Shaded region shows?
- A. 3/4 x 1/2
- B. 3/4 x 3/4
- C. 3/4 x 3/2
- D. 3/4 x 3
Correct Answer & Rationale
Correct Answer: A
The shaded region represents the area of a rectangle formed by multiplying two fractions. Option A, \( \frac{3}{4} \times \frac{1}{2} \), correctly calculates the area of a rectangle with a length of \( \frac{3}{4} \) and a width of \( \frac{1}{2} \), resulting in \( \frac{3}{8} \). Option B, \( \frac{3}{4} \times \frac{3}{4} \), represents a larger area, \( \frac{9}{16} \), which does not match the shaded region. Option C, \( \frac{3}{4} \times \frac{3}{2} \), yields \( \frac{9}{8} \), exceeding the shaded area. Finally, option D, \( \frac{3}{4} \times 3 \), results in \( \frac{9}{4} \), also too large. Thus, only option A accurately reflects the area of the shaded region.
The shaded region represents the area of a rectangle formed by multiplying two fractions. Option A, \( \frac{3}{4} \times \frac{1}{2} \), correctly calculates the area of a rectangle with a length of \( \frac{3}{4} \) and a width of \( \frac{1}{2} \), resulting in \( \frac{3}{8} \). Option B, \( \frac{3}{4} \times \frac{3}{4} \), represents a larger area, \( \frac{9}{16} \), which does not match the shaded region. Option C, \( \frac{3}{4} \times \frac{3}{2} \), yields \( \frac{9}{8} \), exceeding the shaded area. Finally, option D, \( \frac{3}{4} \times 3 \), results in \( \frac{9}{4} \), also too large. Thus, only option A accurately reflects the area of the shaded region.
Other Related Questions
178-degree angle?
- A. Acute
- B. Obtuse
- C. Right
- D. Straight
Correct Answer & Rationale
Correct Answer: B
An angle measuring 178 degrees is classified as obtuse, as it is greater than 90 degrees but less than 180 degrees. Option A, acute, refers to angles less than 90 degrees, which does not apply here. Option C, right, denotes a 90-degree angle, clearly not fitting for 178 degrees. Option D, straight, describes a 180-degree angle, which is also not applicable since 178 degrees is slightly less than that. Thus, the only suitable classification for a 178-degree angle is obtuse.
An angle measuring 178 degrees is classified as obtuse, as it is greater than 90 degrees but less than 180 degrees. Option A, acute, refers to angles less than 90 degrees, which does not apply here. Option C, right, denotes a 90-degree angle, clearly not fitting for 178 degrees. Option D, straight, describes a 180-degree angle, which is also not applicable since 178 degrees is slightly less than that. Thus, the only suitable classification for a 178-degree angle is obtuse.
Prime numbers? Select ALL.
- A. 21
- B. 23
- C. 25
- D. 27
- E. 29
Correct Answer & Rationale
Correct Answer: B,E
Prime numbers are defined as natural numbers greater than 1 that have no positive divisors other than 1 and themselves. - **Option A: 21** is not prime because it can be divided by 1, 3, 7, and 21. - **Option B: 23** is prime; it has no divisors other than 1 and 23. - **Option C: 25** is not prime as it can be divided by 1, 5, and 25. - **Option D: 27** is not prime since it can be divided by 1, 3, 9, and 27. - **Option E: 29** is prime; it has no divisors other than 1 and 29. Thus, 23 and 29 are the only prime numbers in the list.
Prime numbers are defined as natural numbers greater than 1 that have no positive divisors other than 1 and themselves. - **Option A: 21** is not prime because it can be divided by 1, 3, 7, and 21. - **Option B: 23** is prime; it has no divisors other than 1 and 23. - **Option C: 25** is not prime as it can be divided by 1, 5, and 25. - **Option D: 27** is not prime since it can be divided by 1, 3, 9, and 27. - **Option E: 29** is prime; it has no divisors other than 1 and 29. Thus, 23 and 29 are the only prime numbers in the list.
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.
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.