1)Let S be the set of all students at a college. Define a relation on the set S by the rule that two people are related if they live less than 2 miles apart. Is this relation an equivalence relation on S? Justify your answer.

2) Define another relation on the set S from problem 5 by defining two people as related if they have the same classification (freshman, sophomore, junior, senior or graduate student). Is this an equivalence relation on S? Justify.

w much positive and how much negative charge is there in one cup of water (neutral H2O )? Imagine all this positive charge to be concentrated in a point-like particle, and all negative charge in another point-like particle located 250,000 miles away. Note that this is roughly the distance between the Earth and the Moon. By what electrostatic force would these point-like particles attract each other (in vacuum)? What amount of mass would have this weight on Earth?

An automobile manufacturer has given its van a 46.3 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 250 vans, they found a mean MPG of 46.4. Assume the population standard deviation is known to be 2.0. A level of significance of 0.01 will be used. Make the decision to reject or fail to reject the null hypothesis.

Your hospital is considering opening a satellite urgent care center about five miles from your main campus. You have been charged with gathering demographic information that might affect the demand for the center’s services. What data are likely to be relevant? In this forum, list and add All the variables you need, and explain why you need them. Because you are working as a big group, I don't want you to miss anything!

<Vector Calculus>

Please show all step by step work and formulas. Thanks

A current in a river is pushing a ship in a direction of 25 degrees north of east with a speed of 12 knots (nautical miles per hour). There is a 7 knots (kn) wind pushing the ship in a direction 80 degrees south of east. Find the velocity vector of the ship vector of the ship relative to the water if the ship is moving due east at a speed of 40 knots (kn) relative to the ground.

Compare two major foreign policy in the US initiatives in the interwar years (1920s and 1930s) with those that arose in the postwar years (WW2) (Late-1940s, 1950s, and 1960s). Please discuss at least two policy details from each era, and defend their importance

the first category known as the "Great Man" phase, focused on the traits that make an effective leader. this period range from circa 450 B.C. to the 1940s, and includes classic examples such as the aforementioned Egyptian period and the expansive influence of the Roman Empire.

need your help

Listed below is the 48-hour recall for a 72-year-old male who is new to using warfarin. Food or Beverage Item Serving Size Vitamin K (mcg) Day #1 Oatmeal 1 cup 1.2 Whole milk 1 cup 0.5 Orange juice ½ cup 0.1 Tuna salad ½ cup 21.2 Wheat bread 2 slices 1.1 Baby carrots 16 21.1 Roast beef 4 ounces 1.9 Baked potato w/ peel 1 medium 3.5 Butter 2 tsp 0.7 Sour cream 1 Tbsp 0.3 Tomatoes, fresh ½ cup 7.1 Applesauce 1 cup 1.5 Day #2 Special K® 1 cup 0.2 Whole milk 1 cup 0.5 Orange juice 1 cup 0.2 Roast beef 3 ounces 1.4 Wheat bread 2 slices 1.1 Salad greens 1 cup 111.5 Italian dressing 2 Tbsp 16.5 Baked chicken 4 ounces 2.7 Spinach, cooked ½ cup 554 White rice 1 cup 0 Grapes ½ cup 11.7 Q1. Looking the DRI values in the book, what is the recommendation for vitamin K intake? Is he meeting his DRI for vitamin K for Day1? What about vitamin K intake on Day 2? Is he meeting the DRI? Q2. Reading the information on vitamin K intake from the textbook and discussion in the lecture, what advice do you have for him regarding his vitamin K intake over these two days? Also look at the table closely to give specific recommendations about foods consumed. Q 3. Search the Internet for patient education materials on warfarin and vitamin K intake. Are the messages to the patient consistent? Confusing? How do you know the advice is reputable? Summarise what you found and include links for resources you explored.

Tombro Industries is in the process of automating one of its plants and developing a flexible manufacturing system. The company is finding it necessary to make many changes in operating procedures. Progress has been slow, particularly in trying to develop new performance measures for the factory.

In an effort to evaluate performance and determine where improvements can be made, management has gathered the following data relating to activities over the last four months:

The president has read in industry journals that throughput time, MCE, and delivery cycle time are important measures of performance, but no one is sure how they are computed. You have been asked to assist the company, and you have gathered the following data relating to these measures:

Required:

1-a. Compute the throughput time for each month.

1-b. Compute the manufacturing cycle efficiency (MCE) for each month.

1-c. Compute the delivery cycle time for each month.

3-a. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 5 the inspection time, process time, and so forth, are the same as for month 4, except that the company is able to completely eliminate the queue time during production using Lean Production. Compute the new throughput time and MCE.

3-b. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 6 the inspection time, process time, and so forth, are the same as in month 4, except that the company is able to eliminate both the queue time during production and the inspection time using Lean Production. Compute the new throughput time and MCE.

HR Industries (HRI) has a beta of 1.4, while LR Industries's (LRI) beta is 0.8. The risk-free rate is 6%, and the required rate of return on an average stock is 13%. The expected rate of inflation built into rRF falls by 1.5 percentage points; the real risk-free rate remains constant; the required return on the market falls to 10.5%; and all betas remain constant. After all of these changes, what will be the difference in the required returns for HRI and LRI? Round your answer to two decimal places.