When a vertical beam of light passes through a transparent medium, the rate at which its intensity I decreases is proportional to I(t), where t represents the thickness of the medium (in feet). In clear seawater, the intensity 3 feet below the surface is 25% of the initial intensity I0 of the incident beam. What is the intensity of the beam 12 feet below the surface

Aplaintiff filed a civil action based on negligence against a defendant in federal district court, alleging that the defendant negligently ran a red light at an intersection and collided with the plaintiff's vehicle, causing the plaintiff's injuries. a week after the close of discovery, the plaintiff filed a motion for summary judgment on the issue of whether the defendant was negligent. with the motion, the plaintiff filed (i) his own sworn affidavit, which stated that the traffic signal was green as he entered the intersection, (ii) an affidavit of a witness who was driving the car behind him, which stated that the witness saw the entire incident and that the plaintiff's traffic signal was green as he approached and entered the intersection; and (iii) an affidavit of another witness, which stated that she saw the entire incident and that the defendant's signal had been red for several seconds before the defendant entered the intersection and was still red when the defendant entered the intersection. the defendant filed a response to the motion, noting that her answer denied negligence and further denied that her traffic signal was red, and argued that the issue of negligence and the issue of whether her traffic signal was red were in dispute, so those issues should be tried to a jury. how should the court rule on the plaintiff's motion?

What is the rule relating the ratio of marginal utility to prices of two goods at the optimal choice? explain why, if this rule does not hold, the choice cannot be utility-maximizing.

When individuals with a stake in an issue affecting them begin to propose and develop solutions to a problem, they engage in