(a) An elevator of mass m moving upward has two forces acting on it: the upward force of tension in the cable and the downward force due to gravity. When the elevator is accelerating upward, which is greater, T or w?

(b) When the elevator is moving at a constant velocity upward, which is greater, T or w?

(c) When the elevator is moving upward, but the acceleration is downward, which is greater, T or w?

(d) Let the elevator have a mass of 1,575 kg and an upward acceleration of 2.5 m/s². Find T.
-Is your answer consistent with the answer to part (a)?

(e) The elevator of part (d) now moves with constant upward velocity of 10 m/s. Find T.
-Is your answer consistent with your answer to part (b)?

(f) Having initially moved upward with a constant velocity, the elevator begins to accelerate downward at 1.30 m/s². Find T.
-Is your answer consistent with your answer to part (c)?

A 1000-kg elevator is moving downwards in a skyscraper, with constant velocity. The elevator moves a total distance of 400 m. What is the work done on the elevator cage by the tension of the suspension cable? Take g=9.81 m/s².

Two players A and B play a game of dice . They roll a pair of dice alternately . The player who rolls 7 first wins . If A starts then find the probability of B winning the game ?

Let’s see what happens when Let’s Make a Deal is played with four doors.
A prize is hidden behind one of the four doors. Then the contestant picks
a door. Next, the host opens an unpicked door that has no prize behind
it. The contestant is allowed to stick with their original door or to switch
to one of the two unopened, unpicked doors. The contestant wins if their
final choice is the door hiding the prize.

Let’s make the same assumptions as in the original problem:

(a) The prize is equally likely to be behind each door.
(b) The contestant is equally likely to pick each door initially, regardless
of the prize’s location.
(c) The host is equally likely to reveal each door that does not conceal
the prize and was not selected by the player.

Find the following probabilities. If the tree diagram is too large, you can
draw just enough of it for the structure to be clear.

(a) Contestant Stu stays with his original door. What is the probability
that Stu wins the prize?

(b) Contestant Zelda switches to one of the remaining two doors with
equal probability. What is the probability that Zelda wins the prize?

Now let’s revise our assumptions about how contestants choose doors. Say
the doors are labeled A, B, C, and D. Suppose that the host always opens
the earliest door possible (the door whose label is earliest in the alphabet)
with the restriction that the host can neither reveal the prize nor open the
door that the player picked. This gives contestant Priscilla just a little
more information about the location of the prize. Suppose that Priscilla
always switches to the earliest door, excluding her initial pick and the one
the host opened.

(c) What is the probability that Priscilla wins the prize?

Give complete solutions for each of the following problems. All answers must contain the appropriate number of significant figures and the units must be given.

1) You take an elevator from the ground floor to the top of the Empire State Building, a building 102 stories high.

a) What is the work done on you by gravity? (Assume that your mass is 84.0 kg and that the height of the Empire State building is 300 m.)

b) Estimate the amount of work the normal force of the floor did on you.

c) If it takes two minutes to ride the elevator to the top, estimate the average power of the force of gravity.

A sports researcher is interested in determining if there is a relationship between the number of home wins depends on the sport. A random sample of 200 games is selected and the results are given below.

Football Basketball Soccer Baseball

Home team wins 30 20 15 35

Visiting team wins 20 30 35 15

What is the test statistic value for the above data?

A 4

B 10

C 20

D None of the above

In sports​ betting, sports books establish winning margins for a team that is favored to win a game. An individual can place a wager on the game and will win if the team bet upon wins after accounting for this spread. For​ example, if Team A is favored by 5​ points, and wins the game by 7​ points, then a bet on Team A is a winning bet.​ However, if Team A wins the game by only 3​ points, then a bet on Team A is a losing bet. Suppose that in​ games, the margin of victory for the favored team relative to the spread is approximately normally distributed with a mean of −1

point and a standard deviation of 11.4 points.

​(b) What is the probability that the favored team loses by 22 or more points relative to the​ spread?

A gas sample is confined within a chamber that has a movable piston. A small load is placed on the piston; and the system is allowed to reach equilibrium. If the total weight of the piston and load is 70.0 N and the piston has an area of 5.0*10^-4 ,m^2 what is the pressure exerted on the piston by the gas.

Note: Atmospheric pressure is 1.013*10^5 Pa

Draw a block diagram of an elevator controller. Clearly identify inputs and outputs of each block. Assume the elevator has 4 floors. Draw a state diagram for the elevator controller and briefly explain what the input, state variables, and ouput represent.

1. XYZ Manufacturing Company buys 50 tons of coal per month. The price of 50 tons of coal can vary from month to month according to the table shown below:

How much should XYZ budget for coal in 2020? Your answer should be an integer.

2.

Replacement times for computer displays players are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years.

If you want to provide a warranty so that only 2% of the computer displays will be replaced before the warranty expires, what is the time length of the warranty? Include 1 decimal place in your answer.

3. The amount of time a person waits for an elevator in a building is known to follow a uniform distribution between 0 and 60 seconds. What is the expected value of the wait time for an elevator? Your answer should be an integer. What is the probability that a person will wait between 20 and 35 seconds? Include 2 decimal laces in your answer.