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.

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.

A mass of 0.3 kg hangs motionless from a vertical spring whose length is 1.05 m and whose unstretched length is 0.40 m. Next the mass is pulled down to where the spring has a length of 1.30 m and given an initial speed upwards of 1.9 m/s. What is the maximum length of the spring during the motion that follows?

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Question 1 1 pts

Calculate the molarity of 2.45 mol CaCl₂ in 0.3 L solution.

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Question 2 1 pts

What are the products of this acid-base reaction: HI(aq) + Ba(OH)₂(aq)?

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Question 3 1 pts

Write the complete ionic equation for: Pb(NO₃)₂(aq) + 2KCl(aq) -->PbCl₂(s) + 2KNO₃(aq)

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Question 4 1 pts

What is the molarity of CO₃^2- in 0.24 M Al₂(CO₃)₃?

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Question 5 1 pts

If 430 mL of a 5.5 M glucose solution is diluted to 1500 mL, what is the molarity of the diluted solution?

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Question 6 1 pts

To what volume would you dilute 35 mL of a 9.5 M stock HCl solution to obtain a 1.4 M HCl solution?

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Question 7 1 pts

What volume of 2.5 M glucose solution contains 0.78 mols of glucose?

A mass of 0.3 kg hangs motionless from a vertical spring whose length is 0.88 m and whose unstretched length is 0.48 m. Next the mass is pulled down to where the spring has a length of 1.08 m and given an initial speed upwards of 1.9 m/s. What is the maximum length of the spring during the motion that follows?

use a matlab built-in function to numerically solve:

dy/dx= -x^2+((x^3*e^-y)/4) for 1<=x<=5 with y(1)=1

plot the solution