Mathematics Probability Level: Misc Level

During the final exam,the professor answered 35 questions from students (other than,,may I go to the bathroom,,) Obviously, some students asked more than one question, and there may have been some who didn,t ask any.(By the end of the exam,theprofessor couldn,t remember-they may even have all been asked by same student)

Mathematics Probability Level: Misc Level

When preparing for the finalexam, the students decide to form study groups. Six of the students do not want to participate in study groups, so the other 20 students are going to divide themselves into 5 groups of 4.Each group will (separately)study all of the course material together.In how many different ways can the 20 students divide themselves up into the study groups?

Mathematics Probability Level: Misc Level

During the course,19 different students post messages on the discussion boards on the course web site,including exactly 2 of the women.Consider the set of all students who posted discusssions.How many different sets of students are possible?

Mathematics Probability Level: Misc Level

A Committee consists of 8 married couples. In how many ways can a subcommittee of 5 be chosen so that at most one married couple belongs to the subcommittee?

Mathematics Probability Level: Misc Level

Some boys come into a room and sit in a circle.4 girls arrange themselves between 2 boys,The 4 girls sit all together.If 2880 different circles can be formed, How many boys are there?

Physics Circular Motion Level: Misc Level

A certain string breaks when it is subjected to 400 N of tension.A boy uses this string to whirl a 5.0-kg stone in a horizontal circle of radius 5.0 m.The boy continuosly increases the speed of the stone.At approximately what speed will the string break?(multiple choice answers below, but of course,we have to show work)

(a)10, m/s, (b) 20, m/s, (c) 80. m/s, (d)100 m/s (1.0x102 m/s),or (e)400 m/s (4.0xIo2 m/s)

What is the rotaion rate (revolutions per minute (rpm) of the stone just before the string breaks?

(f) 0.050 rpm,(g)0.64 rpm, (h)1.6 rpm, (i)38rpm,or (j)60rpm

Physics Force & Laws Of Motion Level: Misc Level

A block of wood is sliding down a plane which is inclined 50.0. with respect to the ground. The coefficient of kinetic friction between the block of wood and the inclined plane is 0.125.Find the acceleration of the block.

Physics Force & Laws Of Motion Level: Misc Level

The ball in the figure (below) is supported by the two (massless) cables.You are told that the weight of the ball is 175 N.What are the tensions in cable 1 and cable 2?With the information given to you,do the tensions depend on whether or not this problem is being solved on Earth or Zarkon? Assuming that this situation is on Zarkon,what is the mass of the ball?

Physics Gravitation Level: Misc Level

At some point in the future, after the Earth olympics, the milky way olympics are held on the planet zarkon.(zarkon is inhabited by folks who like to think up physics questions.) This planet has a mass that is 0.100 that of the Earth, and a radius that is 0.500 that of the Earth.zarkon also has a little moon Abba (that is rumored to be populated by retired swedish rock stars).Abba hasa mass which is 0.010 that of zarkon,and a radius which is 0.20 that of zarkon.what is the acceleration of gravity (9 abba ) at the surface of Abba?

Physics Kinematics Level: Misc Level

An olympic shot putter is doing his thing; His shotput ball, with a mass of 6.00 kg,Iands 20.0 meters from where he launched it at a 45.0 degree angle.Assuming he accelerated the shot uniformly for 0.4000 seconds, and neglecting the acceleration distance and any height difference between launch and landing (both not quite truei)with how much force did he ,,put,,the shot?

Physics Kinematics Level: Misc Level

In the metric drag races (a previously -unreported olympic event),the hottest cars cross the finish line at speeds of 100 m/s.Assuming these cars accelerate uniformly and continuously,what is the magnitude of their average acceleration if the drag track is 400 meters long?

Physics Kinematics Level: Misc Level

In the Olympic trials,winner of the first heat takes 42 seconds to run the 400 meter sprint.This race completes one lap around the track (assumed to be exactly 400m in circumference), and the finish line is located at the same point on the track where the sprinters began their race.What was the average velocity of the race winner?

Physics Kinematics Level: Misc Level

Some students have gone to visit Valley of Fire State park to study rock formations.They park their car and then begin walking to various interesting areas.First, they walk northeast (45%0 north of east) for 900.meters.Then,they walk 1.200 km in a direction 50.%0 north of west.Finally, they walk 0.700 km in a direction 30.0 south of west and then set up camp for the night.It took two hours for the students to walk from their car to their camp.

A How far is camp from the car (distance and direction (with respect to north)?

B What was the students, average speed between the car and camp?

C What was the students, average velocity between the car and camp?

Mathematics Algebra Level: Misc Level

Let f(x)=ex for -2<x< 3. Use a Riemann sum with n=5 subintervals and sample points the midpoints of the intervals to estimate the area A between the graph of f and the x-axis.The answer that best describes the estimate is

a.A=19.950

b.A=11.611

c.A=19.143

d.A=31.561

e.None of the other choices is the required Riemann sum

Mathematics Calculus Level: Misc Level

Let f (x)=/x for 1<x <7.Use a Riemann sum withn=6 subintervals and sample points the midpoints of the intervals to estimate the area A between the graph of f and the x-axis. The answer that best describes the estimate is

a. A=13.478

b.A=15.306

c.A=11.680

d.A =11.693

E.None of the other choices is the required Riemann sum