There are three possible outcomes for a soccer game: {win, loss, draw (tied)}. For a team, their probabilities are as follows: P(Win) = .53 , P(Loss) = .46, P(Draw) = .01 Use the letters W, P, and D or the words to represent Win, Loss, and Draw. Assume games are independent. What is the probability of the team having a win and a loss (P(Win ∩ Loss)) in two games?  Definition: ∩: and Try to show work/steps. You can leave your answer uncalculated if you want, as long as your steps/answer is clear.

Critical Thinking Following a skiing accident your friend Hakeem has no feeling in his skin from his belly button down and he cannot move his legs.  Use the description and the dermatome map below to answer the following questions: 1. Where was Hakeem’s injury?  Explain your answer. (3 pts) 2. Did Hakeem have damage to ascending tracts, descending tracts, or both spinal cord tract types?  Explain your answer. (3 pts) 3. Based on where his damage is, would Hakeem still be able to blink his eyes and smile?  Explain your answer. (2 pts)  

In the previous questions about the book sliding across a table, how far will the book travel before coming to a rest? For reference, it is a 275 g book initially pushed to the right across a table with a speed of 1.3 m/s. Friction exerts a 0.37 N force on the book, slowing it down.  Show your work or explain your reasoning.

If the table below represents the probabilities for all possible outcomes, what is the missing probability P(HIGH BP and NO Heart Disease)? Hint: P(X) + P(NOT X) = 1, or P(NOT X) = 1 – P(X) High Blood Pressure (BP) and  Heart Disease High BP / Heart Disease Heart Disease No Heart Disease High BP .30 ? No High BP .20 .30

A uniform beam of length 1.0 m with mass 91 kg is attached to a wall by a cable, as shown in the figure. The cable is attached at a 30 degree angle with respect to the beam. The beam is free to pivot at the point where it attaches to the wall but at the present moment it is stationary. What is the tension in the cable? Show your work or explain your reasoning.

Two large lead spheres are sitting in a lab. Sphere 1 has a slightly larger mass than Sphere 2. The gravitational force of Sphere 1 on Sphere 2 is [parta] the gravitational force of Sphere 2 on Sphere 1. If they are moved closer to each other, the gravitational force between the spheres will [partb]. If Sphere 1 is modified to increase its mass, the gravitational force between them now will be [partc] than it was originally. You do NOT need to show your work or explain your reasoning for this question.

A species of plant is tetraploid (4N). Another species of plant is diploid (2N). Genetic analysis reveals that the diploid and tetraploid plants have the same genes and chromosomes, but the diploid plants have 2 copies of each chromosome, while the tetraploid plants have 4 copies of each chromosome. Under the biological species definition, should the plants be considered separate species? Answer yes or no, then explain why they should or should not be considered separate species.

A woman has a mass of 59.5 kg. What is her weight on Mars, where the surface gravity (i.e. free fall acceleration) is 3.76 m/s2? Show your work or explain your reasoning.

The tune-up specifications of a car call for the spark plugs to be tightened to a torque of 15 N∙m. You plan to tighten the plugs by pulling on the end of a 11 cm long wrench. Because of the cramped space under the hood, you’ll need to pull at an angle of 60° with respect to the wrench shaft. With what force must you pull? Show your work or explain your reasoning.

Look back at the previous question about the plastic disk spun on an axle by an electric motor. If that disk has a mass of 225 g and has an 18 cm radius, what torque is required from the motor to achieve the angular acceleration you found? The moment of inertia for a disk about center is ½MR2. Show your work or explain your reasoning.