Numerade

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2. The homogeneous gas-phase decomposition of phosphine $$4 PH_3(g) \rightarrow P_4(g) + 6 H_2 (g)$$ proceeds at 649°C with the first-order rate $$-r(PH_3) = (10/h) C_{PH_3}$$ a) What size of plug flow reactor (PFR) operating at 649°C and 460 kPa can produce 80% conversion of a feed consisting of 40 mol/h of pure phosphine? b) What size of plug flow reactor (PFR) operating at 649°C and 11.4 atm is needed for 75% conversion of 10 mol/hr of phosphine in a 2/3 phosphine-1/3 inert feed?

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Problem 1.1 (10 points) Alice wants to securely send Bob an arbitrary number M from the set {0, 1,..., N - L} for some positive integer N. She wants to have a scheme with perfect secrecy. She's heard of the One Time Pad (OTP), but OTP is for bitstrings, not numbers. She decides to use the following scheme. The key space is {0,1,..., N- 1}. A ciphertext C for M is computed as (M + K) mod N and decryption performs (C - K) mod N.Prove that this scheme is perfectly secure. Problem 1.2 (10 points)Your colleague observed that when the all-zeros key is used with One Time Pad scheme, the message is sent in the clear. In addition, when the all-ones key is used with One Time Pad the ciphertext is simply the complement of the message. He decides to remove the all-zeros key and the all-ones key from the key space.Have a convincing argument of why this is not a good idea, without referring to the impossibility result (optimality of the OTP) we studied. You can use the definition of perfect secrecy.Problem 1.3 (10 points) Alice and Bob have a good scheme to use (described in 1.1), but they don't share any secrets. Alice has a deck of cards but lost all of the Aces. So she shuffles the remaining deck of 48 cards and deals them face down to herself and Bob i.e. each of them gets a half. No one else can see what cards they get. In order to send a secret message to Bob, Alice explains to Bob (publicly) how to get the key. This does not involve any further exchange of cards. After that, and without the use of cards, Alice is able to send Bob a message with perfect secrecy.What is the maximum size of N possible for perfect secrecy?

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Which of the following options is designed for long-term consumer credit? Credit Cards Installment accounts Open charge accounts Revolving charge accounts

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a growth curve that is represented by points of deceleration or acceleration is a

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You throw a ball straight up in the air. Which of the following best describes what happens in terms of energy? In the way up, gravitational potential energy does not change, and kinetic energy of the ball decreases. On the way down, gravitational potential energy does not change, and kinetic energy of the ball increases. The total energy increases. In the way up, gravitational potential energy decreases, and kinetic energy of the ball increases. On the way down, gravitational potential energy increases, and kinetic energy of the ball decreases. The total energy remains the same throughout. In the way up, gravitational potential energy increases, and kinetic energy of the ball decreases. On the way down, gravitational potential energy decreases, and kinetic energy of the ball increases. The total energy remains the same throughout. In the way up, gravitational potential energy does not change, and kinetic energy of the ball increases. On the way down, gravitational potential energy does not change, and kinetic energy of the ball decreases. The total energy decreases.

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On June 30, 2022, Past Company (Past) sold some land to its subsidiary, Sloan Ltd. (Sloan), for $380,000. The land had cost Past $200,000 when it was acquired three years previously. The transaction was subject to income tax at a rate of 20%. On April 1, 2024, Sloan sold the land to an outside party for $475,000. This transaction was also subject to income tax at a 20% rate. Past owns 75% of the outstanding shares of Sloan and accounts for its investment using the cost method. On December 31, 2023, the land account balance in the books of Past is $300,000 and in the books of Sloan is $340,000. No acquisition differential was allocated to land. What will be the amount of land in the consolidated balance sheet at December 31, 2023? Multiple Choice $460,000 $820,000. $555,000 $640,000

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9. \int \frac{x dx}{\sqrt{9 - x^2}} = \\ (a) \frac{1}{2}\sqrt{9 - x^2} + C \\ (b) \frac{1}{2}sin^{-1}(x/2) + C \\ (c) -2\sqrt{9 - x^2} + C \\ (d) -\sqrt{9 - x^2} + C \\ (e) None of the above.

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Describe briefly the current economic situation in the USA. Identify two prominent economic factors the USA is currently facing, such as issues, challenges, advances, innovations, etc Please provide resources.

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12. Jill claims that for positive fractions, $\frac{a}{b} + \frac{a}{c} = \frac{a}{b+c}$ because the fractions have a common numerator. How do you respond? Choose the correct answer below. Jill is confusing this problem with adding fraction with like denominators. She should use A. $\frac{a}{b} + \frac{a}{c} = \frac{ac + ab}{bc}$ Jill is confusing adding fractions with common denominators and she should use B. $\frac{a}{b} + \frac{c}{b} = \frac{a+c}{2b}$ C. Jill is correct and $\frac{a}{b} + \frac{a}{c} = \frac{a}{b+c}$ D. Jill is using the wrong formula. She should use $\frac{a}{b} + \frac{a}{c} = \frac{2a}{b+c}$

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Part A A heat engine does 170 J of work per cycle while exhausting 390 J of waste heat. You may want to review (Page). What is the engine's thermal efficiency? Express your answer using two significant figures. ? = %

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