Nokea
A sandwich shop earns $4 for every sandwich (s) it sells, $2 for every drink (d), and $1 for every cookie (c). If this is all the shop sells, which of the following equations represents what the shop's revenue (r) is over three days?
- A. r = 4s + 2d + 1c
- B. r = 8s + 4d + 2c
- C. r = 12s + 6d + 3c
- D. r = 16s + 8d + 4c
Correct Answer: A
Rationale: Let s be the number of sandwiches sold. Each sandwich earns $4, so selling s sandwiches at $4 each results in revenue of $4s. Similarly, d drinks at $2 each give $2d of income, and cookies bring in $1c. Summing these values gives total revenue = 4s + 2d + 1c. Therefore, option A, r = 4s + 2d + 1c, correctly represents the shop's revenue. Choices B, C, and D are incorrect because they incorrectly multiply the prices of each item by more than one day's sales, which would overstate the total revenue for a three-day period.
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What is the perimeter of a rectangle with a length of 12 cm and a width of 5 cm?
- A. 17 cm
- B. 24 cm
- C. 34 cm
- D. 40 cm
Correct Answer: C
Rationale: The correct formula for the perimeter of a rectangle is P = 2(l + w), where l represents the length and w represents the width. Substituting the given values into the formula: P = 2(12 cm + 5 cm) = 2(17 cm) = 34 cm. Therefore, the perimeter of the rectangle is 34 cm. Choice A (17 cm) is incorrect as it seems to have added only the length and width without multiplying by 2. Choice B (24 cm) is incorrect as it does not consider the multiplication by 2. Choice D (40 cm) is incorrect as it seems to have added the length and width without multiplying by 2.
Adam is painting the outside of a 4-walled shed. The shed is 5 feet wide, 4 feet deep, and 7 feet high. Which of the following is the amount of paint Adam will need for the four walls?
- A. 80 ft²
- B. 126 ft²
- C. 140 ft²
- D. 560 ft²
Correct Answer: B
Rationale: To find the amount of paint needed for the four walls of the shed, calculate the total area of the four walls. The shed has two pairs of identical walls. The area of one pair of walls is 5 feet (width) x 7 feet (height) + 4 feet (depth) x 7 feet (height) = 35 ft² + 28 ft² = 63 ft². Since there are two pairs of walls, the total area for the four walls is 2 x 63 ft² = 126 ft². Therefore, Adam will need 126 ft² of paint for the four walls. Choice A, 80 ft², is incorrect as it does not account for the total surface area of all four walls. Choice C, 140 ft², is incorrect as it overestimates the area required. Choice D, 560 ft², is incorrect as it significantly overestimates the amount of paint needed for the shed.
x · 7 = x − 36. Solve the equation. Which of the following is correct?
- A. x = 6
- B. x = 42
- C. x = 4
- D. x = 252
Correct Answer: B
Rationale: To solve the equation x · 7 = x − 36, start by multiplying both sides by 7 to get 7(x · 7) = 7(x − 36), which simplifies to x = 7x − 252. Next, subtract 7x from both sides to get -6x = -252. Finally, divide both sides by -6 to solve for x, which results in x = 42. Therefore, the correct answer is x = 42. Choice A (x = 6), Choice C (x = 4), and Choice D (x = 252) are incorrect as they do not align with the correct solution derived from the equation.
Which of the following lists is in order from least to greatest? 2−1 , −(4/3), (−1)3 , (2/5)
- A. 2−1 , −(4/3), (−1)3 , (2/5)
- B. −(4/3), (−1)3 , 2−1 , (2/5)
- C. −(4/3), (2/5), 2−1 , (−1)3
- D. −(4/3), (−1)3 , (2/5), 2−1
Correct Answer: D
Rationale: To determine the correct order from least to greatest, start by simplifying the expressions. 2^(-1) = 1/2 and (-1)^3 = -1. Now, comparing the values, (-4/3) is the most negative, followed by -1, then (2/5), and finally 1/2. Therefore, the correct order is (-4/3), (-1)^3, (2/5), 2^(-1), making choice D the correct answer. Choices A, B, and C are incorrect because they do not follow the correct order from least to greatest as determined by comparing the values of the expressions after simplification.
A rectangular field has an area of 1452 square feet. If the length is three times the width, what is the width of the field?
- A. 22 feet
- B. 44 feet
- C. 242 feet
- D. 1452 feet
Correct Answer: A
Rationale: To find the width of the rectangular field, use the formula for the area of a rectangle: A = length width. Given that the length is three times the width, you have A = 3w w. Substituting the given area, 1452 = 3w^2. Solving for w, you get 484 = w^2. Taking the square root gives ±22, but since the width must be positive, the width of the field is 22 feet. Choice B, 44 feet, is incorrect because it represents the length, not the width. Choice C, 242 feet, is incorrect as it is not a factor of the area. Choice D, 1452 feet, is incorrect as it represents the total area of the field, not the width.