Different types of light bulbs use different amounts of electricity. Electricity use is measured in kilowatt hours (kWh). The electricity use per hour (kWh) of an electrical device can be calculated using the following equation:
A 60W light bulb used .48 kilowatt hours of electricity. How long was the light bulb on?
- A. 0.48 hours
- B. 28.8 hours
- C. 0.125 hours
- D. 8 hours
Correct Answer & Rationale
Correct Answer: D
To determine how long the 60W light bulb was on, we first convert the energy used from kilowatt hours to watt hours: 0.48 kWh equals 480 watt hours. Using the formula: time (hours) = energy (watt hours) / power (watts), we calculate: 480 watt hours / 60 watts = 8 hours. Option A (0.48 hours) underestimates the time significantly. Option B (28.8 hours) incorrectly suggests the bulb was on much longer than the energy consumed allows. Option C (0.125 hours) miscalculates by assuming a much higher power consumption. Only option D accurately reflects the time the bulb was on based on the energy used.
To determine how long the 60W light bulb was on, we first convert the energy used from kilowatt hours to watt hours: 0.48 kWh equals 480 watt hours. Using the formula: time (hours) = energy (watt hours) / power (watts), we calculate: 480 watt hours / 60 watts = 8 hours. Option A (0.48 hours) underestimates the time significantly. Option B (28.8 hours) incorrectly suggests the bulb was on much longer than the energy consumed allows. Option C (0.125 hours) miscalculates by assuming a much higher power consumption. Only option D accurately reflects the time the bulb was on based on the energy used.
Other Related Questions
If these results correctly predict the performance of this kneepad design, what is the probability that one of the kneepads will require a force of 145 N or greater to cause failure?
- A. 53%
- B. 22%
- C. 75%
- D. 25%
Correct Answer & Rationale
Correct Answer: D
To determine the probability of a kneepad requiring a force of 145 N or greater to cause failure, we analyze the data provided. The correct option, 25%, indicates that one-fourth of the kneepads are expected to fail under this force, aligning with statistical predictions for this design. Option A (53%) overestimates the likelihood, suggesting more than half will fail, which is not supported by the data. Option B (22%) underestimates the probability, indicating fewer kneepads will fail than expected. Option C (75%) is excessively high, implying a significant majority would fail, which contradicts the predicted performance. Thus, 25% accurately reflects the failure rate at this force threshold.
To determine the probability of a kneepad requiring a force of 145 N or greater to cause failure, we analyze the data provided. The correct option, 25%, indicates that one-fourth of the kneepads are expected to fail under this force, aligning with statistical predictions for this design. Option A (53%) overestimates the likelihood, suggesting more than half will fail, which is not supported by the data. Option B (22%) underestimates the probability, indicating fewer kneepads will fail than expected. Option C (75%) is excessively high, implying a significant majority would fail, which contradicts the predicted performance. Thus, 25% accurately reflects the failure rate at this force threshold.
A scientist studying solubility increased the temperature of a constant volume of water and measured the amount of sugar that dissolved into solution... Which of the following describes the relationship between the independent and dependent variables?
- A. As the amount of dissolved sugar increased, the temperature of the water decreased.
- B. As the water temperature increased, the amount of dissolved sugar increased.
- C. As the amount of dissolved sugar increased, the amount of water remained constant.
- D. As the water temperature increased, the amount of water decreased.
Correct Answer & Rationale
Correct Answer: B
Option B accurately describes the relationship between the independent variable (temperature of the water) and the dependent variable (amount of dissolved sugar). As temperature rises, solubility typically increases, allowing more sugar to dissolve. Option A incorrectly suggests an inverse relationship; higher temperatures do not cause the amount of dissolved sugar to decrease. Option C, while true, does not address the relationship between the two variables in question. Option D incorrectly implies that increasing temperature leads to a decrease in water volume, which is not relevant in this context.
Option B accurately describes the relationship between the independent variable (temperature of the water) and the dependent variable (amount of dissolved sugar). As temperature rises, solubility typically increases, allowing more sugar to dissolve. Option A incorrectly suggests an inverse relationship; higher temperatures do not cause the amount of dissolved sugar to decrease. Option C, while true, does not address the relationship between the two variables in question. Option D incorrectly implies that increasing temperature leads to a decrease in water volume, which is not relevant in this context.
A substance has a mass of 10 grams. This substance has 45 joules of heat added to it, and the change in temperature is 5 degrees. What is the specific heat of the substance? J/gK
Correct Answer & Rationale
Correct Answer: 0.9
To determine the specific heat, we use the formula \( c = \frac{Q}{m \Delta T} \), where \( Q \) is the heat added (45 J), \( m \) is the mass (10 g), and \( \Delta T \) is the temperature change (5 °C). Plugging in the values: \( c = \frac{45 \, \text{J}}{10 \, \text{g} \times 5 \, \text{°C}} = 0.9 \, \text{J/g°C} \). Other options may arise from calculation errors, such as misapplying the formula or using incorrect units. For instance, if one mistakenly divides by a different temperature change or mass, it would yield incorrect specific heat values. Thus, 0.9 J/gK accurately reflects the relationship between heat, mass, and temperature change for this substance.
To determine the specific heat, we use the formula \( c = \frac{Q}{m \Delta T} \), where \( Q \) is the heat added (45 J), \( m \) is the mass (10 g), and \( \Delta T \) is the temperature change (5 °C). Plugging in the values: \( c = \frac{45 \, \text{J}}{10 \, \text{g} \times 5 \, \text{°C}} = 0.9 \, \text{J/g°C} \). Other options may arise from calculation errors, such as misapplying the formula or using incorrect units. For instance, if one mistakenly divides by a different temperature change or mass, it would yield incorrect specific heat values. Thus, 0.9 J/gK accurately reflects the relationship between heat, mass, and temperature change for this substance.
Which statement explains the central idea of the passage?
- A. People should consume as much magnesium as possible to ensure good cardiovascular health.
- B. People may experience health benefits from drinking hard water because it contains magnesium.
- C. People who live in rural environments are healthier than people who live in urban environments.
- D. People should stop the practice of softening water because it removes minerals that are necessary for good health.
Correct Answer & Rationale
Correct Answer: B
Option B accurately reflects the central idea by highlighting the potential health benefits of magnesium found in hard water. This aligns with the passage's focus on the relationship between magnesium intake and cardiovascular health. Option A is misleading as it suggests an excessive intake of magnesium is necessary, while the passage likely emphasizes balance rather than maximum consumption. Option C incorrectly generalizes health comparisons between rural and urban populations without specific evidence from the passage. Option D misrepresents the passage's message by implying a complete cessation of water softening, rather than discussing the importance of maintaining essential minerals like magnesium.
Option B accurately reflects the central idea by highlighting the potential health benefits of magnesium found in hard water. This aligns with the passage's focus on the relationship between magnesium intake and cardiovascular health. Option A is misleading as it suggests an excessive intake of magnesium is necessary, while the passage likely emphasizes balance rather than maximum consumption. Option C incorrectly generalizes health comparisons between rural and urban populations without specific evidence from the passage. Option D misrepresents the passage's message by implying a complete cessation of water softening, rather than discussing the importance of maintaining essential minerals like magnesium.