A rigid tank of volume 0.3 m³ contains water initially at its critical point. The water is now cooled to 150°C

a) What mass of water is in the tank?

b) Has the average specific volume of this water changed during the cooling process?

c) Find the mass of liquid water and the mass of water vapor in the tankat the end of the process.

d) Find the volume of liquid water and the volume of water vapor in the tank at the end of the process.

e)Find the quality of the final mixture. Is it meaningful to talk about the quality of the water at the initial state of this process? Why or why not?

f) Find the enthalpy change of the water in the tank.

1A) A 0.3-kg block, attached to a spring, executes simple harmonic motion according to x = 0.08 cos (35 rad/s⋅t), where x is in meters and t is in seconds. Find the total energy of the spring-mass system.

Ans.E =1.18 J

1B) A 1.5-kg cart attached to an ideal spring with a force constant (spring constant) of 20 N/m oscillates on a horizontal, frictionless track. At time t = 0.00 s, the cart is released from rest at position x = 10 cm from the equilibrium point. Find the position of the cart and its velocity at t = 5.0 s

Ans. x=8.25 cm

A polytropic process (n= 1.25) compresses air from 0.3 m³ at 22 ⁰C and pressure of 125 kPa to   0.15 m³. It is then expanded at constant temperature to its original volume.

1. Sketch the P-V diagram                                                                                       [1 mark] Determine the;
2. Mass of air                                                                                                          [2 marks]     
3. Pressure at the end of the compression                                                           [2 marks]
4. Final Temperature                                                                                             [2 marks]
5. Net work                                                                                                            [4 marks]
6. Net heat transfer                                                                                               [4 marks]

LetXbe a discrete random variable with the following PMF:

P(X=x) =

0.3 for x = 1,

a for x = 2,

0.5 for x= 3,

0 otherwise

(a) Find the value of a.

(b) Find Fx(x), the CDF of X.

(c) What is the value of Fx(2)?

(d) Find E[X].

(e) FindE[X^2].

(f) Find V ar(X)

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A certain area of the eastern United States is, on average,hit by 2 hurricanes a year. Find the probability that the area will be hit byexactly 3 hurricanes in a given year.

32. Every day, Jorge buys a lottery ticket. Each ticket has a probability of 0.3 of winning a prize. After seven days, what is the probability that Jorge has won at least one prize? Round your answer to four decimal places.

26. Charles has seven songs on a playlist. Each song is by a different artist. The artists are Shania Twain, Nick Carter, Aaron Carter, Joey McIntyre, Phil Collins, Shakira, and Michael Jackson. He programs his player to play the songs in a random order, without repetition. What is the probability that the first song is by Nick Carter and the second song is by Joey McIntyre? Write your answer as a fraction or a decimal, rounded to four decimal places.

25. An unfair coin has probability 0.3 of landing heads. The coin is tossed seven times. What is the probability that it lands heads at least once? Round the answer to four decimal places.

21. Let A and B be events with =PA0.7 and =PB0.5. Assume that A and B are independent. Find PA and B.

A heavy rope, 40 feet long, weighs 0.3 lb/ft and hangs over the edge of a building 110 feet high. Let x be the distance in feet below the top of the building.
Find the work required to pull the entire rope up to the top of the building.

1. Draw a sketch of the situation.
We can look at this problem two different ways. In either case, we will start by thinking of approximating the amount of work done by using Riemann sums. First, let’s imagine “constant force changing distance.”

2. Imagine chopping the rope up into n pieces of length ∆x. How much does each little
piece weigh? (This is the force on that piece of rope. It should be the SAME for each
piece of rope.)
3. How far does the piece of the rope located at xi have to travel to get to the top of the
building? (Notice that this is DIFFERENT for each piece of rope; it depends on the
location of the piece.)
4. How much work is done (approximately) to move one piece of rope to the top of the
building?
5. Find the amount of work required to pull the entire rope to the top of the building,
using an integral.

Now, let’s do the same problem, but this time, imagining “constant distance, changing force.” Imagine pulling up the rope a little bit at a time, say, we pull up ∆x feet of rope with each pull.
6. After you have pulled up xi feet of rope, how much of the rope remains to be pulled?
7. What is the force on the remaining amount of rope?
8. Remembering that each pull moves the rope ∆x feet, how much work is done for each
pull?
9. Find the amount of work required to pull the entire rope to the top of the building,
using an integral.

Help 6 to 9 and write it in order with number.

1. Given  P(A) = 0.3 and P(B) = 0.2, do the following. (For each answer, enter a number.)

(a) If A and B are mutually exclusive events, compute P(A or B).

