Digit 1 in ten thousands 9 in ones? Select ALL.
- A. 12,679
- B. 12,769
- C. 12,796
- D. 21,679
- E. 21,769
Correct Answer & Rationale
Correct Answer: A,B: 1 ten thousands, 9 ones. C: 6 ones. D,E,F: 2 ten thousands. Place values must match both conditions.
To identify numbers with 1 in the ten thousands place and 9 in the ones place, we analyze each option. - **A (12,679)**: The digit 1 is in the ten thousands place, and 9 is in the ones place, meeting both criteria. - **B (12,769)**: Here, 1 is again in the ten thousands place, and 9 is in the ones place, satisfying the conditions. - **C (12,796)**: The digit in the ones place is 6, not 9, which disqualifies it. - **D (21,679)**: The digit in the ten thousands place is 2, failing to meet the first condition. - **E (21,769)**: Similarly, 2 is in the ten thousands place, not 1. - **F (21,796)**: Again, 2 is in the ten thousands place, disqualifying this option. Only options A and B fulfill both requirements, confirming their validity.
To identify numbers with 1 in the ten thousands place and 9 in the ones place, we analyze each option. - **A (12,679)**: The digit 1 is in the ten thousands place, and 9 is in the ones place, meeting both criteria. - **B (12,769)**: Here, 1 is again in the ten thousands place, and 9 is in the ones place, satisfying the conditions. - **C (12,796)**: The digit in the ones place is 6, not 9, which disqualifies it. - **D (21,679)**: The digit in the ten thousands place is 2, failing to meet the first condition. - **E (21,769)**: Similarly, 2 is in the ten thousands place, not 1. - **F (21,796)**: Again, 2 is in the ten thousands place, disqualifying this option. Only options A and B fulfill both requirements, confirming their validity.
Other Related Questions
Prism: 5.0cm, 7.3cm, 9.2cm. Surface area?
- A. 149.66
- B. 167.9
- C. 299.32
- D. 335.18
Correct Answer & Rationale
Correct Answer: C
To find the surface area of a rectangular prism, the formula is SA = 2(lw + lh + wh), where l, w, and h are the length, width, and height, respectively. Substituting the given dimensions (5.0 cm, 7.3 cm, and 9.2 cm) into the formula yields a surface area of 299.32 cm². Option A (149.66) likely results from miscalculating or omitting a dimension. Option B (167.9) may arise from incorrect multiplication or addition. Option D (335.18) could be a result of doubling the correct surface area without proper calculation. Thus, only option C accurately represents the surface area of the prism.
To find the surface area of a rectangular prism, the formula is SA = 2(lw + lh + wh), where l, w, and h are the length, width, and height, respectively. Substituting the given dimensions (5.0 cm, 7.3 cm, and 9.2 cm) into the formula yields a surface area of 299.32 cm². Option A (149.66) likely results from miscalculating or omitting a dimension. Option B (167.9) may arise from incorrect multiplication or addition. Option D (335.18) could be a result of doubling the correct surface area without proper calculation. Thus, only option C accurately represents the surface area of the prism.
3 in 321,745 vs 4,631?
- A. 100
- B. 1000
- C. 10000
- D. 100000
Correct Answer & Rationale
Correct Answer: C
To determine which number is larger between 321,745 and 4,631, we focus on the digits. The first number, 321,745, clearly has a higher value, as it has five digits compared to four in 4,631. Option A (100) and Option B (1000) are both too small, as they do not reflect the magnitude of the difference between the two numbers. Option D (100,000) is also incorrect, as it exceeds the value of 321,745. Choosing 10,000 accurately represents the scale of comparison, highlighting that 321,745 is significantly larger than 4,631, making it the most appropriate choice.
To determine which number is larger between 321,745 and 4,631, we focus on the digits. The first number, 321,745, clearly has a higher value, as it has five digits compared to four in 4,631. Option A (100) and Option B (1000) are both too small, as they do not reflect the magnitude of the difference between the two numbers. Option D (100,000) is also incorrect, as it exceeds the value of 321,745. Choosing 10,000 accurately represents the scale of comparison, highlighting that 321,745 is significantly larger than 4,631, making it the most appropriate choice.
Joe’s age 4 more than 3x Amy’s. Equation?
- A. A=J/3+4
- B. A=3J+4
- C. J=3A+4
- D. J=3(A+4)
Correct Answer & Rationale
Correct Answer: C
To find the equation representing Joe's age in relation to Amy's, we start with the statement: Joe's age (J) is 4 more than 3 times Amy's age (A). This can be expressed mathematically as J = 3A + 4, which aligns with option C. Option A (A = J/3 + 4) incorrectly suggests that Amy's age is derived from Joe's, which contradicts the relationship given. Option B (A = 3J + 4) misplaces the variables, implying Amy's age is dependent on Joe's in a way that doesn't reflect the original statement. Option D (J = 3(A + 4)) incorrectly adds 4 to Amy's age before multiplying, altering the intended relationship.
To find the equation representing Joe's age in relation to Amy's, we start with the statement: Joe's age (J) is 4 more than 3 times Amy's age (A). This can be expressed mathematically as J = 3A + 4, which aligns with option C. Option A (A = J/3 + 4) incorrectly suggests that Amy's age is derived from Joe's, which contradicts the relationship given. Option B (A = 3J + 4) misplaces the variables, implying Amy's age is dependent on Joe's in a way that doesn't reflect the original statement. Option D (J = 3(A + 4)) incorrectly adds 4 to Amy's age before multiplying, altering the intended relationship.
Associative operations? Select ALL.
- A. Addition
- B. Subtraction
- C. Multiplication
- D. Division
- E. Exponentiation
Correct Answer & Rationale
Correct Answer: A,C
Associative operations allow the grouping of numbers in different ways without changing the result. Addition (A) and multiplication (C) are associative; for example, (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c). Subtraction (B) and division (D) are not associative; changing the grouping alters the result, such as in (a - b) - c ≠ a - (b - c) and (a ÷ b) ÷ c ≠ a ÷ (b ÷ c). Exponentiation (E) is also not associative, as (a^b)^c ≠ a^(b^c). Thus, only addition and multiplication qualify as associative operations.
Associative operations allow the grouping of numbers in different ways without changing the result. Addition (A) and multiplication (C) are associative; for example, (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c). Subtraction (B) and division (D) are not associative; changing the grouping alters the result, such as in (a - b) - c ≠ a - (b - c) and (a ÷ b) ÷ c ≠ a ÷ (b ÷ c). Exponentiation (E) is also not associative, as (a^b)^c ≠ a^(b^c). Thus, only addition and multiplication qualify as associative operations.