A kneepad manufacturer tested a new kneepad design for use in industrial settings. In order to be rated for the intended use, the kneepads each needed to withstand a force of 100 newtons (N) on the outside of the kneepad without distorting the inside by more than 5 millimeters. During testing, the force on each kneepad was steadily increased until the kneepad failed. The table shows the manufacturer's results from testing 100 of the kneepads.
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.
Other Related Questions
Two people are standing at the edge of a high cliff. One person throws a rock horizontally off the cliff. Which uncontrolled part of this investigation can prevent the rocks from hitting the ground at the same time?
- A. gravity
- B. mass of the rocks
- C. air resistance
- D. strength of the person
Correct Answer & Rationale
Correct Answer: C
When a rock is thrown horizontally, it is influenced by both gravity and air resistance. Gravity acts equally on both rocks, ensuring they fall at the same rate. The mass of the rocks does not affect the time it takes to hit the ground in a vacuum, as all objects fall at the same rate regardless of mass. The strength of the person throwing the rock only affects the initial horizontal velocity, not the fall time. However, air resistance can vary based on the shape and size of the rocks, potentially causing differences in descent time. Thus, air resistance is the uncontrolled factor that can prevent the rocks from hitting the ground simultaneously.
When a rock is thrown horizontally, it is influenced by both gravity and air resistance. Gravity acts equally on both rocks, ensuring they fall at the same rate. The mass of the rocks does not affect the time it takes to hit the ground in a vacuum, as all objects fall at the same rate regardless of mass. The strength of the person throwing the rock only affects the initial horizontal velocity, not the fall time. However, air resistance can vary based on the shape and size of the rocks, potentially causing differences in descent time. Thus, air resistance is the uncontrolled factor that can prevent the rocks from hitting the ground simultaneously.
Which hypothesis was Dilger testing in his experiment?
- A. If hybrid offspring have a mixture of behaviors, then the species are within the same genus.
- B. If a hybrid offspring carries nesting material in its beak, then it is more closely related to modern lovebirds.
- C. If behavior in lovebirds is genetic, then a hybrid offspring will display a mixture of behaviors.
- D. If lovebird species can interbreed, then a hybrid offspring will have a mixture of behaviors.
Correct Answer & Rationale
Correct Answer: C
Dilger aimed to investigate the genetic basis of behavior in lovebirds, specifically focusing on whether hybrid offspring exhibit a blend of behaviors from their parent species. Option C accurately reflects this hypothesis, linking genetic inheritance to behavioral traits in hybrids. Option A incorrectly connects hybrid behavior to taxonomic classification, which is not the primary focus of Dilger’s study. Option B suggests a direct relationship between nesting material behavior and modern lovebirds, overlooking the broader genetic implications. Option D, while related to interbreeding, does not emphasize the genetic aspect of behavior, which is central to Dilger's hypothesis.
Dilger aimed to investigate the genetic basis of behavior in lovebirds, specifically focusing on whether hybrid offspring exhibit a blend of behaviors from their parent species. Option C accurately reflects this hypothesis, linking genetic inheritance to behavioral traits in hybrids. Option A incorrectly connects hybrid behavior to taxonomic classification, which is not the primary focus of Dilger’s study. Option B suggests a direct relationship between nesting material behavior and modern lovebirds, overlooking the broader genetic implications. Option D, while related to interbreeding, does not emphasize the genetic aspect of behavior, which is central to Dilger's hypothesis.
Based on these results and assuming that whenever two materials are present their remaining energy is averaged, what would the scientist best conclude to be the composition of Saturn's rings?
- A. equal amounts of loose rocks and loose snow
- B. equal amounts of ice and bedrock
- C. a small amount of bedrock and a large amount of carbon rock
- D. large amounts of ice and smaller amounts of carbon rock
Correct Answer & Rationale
Correct Answer: D
The conclusion about Saturn's rings is supported by the composition of ice and carbon rock. Large amounts of ice are consistent with observations of Saturn’s rings, which are primarily composed of water ice particles. Smaller amounts of carbon rock align with the presence of darker materials found in the rings. Options A and B suggest equal amounts of materials that do not reflect the observed predominance of ice. Option C overestimates the presence of bedrock, which is not supported by scientific data. Thus, option D accurately captures the dominant composition of Saturn's rings.
The conclusion about Saturn's rings is supported by the composition of ice and carbon rock. Large amounts of ice are consistent with observations of Saturn’s rings, which are primarily composed of water ice particles. Smaller amounts of carbon rock align with the presence of darker materials found in the rings. Options A and B suggest equal amounts of materials that do not reflect the observed predominance of ice. Option C overestimates the presence of bedrock, which is not supported by scientific data. Thus, option D accurately captures the dominant composition of Saturn's rings.
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.