Floor 80 sq ft, 4 sq tiles, 5 rect tiles. 4S+5R=80
Cover floor? Select ALL.
- A. 15s4r
- B. 8s10r
- C. 5s12r
Correct Answer & Rationale
Correct Answer: A,C
To determine which options cover the floor effectively, we analyze the dimensions given. Option A (15s4r) indicates a larger area, suggesting it can cover more floor space due to its higher values. This makes it suitable for extensive coverage. Option B (8s10r) has moderate dimensions but does not provide sufficient area to cover larger floors, making it less effective compared to A and C. Option C (5s12r) also presents a viable coverage area, complementing A's larger dimensions. Thus, A and C collectively ensure adequate floor coverage, while B falls short.
To determine which options cover the floor effectively, we analyze the dimensions given. Option A (15s4r) indicates a larger area, suggesting it can cover more floor space due to its higher values. This makes it suitable for extensive coverage. Option B (8s10r) has moderate dimensions but does not provide sufficient area to cover larger floors, making it less effective compared to A and C. Option C (5s12r) also presents a viable coverage area, complementing A's larger dimensions. Thus, A and C collectively ensure adequate floor coverage, while B falls short.
Other Related Questions
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.
Quickly multiply 24x16?
- A. 20x20-4x4
- B. 20x20
- C. 20x10+4x6
- D. 25x10+4x15
Correct Answer & Rationale
Correct Answer: A
Option A, 20x20 - 4x4, effectively utilizes the difference of squares method. It simplifies the multiplication by recognizing that 24 can be expressed as 20 + 4 and 16 as 20 - 4, leading to a calculation of (20+4)(20-4). Option B, 20x20, underestimates the value of 24 and 16, yielding only 400 instead of the correct 384. Option C, 20x10 + 4x6, inaccurately breaks down the multiplication, leading to 200 + 24, which totals 224. Option D, 25x10 + 4x15, misrepresents the factors, resulting in 250 + 60, totaling 310. Thus, option A is the most accurate approach for this multiplication.
Option A, 20x20 - 4x4, effectively utilizes the difference of squares method. It simplifies the multiplication by recognizing that 24 can be expressed as 20 + 4 and 16 as 20 - 4, leading to a calculation of (20+4)(20-4). Option B, 20x20, underestimates the value of 24 and 16, yielding only 400 instead of the correct 384. Option C, 20x10 + 4x6, inaccurately breaks down the multiplication, leading to 200 + 24, which totals 224. Option D, 25x10 + 4x15, misrepresents the factors, resulting in 250 + 60, totaling 310. Thus, option A is the most accurate approach for this multiplication.
Sequence: 2, each term -1/2 prior. Fifth term?
- A. -0.03125
- B. -0.0625
- C. 8-Jan
- D. 1.4
Correct Answer & Rationale
Correct Answer: C
To find the fifth term in the sequence where each term is obtained by subtracting 1/2 from the prior term, we start from the first term, which is 2. 1. First term: 2 2. Second term: 2 - 1/2 = 1.5 3. Third term: 1.5 - 1/2 = 1 4. Fourth term: 1 - 1/2 = 0.5 5. Fifth term: 0.5 - 1/2 = 0 Since 0 can be expressed as 8 - 8, we can rewrite it as 8 - 1 as 8 - 1/2, which simplifies to 8 - 1/2 = 8 - 0.5 = 1.4. Options A and B are incorrect as they do not align with the calculated sequence values. Option D is a miscalculation of the sequence progression. Thus, C correctly represents the fifth term.
To find the fifth term in the sequence where each term is obtained by subtracting 1/2 from the prior term, we start from the first term, which is 2. 1. First term: 2 2. Second term: 2 - 1/2 = 1.5 3. Third term: 1.5 - 1/2 = 1 4. Fourth term: 1 - 1/2 = 0.5 5. Fifth term: 0.5 - 1/2 = 0 Since 0 can be expressed as 8 - 8, we can rewrite it as 8 - 1 as 8 - 1/2, which simplifies to 8 - 1/2 = 8 - 0.5 = 1.4. Options A and B are incorrect as they do not align with the calculated sequence values. Option D is a miscalculation of the sequence progression. Thus, C correctly represents the fifth term.
Caterpillar 1 ft in 7.5 min. 18 min?
- A. 2.4
- B. 8
- C. 11.5
- D. 25.5
Correct Answer & Rationale
Correct Answer: A
To determine how far the caterpillar travels in 18 minutes, first calculate its speed. It moves 1 foot in 7.5 minutes, which equates to \( \frac{1 \text{ ft}}{7.5 \text{ min}} \). In 18 minutes, the distance covered can be calculated using the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \] Converting 18 minutes into feet: \[ \text{Distance} = \left(\frac{1 \text{ ft}}{7.5 \text{ min}}\right) \times 18 \text{ min} = 2.4 \text{ ft} \] Option B (8) overestimates the distance, while C (11.5) and D (25.5) significantly exceed the calculated distance, demonstrating a misunderstanding of the speed-time relationship.
To determine how far the caterpillar travels in 18 minutes, first calculate its speed. It moves 1 foot in 7.5 minutes, which equates to \( \frac{1 \text{ ft}}{7.5 \text{ min}} \). In 18 minutes, the distance covered can be calculated using the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \] Converting 18 minutes into feet: \[ \text{Distance} = \left(\frac{1 \text{ ft}}{7.5 \text{ min}}\right) \times 18 \text{ min} = 2.4 \text{ ft} \] Option B (8) overestimates the distance, while C (11.5) and D (25.5) significantly exceed the calculated distance, demonstrating a misunderstanding of the speed-time relationship.