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The reaction of tert-butyl chloride, (CH3)3CCl, with water in an inert solvent gives tert-butyl alcohol, (CH3)3COH. What is the effect of doubling the concentration of water on the rate of the reaction? Group of answer choices the rate increases by a factor of 2 the rate increases by a factor of 4 the rate decreases by a factor of 2 the rate remains the same

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Suppose a slide similar to Der Stuka is 38.3 meters high, but is a straight slope, inclined at 45° with respect to the horizontal. (a) Find the speed of a 51.2 kg thrill seeker at the bottom of the slide, assuming no friction. (b) If the thrill seeker has a speed of 22.4 m/s at the bottom, find the change in mechanical energy due to friction. (c) Find the magnitude of the force of friction, assumed constant.

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Compute $2^{121} \pmod{231}$. Arrange the steps given below in the correct order. $2^{121} \pmod{231} = 2$ by Chinese Remainder Theorem. Since 3, 7 and 11 are pairwise relatively prime and $231 = 3 \cdot 7 \cdot 11$, we can write the following: Then we have $\bullet \quad 2^{121} \equiv 2^{1} \cdot 2^{120} \equiv 2 \cdot 1 \equiv 2 \pmod 3$ $\bullet \quad 2^{121} \equiv 2^{1} \cdot 2^{120} \equiv 2 \cdot 1 \equiv 2 \pmod 7$ $\bullet \quad 2^{121} \equiv 2^{1} \cdot 2^{120} \equiv 2 \cdot 1 \equiv 2 \pmod {11}$ $\bullet \quad 2^2 \equiv 1 \pmod 3$ $\bullet \quad 2^6 \equiv 1 \pmod 7$ $\bullet \quad 2^{10} \equiv 1 \pmod {11}$ $\bullet \quad 2^{120} \equiv (2^2)^{60} \equiv 1^{60} \equiv 1 \pmod 3$ $\bullet \quad 2^{120} \equiv (2^6)^{20} \equiv 1^{20} \equiv 1 \pmod 7$ $\bullet \quad 2^{120} \equiv (2^{10})^{12} \equiv 1^{12} \equiv 1 \pmod {11}$ Since 2, 3, and 7 are prime numbers none of which divides 2, we can write the following by Fermat's Little Theorem: Hence, we can write the following congruences:

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A student bought a calculator and a textbook for a course in algebra. He told his friend that the total cost was $170 (without tax) and that the calculator cost $20 more than twice the cost of the textbook. What was the cost of each item? Let $x$ = the cost of a calculator and $y$ = the cost of the textbook. The corresponding modeling system is \begin{cases} x + y = 170 \\ x = 2y + 20 \end{cases}. Solve the system by using the method of substitution.

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Question 5 CLO 2.2/8 marks A. Cloud computing is the practice of using a network of remote servers hosted on the internet. Therefore, your data is going to be with the cloud provider's system A.1 If your company is dealing with sensitive data, what you need to do to use the cloud- based backup securely? Explain that. A.2 Your company now is using cloud-based backup, what you need to do to guard against ransomware attack? Explain that. A3 If you restore the backup from the cloud and noticed that the restored data are encrypted by a ransomware. What you need to do to restore your data? B.1 What technology you may use to establish secure communication with a system in the cloud over the insecure channel (Internet)? Jackade B.2 What are the two configuration types of this technology?

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Equilibrium price P* and quantity Q* in this market are calculated as follows: First, set the inverse supply equal to the inverse demand: (1/20)QS = 45 – (1/10)QD Then, solve for QS and QD: QS = 900 - (1/2)QD Now, set QS equal to QD to find the equilibrium quantity: 900 - (1/2)QD = QD 900 = (3/2)QD QD = 600 Finally, plug QD back into the inverse demand equation to find the equilibrium price: P* = 45 - (1/10)(600) P* = 45 - 60 P* = -15 Therefore, the equilibrium price P* is -15 and the equilibrium quantity Q* is 600.

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iii. Chemical content analysis for Bituminous and Anthracite are shown in Table 1. Using information given, prove that the HHV of Anthracite is higher than Bituminous. Table 1 Chemical Content Anthracite [%] Bituminous [%] Carbon 90 80 Hydrogen 4.0 6.0 Sulphur 2.5 4.0 Oxygen 1.5 4.0 Moisture 1.5 4.5 Ash 0.5 1.5 Total 100 100

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Assume the following facts for Lowmann Company: The month-end bank statement shows a balance of $40,000; outstanding checks total $2,000; a deposit of $8,000 is in transit at month-end; and a check for $400 was erroneously charged against the account by the bank. What is the correct cash balance at the end of the month? a. $45,600 b. $46,400 c. $33,600 d. $34,400

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7-2~? 1. Prove by mathematical induction that 7<sup>n</sup>-2<sup>n</sup> is divisible by 5, for all integers n ?1. 2. For all sets A, B, and C, prove that (A-B)(C-B) = (A?C)-B, using the element approach. 3. Define (S*)* = S*, where * denotes the Kleene star. Define (S***)* = S*** Is this set bigger than S*? Is it bigger than S? 4. Give a recursive definition for the set of odd integers {1,2,3...}. Can you define the set of prime numbers using the recursive definition? Explain. 5. Construct a regular expression over the alphabet ? = {a,b} defining a language such that a) All strings end in a double letter b) All strings that do not end in a double letter c) All strings that has abab in it 6. Show that the following pairs of regular expressions over the alphabet ? = {a,b} define the same language: a) (ab)a and a(ba)' b) a(ba+a)'b and aa'b(aa'b) 7. Construct a finite automaton for the following vending machine. The machine accepts dispenses a candy bar for 30 cents, a bag of chips

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Accident Analysis 8.77 intersection traveling from north to south when it is hit by a 2200-kg SUV traveling from east to west. The two cars become enmeshed due to the impact and slide as one thereafter. On-the- scene measurements show that the coefficient of kinetic friction between the tires of these cars and the pavement is 0.75, and the cars slide to a halt at a point 5.39 m west and 6.43 m south of the impact point. How fast was each car traveling just before the collision? Figure P8.78 8.78 CP A 0.150-kg frame, when suspended from a coil spring, stretches the spring 0.0400 m. A 0.200-kg lump of putty is dropped from rest onto the frame from a height of 30.0 cm (Fig. P8.78). Find the maximum distance the frame moves downward from its initial equilibrium position.

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