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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.
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After spending 80% of her $60, Lana is left with how much money when she invests the remaining amount and earns an 80% profit?
- A. $21.60
- B. $9.60
- C. $86.40
- D. $60.00
Correct Answer: A
Rationale: After spending 80% of $60, Lana spends $48, leaving her with $12. When she invests this remaining amount and earns an 80% profit on $12, it amounts to $21.60 ($12 + 80% of $12 = $12 + $9.60 = $21.60). Therefore, Lana now has $21.60 in total.
A macaroni and cheese recipe calls for 1/3 cup of flour for every 1 1/5 cups of milk. To make a bigger batch, the chef uses 2 cups of flour. Which of the following would be the amount of milk needed for the bigger batch?
- A. 2 2/5 cups
- B. 7 1/5 cups
- C. 6 cups
- D. 3 8/15 cups
Correct Answer: B
Rationale: To determine the amount of milk needed for the bigger batch, we first establish the ratio of flour to milk, which is 1/3 : 1 1/5. Converting 1 1/5 to an improper fraction gives us 6/5. Therefore, the ratio becomes 1:6/5 = 1:1.2. If the chef uses 2 cups of flour, the calculation would be 2 x 1.2 = 2.4 cups of milk needed. This is equivalent to 2 2/5 cups. Hence, the correct answer is 7 1/5 cups.
A recipe calls for 2 1/2 cups of flour to yield 36 cookies. How much flour will be needed to make 90 cookies using the same recipe?
- A. 6 1/2 cups
- B. 10 1/2 cups
- C. 5 1/2 cups
- D. 4 1/2 cups
Correct Answer: A
Rationale: To determine the amount of flour needed for 90 cookies using the same recipe, set up a proportion: (90 cookies / 36 cookies) * 2.5 cups = 6.25 cups, which simplifies to 6 1/2 cups of flour. Therefore, to make 90 cookies, you will need 6 1/2 cups of flour, based on the original recipe's ratio of flour to cookies.
Given x/y - 3x = rw, solve for x in the equation above.
- A. x = rw y + z
- B. x = rw y - z
- C. x = rw(y - z)
- D. None of the Above
Correct Answer: D
Rationale: To solve for x in the equation x/y - 3x = rw, you need to isolate x. This equation involves a term with x on both sides and a division by y, making it challenging to find a direct solution for x. By combining these complexities, there is no single correct expression for x. Therefore, 'None of the Above' is the correct answer as there is no straightforward solution for x in this particular equation.
Which term best describes the data set below: 1, 1, 2, 2, 2, 2, 3, 3, 7, 7, 8, 8, 8, 8, 9, 9?
- A. Uniform
- B. Bimodal
- C. Right-skewed
- D. Left-skewed
Correct Answer: B
Rationale: A bimodal distribution is characterized by two peaks or distinct values that occur most frequently in the data set. In this specific data set, the values '2' and '8' appear more frequently than other values, indicating two modes, making it a bimodal distribution. The presence of two prominent peaks or modes distinguishes it from a uniform, right-skewed, or left-skewed distribution. In a uniform distribution, all values have similar frequencies, which is not the case here. Right-skewed and left-skewed distributions have a single peak but differ in the tail direction; however, this data set does not exhibit such characteristics.