Nokea
Simplify the expression. Which of the following is the value of x? (5(4x - 5) = (3/2)(2x - 6))
- A. −(2/7)
- B. −(4/17)
- C. (16/17)
- D. (8/7)
Correct Answer: C
Rationale: To solve the given proportion 5(4x - 5) = (3/2)(2x - 6), first distribute to get 20x - 25 = 3x - 9. Then, simplify the linear equation by isolating x: 20x - 3x = 25 - 9, which leads to 17x = 16. Finally, solving for x gives x = 16/17. Choice A is incorrect as it does not match the calculated value of x. Choice B is incorrect as it does not correspond to the correct solution for x. Choice D is incorrect as it does not align with the accurate value of x obtained from solving the equation.
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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.
Which of the following is equivalent to 3.28?
- A. (328/100)
- B. (41/5)
- C. (3/28)
- D. (7/25)
Correct Answer: D
Rationale: To convert a decimal to a fraction, we can treat it as a fraction over 1 and then simplify. For 3.28, it can be written as 3.28/1. To convert this to a fraction, we multiply by 100 to get (328/100). Then, to simplify, we divide both the numerator and denominator by 4 to get (82/25). This simplifies further to (7/25). Therefore, (7/25) is equivalent to 3.28. Choices A, B, and C are incorrect as they do not represent the decimal 3.28.
Which of the following lists is in order from least to greatest? (1/7), 0.125, (6/9), 0.60
- A. (1/7), 0.125, (6/9), 0.60
- B. (1/7), 0.125, 0.60, (6/9)
- C. 0.125, (1/7), 0.60, 6/9
- D. 0.125, (1/7), (6/9), 0.60
Correct Answer: C
Rationale: To determine the order from least to greatest, convert all fractions to decimals and compare them. Converting the fractions: (1/7) ≈ 0.14, (6/9) ≈ 0.67. The decimals in order from least to greatest are: 0.125 < 0.14 < 0.60 < 0.67. Therefore, the correct order is 0.125, (1/7), 0.60, 6/9, making choice C the correct answer. Choice A is incorrect as it lists (1/7) before 0.125. Choice B is incorrect as it places 0.60 before (6/9). Choice D is incorrect as it lists (6/9) before 0.60.
A circular swimming pool has a circumference of 49 feet. What is the diameter of the pool?
- A. 15.6 feet
- B. 17.8 feet
- C. 49 feet
- D. 153.9 feet
Correct Answer: A
Rationale: The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter. Given C = 49 feet, we can rearrange the formula to solve for d: 49 feet = πd. To find the diameter, we divide both sides by π, giving us d = 49 feet / π ≈ 15.6 feet. Therefore, the diameter of the swimming pool is approximately 15.6 feet. Choices B, C, and D are incorrect because they do not align with the calculation based on the formula for the circumference of a circle.
A woman's dinner bill comes to $48.30. If she adds a 20% tip, which of the following will be her total bill?
- A. $9.66
- B. $38.64
- C. $48.30
- D. $57.96
Correct Answer: D
Rationale: To calculate the total bill after adding a 20% tip, you need to find 120% of the original bill. This is because adding a 20% tip means paying 120% of the bill. So, $48.30 120/100 = $57.96. Therefore, the correct answer is $57.96. Choice A ($9.66) is incorrect as it represents only the 20% tip amount. Choice B ($38.64) is incorrect as it is the original bill amount without the tip. Choice C ($48.30) is incorrect as it is the original bill amount and does not include the additional 20% tip.