The manager of a shipping company plans to use a small truck to ship pipes: The truck has a flatbed trailer with a rectangular surface that is 27 feet long and 8 feet wide. The truck will travel from Atherton to Bakersfield, where some pipes will be delivered, and then on to Castlewood to deliver the remaining pipes. The map shows the roads that connect Atherton. Bakersfield. and Castlewood.
The manager is planning to buy a new truck with better gas mileage. He collected data bout the gas mileage of one of the company's trucks. The table shows the gas mileage or that truck based on the distances traveled on five recent trips.
How many different ways can the truck travel from Atherton to Bakersfield a to Castlewood, using the roads on the map?
- A. 6
- B. 8
- C. 9
- D. 5
Correct Answer & Rationale
Correct Answer: A
To determine the number of different routes from Atherton to Bakersfield and then to Castlewood, we analyze the connections between these locations. If there are 3 distinct paths from Atherton to Bakersfield and 2 distinct paths from Bakersfield to Castlewood, the total number of combinations is found by multiplying the number of options: 3 paths (Atherton to Bakersfield) × 2 paths (Bakersfield to Castlewood) = 6 routes. Options B (8), C (9), and D (5) miscalculate the available paths or overlook the combinations of routes, leading to incorrect totals. Thus, the correct answer accurately reflects the possible travel routes.
To determine the number of different routes from Atherton to Bakersfield and then to Castlewood, we analyze the connections between these locations. If there are 3 distinct paths from Atherton to Bakersfield and 2 distinct paths from Bakersfield to Castlewood, the total number of combinations is found by multiplying the number of options: 3 paths (Atherton to Bakersfield) × 2 paths (Bakersfield to Castlewood) = 6 routes. Options B (8), C (9), and D (5) miscalculate the available paths or overlook the combinations of routes, leading to incorrect totals. Thus, the correct answer accurately reflects the possible travel routes.
Other Related Questions
On a number line, what is the distance, in units, between 16 and -25
Correct Answer & Rationale
Correct Answer: 41 units
To find the distance between two points on a number line, subtract the smaller number from the larger number. Here, the calculation is |16 - (-25)|, which simplifies to |16 + 25| = |41|. This results in a distance of 41 units. Other options may suggest incorrect calculations. For instance, an answer like 9 units might arise from simply adding the two numbers without considering their positions on the number line, leading to an inaccurate interpretation of distance. Similarly, options like 25 or 16 units misrepresent the actual distance by not accounting for both numbers' magnitudes relative to zero.
To find the distance between two points on a number line, subtract the smaller number from the larger number. Here, the calculation is |16 - (-25)|, which simplifies to |16 + 25| = |41|. This results in a distance of 41 units. Other options may suggest incorrect calculations. For instance, an answer like 9 units might arise from simply adding the two numbers without considering their positions on the number line, leading to an inaccurate interpretation of distance. Similarly, options like 25 or 16 units misrepresent the actual distance by not accounting for both numbers' magnitudes relative to zero.
Which graph represents the solution of x + 5 ≤ 3?
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A.
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B.
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C.
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D.
Correct Answer & Rationale
Correct Answer: A
To solve the inequality x + 5 ≤ 3, we first isolate x by subtracting 5 from both sides, giving us x ≤ -2. Option A correctly represents this solution with a closed circle at -2, indicating that -2 is included in the solution set, and a shaded line extending to the left, showing all values less than -2. Options B, C, and D either depict open circles, which imply that the endpoint is not included, or incorrectly shade in the wrong direction or range, failing to accurately represent the solution x ≤ -2.
To solve the inequality x + 5 ≤ 3, we first isolate x by subtracting 5 from both sides, giving us x ≤ -2. Option A correctly represents this solution with a closed circle at -2, indicating that -2 is included in the solution set, and a shaded line extending to the left, showing all values less than -2. Options B, C, and D either depict open circles, which imply that the endpoint is not included, or incorrectly shade in the wrong direction or range, failing to accurately represent the solution x ≤ -2.
What is the value of 2/5 multiplied by ¾ divide by 8/5
- A. 12\25
- B. 1\3
- C. 3\16
- D. 64/75
Correct Answer & Rationale
Correct Answer: C
To solve \( \frac{2}{5} \times \frac{3}{4} \div \frac{8}{5} \), first, convert the division into multiplication by flipping the second fraction: \[ \frac{2}{5} \times \frac{3}{4} \times \frac{5}{8} \] Next, multiply the fractions: \[ \frac{2 \times 3 \times 5}{5 \times 4 \times 8} = \frac{30}{160} \] Simplifying \( \frac{30}{160} \) gives \( \frac{3}{16} \), confirming option C. Option A (12/25) is incorrect as it does not simplify correctly from the original operation. Option B (1/3) results from an incorrect multiplication or division process. Option D (64/75) does not match the calculated result and suggests an error in fraction handling.
To solve \( \frac{2}{5} \times \frac{3}{4} \div \frac{8}{5} \), first, convert the division into multiplication by flipping the second fraction: \[ \frac{2}{5} \times \frac{3}{4} \times \frac{5}{8} \] Next, multiply the fractions: \[ \frac{2 \times 3 \times 5}{5 \times 4 \times 8} = \frac{30}{160} \] Simplifying \( \frac{30}{160} \) gives \( \frac{3}{16} \), confirming option C. Option A (12/25) is incorrect as it does not simplify correctly from the original operation. Option B (1/3) results from an incorrect multiplication or division process. Option D (64/75) does not match the calculated result and suggests an error in fraction handling.
Solve the equation for x: (2x-3)/5 = x/10
- A. 2
- B. 3
- C. 1\5
- D. 10
Correct Answer & Rationale
Correct Answer: A
To solve the equation \((2x-3)/5 = x/10\), first eliminate the fractions by multiplying both sides by 10, resulting in \(2(2x - 3) = x\). Simplifying gives \(4x - 6 = x\). Rearranging leads to \(4x - x = 6\), or \(3x = 6\), giving \(x = 2\). Option B (3) does not satisfy the equation when substituted back. Option C (1/5) results in a negative left side, while Option D (10) leads to an incorrect balance in the original equation. Thus, the only solution that holds true is \(x = 2\).
To solve the equation \((2x-3)/5 = x/10\), first eliminate the fractions by multiplying both sides by 10, resulting in \(2(2x - 3) = x\). Simplifying gives \(4x - 6 = x\). Rearranging leads to \(4x - x = 6\), or \(3x = 6\), giving \(x = 2\). Option B (3) does not satisfy the equation when substituted back. Option C (1/5) results in a negative left side, while Option D (10) leads to an incorrect balance in the original equation. Thus, the only solution that holds true is \(x = 2\).