(b) If P(A and B) = 0.3, compute P(A or B).

2. Given P(A) = 0.8 and P(B) = 0.4, do the following. (For each answer, enter a number.)

(a) If A and B are independent events, compute P(A and B).

(b) If P(A | B) = 0.1, compute P(A and B).

3.  The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck.

You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second.

(a) Are the outcomes on the two cards independent? Why?

No. The probability of drawing a specific second card depends on the identity of the first card.

Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.   

No. The events cannot occur together.

Yes. The events can occur together.

(b)Find P(ace on 1st card and nine on 2nd). (Enter your answer as a fraction.)

(c) Find P(nine on 1st card and ace on 2nd). (Enter your answer as a fraction.)

(d) Find the probability of drawing an ace and a nine in either order. (Enter your answer as a fraction.)

4.  

You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck.

(a)Are the outcomes on the two cards independent? Why?

Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.

Yes. The events can occur together.    

No. The events cannot occur together.

No. The probability of drawing a specific second card depends on the identity of the first card.

(b) Find P(ace on 1st card and king on 2nd). (Enter your answer as a fraction.)

(c)  Find P (king on 1st card and ace on 2nd). (Enter your answer as a fraction.)

(d)Find the probability of drawing an ace and a king in either order. (Enter your answer as a fraction.)

1. Using the equation for the Hardy-Weinberg Equilibrium, calculate the following for p=0.7 and q=0.3 and enter in the ratios for the following values.
a. homozygous dominants

b. homozygous recessives|

c. heterozygotes

d. dominant phenotype

2.

Blank 1: Which kind of selection, directional, stabilizing, or disruptive, occurred when beads representing homozygous recessives were removed in the evolution lab?

Blank 2: What kind of selective agent or selective pressure could this activity have imitated?

Question 4 options:

Thank you for your time and help.

7. Consider the following scenario:

• Let P(C) = 0.2

• Let P(D) = 0.3

• Let P(C | D) = 0.4

• Part (a)
  Find P(C AND D).

• Part (b)
  Are C and D mutually exclusive? Why or why not?C and D are not mutually exclusive because
  P(C) + P(D) ≠ 1
  .C and D are mutually exclusive because they have different probabilities. C and D are not mutually exclusive because
  P(C AND D) ≠ 0
  .There is not enough information to determine if C and D are mutually exclusive.

• Part (c)
  Are C and D independent events? Why or why not?The events are not independent because the sum of the events is less than 1.The events are not independent because
  P(C) × P(D) ≠ P(C | D)
  . The events are not independent because
  P(C | D) ≠ P(C)
  .The events are independent because they are mutually exclusive.

• Part (d)
  Find P(D | C).

8. G and H are mutually exclusive events.

• P(G) = 0.5

• P(H) = 0.3

• Part (a)
  Explain why the following statement MUST be false:
  P(H | G) = 0.4.
  The events are mutually exclusive, which means they can be added together, and the sum is not 0.4.The statement is false because P(H | G) =

• = 0.6. To find conditional probability, divide
  P(G AND H) by P(H)
  , which gives 0.5.The events are mutually exclusive, which makes
  P(H AND G) = 0
  ; therefore,
  P(H | G) = 0.

• Part (b)
  Find
  P(H OR G).

• Part (c)
  Are G and H independent or dependent events? Explain

• G and H are dependent events because they are mutually exclusive.

• G and H are dependent events because

• P(G OR H) ≠ 1.

• G and H are independent events because they are mutually exclusive.

• There is not enough information to determine if G and H are independent or dependent events.

9.

Approximately 281,000,000 people over age five live in the United States. Of these people, 55,000,000 speak a language other than English at home. Of those who speak another language at home, 62.3 percent speak Spanish.

• E = speaks English at home

• E' = speaks another language at home

• S = speaks Spanish at home

Finish each probability statement by matching the correct answer.

• Part (a)
  P(E' )
  = ---Select--- 0.1219 0.1957 0.6230 0.8043

• Part (b)
  P(E)
  = ---Select--- 0.1219 0.1957 0.6230 0.8043

• Part (c)
  P(S and E' )
  = ---Select--- 0.1219 0.1957 0.6230 0.8043

• Part (d)
  P(S | E' )
  = ---Select--- 0.1219 0.1957 0.6230 0.8043

Calculate the pH during titration of 25 mL of 0.175 M HCN with 0.3 M NaOH after the addition of 0 mL, 7.29mL, 14.5833 mL, and 20 mL base. Kb of CN- is 2.03 x 10^-5. Show all work.