A bag of dog food weighs 40 pounds. The amount of food in the bag is more than 3 times the amount needed to feed a dog for one week. Which inequality can be used to determine the possible values for p, the pounds of food needed to feed the dog for one week?
- A. p < 3(40)
- B. 3p < 40
- C. p > 3(40)
- D. 3p > 40
Correct Answer & Rationale
Correct Answer: D
To find the amount of food needed for one week, we know that the total weight of the dog food (40 pounds) is more than three times the weekly requirement (3p). Therefore, the relationship can be expressed as 3p < 40, indicating that the total food exceeds three times the weekly amount. Option A (p < 3(40)) incorrectly suggests that the weekly requirement is less than three times the total weight, which is not supported by the problem statement. Option B (3p < 40) misrepresents the relationship, as it implies the total food is less than three times the weekly need, contradicting the given information. Option C (p > 3(40)) inaccurately states that the weekly requirement exceeds three times the total weight, which is impossible given the context. Thus, the correct inequality is 3p > 40, indicating the total food is indeed more than three times the weekly requirement.
To find the amount of food needed for one week, we know that the total weight of the dog food (40 pounds) is more than three times the weekly requirement (3p). Therefore, the relationship can be expressed as 3p < 40, indicating that the total food exceeds three times the weekly amount. Option A (p < 3(40)) incorrectly suggests that the weekly requirement is less than three times the total weight, which is not supported by the problem statement. Option B (3p < 40) misrepresents the relationship, as it implies the total food is less than three times the weekly need, contradicting the given information. Option C (p > 3(40)) inaccurately states that the weekly requirement exceeds three times the total weight, which is impossible given the context. Thus, the correct inequality is 3p > 40, indicating the total food is indeed more than three times the weekly requirement.
Other Related Questions
Which graph represents the equation x - 2y = 4?
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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 determine which graph represents the equation \( x - 2y = 4 \), we can rearrange it into slope-intercept form: \( y = \frac{1}{2}x - 2 \). This indicates a slope of \( \frac{1}{2} \) and a y-intercept at \( -2 \). Option A accurately reflects these characteristics, showing a line that rises gradually and crosses the y-axis at \( -2 \). Options B, C, and D do not have the correct slope or y-intercept. B has a steeper slope, C slopes downward, and D does not intersect the y-axis at the correct point. Thus, only Option A is consistent with the equation's graph.
To determine which graph represents the equation \( x - 2y = 4 \), we can rearrange it into slope-intercept form: \( y = \frac{1}{2}x - 2 \). This indicates a slope of \( \frac{1}{2} \) and a y-intercept at \( -2 \). Option A accurately reflects these characteristics, showing a line that rises gradually and crosses the y-axis at \( -2 \). Options B, C, and D do not have the correct slope or y-intercept. B has a steeper slope, C slopes downward, and D does not intersect the y-axis at the correct point. Thus, only Option A is consistent with the equation's graph.
The world's highest suspension bridge spans the Arkansas River at a height of 1,053 feet above the water. If a ball is dropped from the bridge. The height of the ball, In feet, after t seconds can be modeled by the equation f(t)= -16(t)^2 + 1053. How many feet above the water is the ball 7 seconds after being dropped?
Correct Answer & Rationale
Correct Answer: A
To determine the height of the ball 7 seconds after being dropped, substitute \( t = 7 \) into the equation \( f(t) = -16(t)^2 + 1053 \). Calculating this gives \( f(7) = -16(7)^2 + 1053 = -16(49) + 1053 = -784 + 1053 = 269 \) feet. Option A provides this correct height of 269 feet. Other options are incorrect because they result from miscalculations or incorrect substitutions into the equation. For example, using an incorrect value for \( t \) or failing to properly apply the formula leads to heights that do not reflect the physics of the scenario.
To determine the height of the ball 7 seconds after being dropped, substitute \( t = 7 \) into the equation \( f(t) = -16(t)^2 + 1053 \). Calculating this gives \( f(7) = -16(7)^2 + 1053 = -16(49) + 1053 = -784 + 1053 = 269 \) feet. Option A provides this correct height of 269 feet. Other options are incorrect because they result from miscalculations or incorrect substitutions into the equation. For example, using an incorrect value for \( t \) or failing to properly apply the formula leads to heights that do not reflect the physics of the scenario.
On Monday; Alicia buys x shirts at $8 each and y slacks at $25 each. On Wednesday, Alicia returns 2 pairs of slacks. Which expression represents the total value of her purchases?
- A. 8x + 23y
- B. 8x + 25(y - 2)
- C. 8x - 2) + 25y
- D. 8x + 25y - 2
Correct Answer & Rationale
Correct Answer: B
To calculate the total value of Alicia's purchases, we need to account for the cost of shirts and slacks, as well as the return of 2 pairs of slacks. Option B, \(8x + 25(y - 2)\), correctly reflects the initial cost of \(x\) shirts at $8 each and \(y\) slacks at $25 each, while subtracting the cost of the 2 returned slacks, which is \(2 \times 25\). Option A, \(8x + 23y\), incorrectly reduces the price of slacks to $23, which is not stated in the problem. Option C, \(8x - 2 + 25y\), miscalculates by subtracting $2 instead of the cost of the returned slacks. Option D, \(8x + 25y - 2\), also incorrectly subtracts $2 instead of the total cost of the slacks returned.
To calculate the total value of Alicia's purchases, we need to account for the cost of shirts and slacks, as well as the return of 2 pairs of slacks. Option B, \(8x + 25(y - 2)\), correctly reflects the initial cost of \(x\) shirts at $8 each and \(y\) slacks at $25 each, while subtracting the cost of the 2 returned slacks, which is \(2 \times 25\). Option A, \(8x + 23y\), incorrectly reduces the price of slacks to $23, which is not stated in the problem. Option C, \(8x - 2 + 25y\), miscalculates by subtracting $2 instead of the cost of the returned slacks. Option D, \(8x + 25y - 2\), also incorrectly subtracts $2 instead of the total cost of the slacks returned.
What is the volume, in cubic inches, of the pyramid?
- A. 21,600
- B. 1,440
- C. 7,200
- D. 5,760
Correct Answer & Rationale
Correct Answer: C
To find the volume of a pyramid, the formula used is \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \). In this case, with the appropriate base area and height values, the calculation leads to a volume of 7,200 cubic inches. Option A, 21,600, is too high, suggesting an error in calculations or misinterpretation of the dimensions. Option B, 1,440, underestimates the volume, likely due to incorrect base area or height. Option D, 5,760, also falls short, as it does not account for the correct scaling of the dimensions. Thus, 7,200 cubic inches accurately reflects the pyramid's volume based on the given measurements.
To find the volume of a pyramid, the formula used is \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \). In this case, with the appropriate base area and height values, the calculation leads to a volume of 7,200 cubic inches. Option A, 21,600, is too high, suggesting an error in calculations or misinterpretation of the dimensions. Option B, 1,440, underestimates the volume, likely due to incorrect base area or height. Option D, 5,760, also falls short, as it does not account for the correct scaling of the dimensions. Thus, 7,200 cubic inches accurately reflects the pyramid's volume based on the given measurements.