2 + (2 × 2) + 2 =
- A. 8
- B. 10
- C. 12
- D. 16
Correct Answer & Rationale
Correct Answer: A
To solve the expression 2 + (2 × 2) + 2, it’s essential to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). First, calculate the value inside the parentheses: 2 × 2 equals 4. Next, substitute this back into the expression: 2 + 4 + 2. Then, perform the addition from left to right: 2 + 4 equals 6, and then 6 + 2 equals 8. Options B (10), C (12), and D (16) are incorrect because they do not adhere to the proper order of operations or miscalculate the addition steps.
To solve the expression 2 + (2 × 2) + 2, it’s essential to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). First, calculate the value inside the parentheses: 2 × 2 equals 4. Next, substitute this back into the expression: 2 + 4 + 2. Then, perform the addition from left to right: 2 + 4 equals 6, and then 6 + 2 equals 8. Options B (10), C (12), and D (16) are incorrect because they do not adhere to the proper order of operations or miscalculate the addition steps.
Other Related Questions
If 4 is x percent of 16, what is x?
- A. 1/4
- B. 4
- C. 16
- D. 25
Correct Answer & Rationale
Correct Answer: D
To find x, we start with the equation \(4 = \frac{x}{100} \times 16\). Rearranging this gives \(x = \frac{4 \times 100}{16}\), which simplifies to \(x = 25\). Option A (1/4) is incorrect as it does not represent a percentage of 16. Option B (4) misinterprets the relationship, as it does not reflect the percentage context. Option C (16) suggests that 4 is 16% of itself, which is also incorrect. Only option D (25) accurately represents that 4 is 25% of 16, confirming the correct calculation.
To find x, we start with the equation \(4 = \frac{x}{100} \times 16\). Rearranging this gives \(x = \frac{4 \times 100}{16}\), which simplifies to \(x = 25\). Option A (1/4) is incorrect as it does not represent a percentage of 16. Option B (4) misinterprets the relationship, as it does not reflect the percentage context. Option C (16) suggests that 4 is 16% of itself, which is also incorrect. Only option D (25) accurately represents that 4 is 25% of 16, confirming the correct calculation.
Fred worked 39.5 hours last week. Alice worked 6.75 fewer hours than Fred. How many hours did Alice work?
- A. 33.75 HOURS
- B. 33.25 HOURS
- C. 33.35 HOURS
- D. 33.85 HOURS
Correct Answer & Rationale
Correct Answer: A
To determine how many hours Alice worked, subtract the hours she worked less than Fred from Fred's total. Fred worked 39.5 hours, and Alice worked 6.75 hours fewer. Calculating this: 39.5 - 6.75 = 32.75 hours. However, this calculation is incorrect. The correct calculation should be: 39.5 - 6.75 = 32.75 hours. This means option A (33.75 hours) is incorrect. Option B (33.25 hours), C (33.35 hours), and D (33.85 hours) also do not match the correct calculation. Thus, none of the options are correct based on the provided data.
To determine how many hours Alice worked, subtract the hours she worked less than Fred from Fred's total. Fred worked 39.5 hours, and Alice worked 6.75 hours fewer. Calculating this: 39.5 - 6.75 = 32.75 hours. However, this calculation is incorrect. The correct calculation should be: 39.5 - 6.75 = 32.75 hours. This means option A (33.75 hours) is incorrect. Option B (33.25 hours), C (33.35 hours), and D (33.85 hours) also do not match the correct calculation. Thus, none of the options are correct based on the provided data.
The coordinate of pointP on the number line above is x. The value of 10x is between
- A. 1 and 4
- B. 4 and 6
- C. 6 and 8
- D. 8 and 12
Correct Answer & Rationale
Correct Answer: B
To determine the correct range for \(10x\), we first need to assess the implications of each option based on the value of \(x\). - **Option A: 1 and 4** suggests \(0.1 < x < 0.4\). This would yield \(10x\) values less than 4, which is too low. - **Option B: 4 and 6** indicates \(0.4 < x < 0.6\). This range results in \(10x\) values between 4 and 6, aligning perfectly with the requirement. - **Option C: 6 and 8** implies \(0.6 < x < 0.8\). Here, \(10x\) would exceed 6, which is not valid. - **Option D: 8 and 12** indicates \(0.8 < x < 1.2\), leading to values of \(10x\) that exceed 8, thus also incorrect. Therefore, only Option B accurately reflects the condition for \(10x\) being between 4 and 6.
To determine the correct range for \(10x\), we first need to assess the implications of each option based on the value of \(x\). - **Option A: 1 and 4** suggests \(0.1 < x < 0.4\). This would yield \(10x\) values less than 4, which is too low. - **Option B: 4 and 6** indicates \(0.4 < x < 0.6\). This range results in \(10x\) values between 4 and 6, aligning perfectly with the requirement. - **Option C: 6 and 8** implies \(0.6 < x < 0.8\). Here, \(10x\) would exceed 6, which is not valid. - **Option D: 8 and 12** indicates \(0.8 < x < 1.2\), leading to values of \(10x\) that exceed 8, thus also incorrect. Therefore, only Option B accurately reflects the condition for \(10x\) being between 4 and 6.
1 is 3 percent of what number?
- A. 1/3
- B. 3
- C. 30
- D. 33,1/3
Correct Answer & Rationale
Correct Answer: D
To find the number of which 1 is 3 percent, set up the equation: 1 = 0.03 × x. Solving for x gives x = 1 / 0.03, which equals 33.33 (or 33 1/3). Option A (1/3) is incorrect as it represents a fraction far smaller than 1. Option B (3) fails because 3 percent of 3 is 0.09, not 1. Option C (30) is also incorrect; 3 percent of 30 equals 0.9. Thus, only option D (33 1/3) correctly satisfies the equation, making it the right choice.
To find the number of which 1 is 3 percent, set up the equation: 1 = 0.03 × x. Solving for x gives x = 1 / 0.03, which equals 33.33 (or 33 1/3). Option A (1/3) is incorrect as it represents a fraction far smaller than 1. Option B (3) fails because 3 percent of 3 is 0.09, not 1. Option C (30) is also incorrect; 3 percent of 30 equals 0.9. Thus, only option D (33 1/3) correctly satisfies the equation, making it the right choice.