You are going up an elevator to reach the top of the Stratosphere casino in Las Vegas. The elevator has a mass of 900 kg. It initially starts accelerates, while moving upwards with an initial velocity of 10 m/s until it comes to rest at a height of 40 m. You have a mass of 50 kg.
a) Draw two FBD one of the elevator and one of you in the elevator. [4 points]
b) Determine the Tension force of the cable on the elevator. [6 points]
c) Determine the magnitude of the normal force you feel from the elevator [2 points]
d) Is the normal force the same as your weight? Why or why not

Suppose an elevator is controlled by two commands: ↑ to move the elevator up one floor and ↓ to move the elevator down one floor. Assume that the building is arbitrarily tall and that the elevator starts at floor x.

A)Write an LL(1) grammar that generates arbitrary command sequences that (1) never cause the elevator to go below floor x and (2) always return the elevator to floor x at the end of the sequence. For example, ↑↑↓↓ and ↑↓↑↓ are valid command sequences, but ↑↓↓↑ and ↑↓↓ are not. For convenience, you may consider a null sequence as valid.

B)Prove that your grammar is LL(1) (you need to provide the first, follow, and predict sets, as well as the complete parse table).

Sale amounts during lunch hour at a local subway are normally ditributed, with a mean $ 8.35, and a standard deviation og $ 1.1. a. Find the probability that a randomly selected sale was at least $ 9.42? b. A particular sale was $ 10.28. What is the percentile rank for this sale amount? % c. Give the sale amount that is the cutoff for the highest 72 %? d.What is the probability that a randomly selected sale is between $5.00 and $8.00? e. What sale amount represents the cutoff for the middle 34 percent of sales? ( The smaller number here)(Bigger number here)

5) In the MegaMillions lottery a player buys a $1 ticket and picks five numbers from the numbers 1 to 70. The lottery has a bin with seventy white balls, each with a number from 1 to 70. The lottery picks five balls from the bin with the white balls. If the five numbers the player picked match the numbers drawn on the five white balls then the player wins $1,000,000 (in most states, but not including California, where the rules are different). In addition, the player picks one Mega number from the numbers 1 to 25. The lottery has a bin with twenty-five gold balls, each with a number from 1 to 25. The lottery picks one gold ball from the bin. If the player matches all five numbers on the white balls, plus the number on the gold ball, the player wins the MegaMillions jackpot (which is a minimum of $40 million). Assume you buy your ticket outside of California. Calculate the exact probability of winning exactly $1,000,000 (no more and no less) in the MegaMillions lottery if you buy one ticket. Include 11 decimal points in your answer. In order to earn the extra credit you must show your work. Hint: Use the Multiplication Law for Independent Events.

Consider the discrete Bertrand game. According to the rules of this game each student selects a number from the set {0,1,2, 3, 4, 5, 6, 7, 8, 9, 10} and is randomly matched with another student. Whoever has the lowest number wins that amount in dollars and whoever has the high number wins zero. In the event of ties, each student receives half their number in dollars. What number would you select if you played this game? Explain your reasoning.

Suppose a single good is being sold in a sealed-bid auction (no bidder can observe the bids of other bidders). The rules of the auction are such that the person who bids the highest value for the good wins, but the winner only has to pay the value of the second-highest bid submitted.

Assume that there are three people bidding for the good (?=1,2,3), and each values the good according to:

• ?1=$12
• ?2=$16
• ?3=$3

where ??v_i is the maximum willingness to pay for the good for player ?i.

What is the Nash equilibrium bid for each player? Who will win the auction? How much will the winner pay?

Alice, Bob, and Charlie are rolling a fair die in that order. They keep rolling until one of them rolls a 6.

What is the probability that each of them wins?

The space elevator project is an effort that intends to place an elevator system grounded on the Earth into geosynchronous orbit. Carbon nanotubes are the only material strong enough to make this elevator. What is it about carbon nanotubes that make people think this way? Do you think a space elevator is possible? What are some potential issues?

A 500 kg elevator accelerates upward at 1.9 m/s2 for 20 m, starting from rest.

a) How much work does gravity do on the elevator?

b) How much work does the tension in the elevator cable do on the elevator?

c) What is the elevator’s kinetic energy after traveling 20 m?

Homework #6

which of the following values cannot be probabilities of events.

select all that apply.

15, 0.94, -0.59, 1.58, 53, 0.0, -27, 1.0

#3.
In a group of people, some are in favor of a tax increase on rich people to reduce the federal deficit and others are against it. (Assume that there is no other outcome such as "no opinion" and "do not know.") There persons are selected at random from this group and their opinions in favor or against raising such taxes are noted. How many total outcomes are possible?

#4. Show outcomes and classify events are simple and compound.

An automated teller machine at a local bank is stocked with $10 and $20 bills. when a customer withdraws $40 from the machine, it dispenses either two $20 bills or four $10 bills

Let T= the ATM dispenses two $20 bills.
Let F= the ATM dispenses four $10 bills.
Two customers withdraw $40 each

Part 1.

How many outcomes are there?

#5. A hat contains 33 marbles. Of them, 18 are red and 15 are green. If one marble is randomly selected out of this hat, what is the probability that this marble is green?

Round your answer to two decimal places.

P(A)=

#6. A regular, six-sided die is rolled once .

Round your answers to four decimal places.

(a) What is the probability that a number less than 4 is obtained?

P( a number less than 4 is obtained)=

(b) what is the probability that a number 3 to 6 is obtained?

P( a number 3 to 6 is obtained)=

#7. A random sample of 1498 adults showed that 812 of them have shopped at least once on the internet. What is the (approximate) probability that a randomly selected adult has shopped on the internet.

Round your answer to three decimal places.

#8 Out of the 3572 families who live in an apartment complex in New York City, 623 paid no income tax last year. What is the probability that a randomly selected family from these 3572 families paid income tax last year?

Round your answer to three decimal places.

#9. A television game show has a game called the shell game. The game has six shells, and one of those six shells has a ball under it. The contestant chooses one shell. If this shell contains the ball, the contestant wins. If a contestant chooses one shell randomly, what is the probability of each of the following outcomes.

(a) contestant wins?

Round your answer to two decimal places.

P( the contestant wins)=

(b) contestant loses

Round your answer to two decimal places.

P( the contestant loses)

Do these two probabilities add up to 1.0?

#10. In a large city, 15,000 workers lost their job last year. Of them, 7900 lost their jobs because their companies closed down or moved, 4200 lost their jobs due to insufficient work, and the remainder lost their jobs because their position were abolished.

(a) If one of these 15,000 workers is selected at random, find the probability that this worker lost his or her job because the company closed down or moved.

The Probability is=

(b) If one of these 15,000 workers is selected at random, find the probability that this worker lost his or her job due to insufficient work.

The probability is=

(c) If one of these workers is selected at random, find the probability that this worker lost his or her job because the position was abolished.

The Probability is=

Do these probabilities add up to 1.0?