 'Five less than' implies subtraction, and 'twice the number' is represented by 2x. Thus, when you subtract 5 from twice the number, the correct expression is 2x-5.
A bag contains five green balls, four red balls, and three yellow balls. If one ball is randomly selected from the bag, what is the probability that the ball is red?
- A. 4/12
- B. 5/12
- C. 1/4
- D. 1/2
Correct Answer: A
Rationale: To find the probability of selecting a red ball, we calculate the total number of balls in the bag, which is 5 (green) + 4 (red) + 3 (yellow) = 12 balls. The probability is the number of favorable outcomes (4 red balls) divided by the total number of outcomes (12 balls), giving us 4/12 or 1/3. Therefore, the correct answer is A, representing a probability of 1/3 for selecting a red ball from the bag.