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question:What is the number of strings of four decimal digits that contain exactly one digit repeated twice? (e.g 1198)

answer:Assume that the constraint is exactly one digit is repeated exactly twice. STEP 1: Choose the number to be repeated: 10 options STEP 2: Choose the other two numbers: binom{9}{2} text{ options.} STEP 3: Calculate all the permutations of this four characters: 4!=24 This leads to 10times 24times binom{9}{2} text{options,} however, you must divide by 2 since this distinguish between the repeated digits (e.g. 1189 is being counted twice as 1bar189 and bar1189), thus, the final number is: 5times 24times binom{9}{2} = 4500

question:What does equality mean?

answer:Equality refers to the state of being equal in terms of rights, opportunities, and treatment. It encompasses the idea that all individuals should have the same access to resources, opportunities, and privileges, regardless of their gender, race, ethnicity, religion, sexual orientation, or any other factor. Equality promotes fairness, justice, and inclusivity in society.

question:Find the sum of x and y, where x = frac{26 + 2i}{pi} and y = -frac{11 + 31i}{pi}.

answer:** frac{15 - 29i}{pi} **Explanation:** Given, x = frac{26 + 2i}{pi} and y = -frac{11 + 31i}{pi} To find the sum of x and y, we can simply add them up. x + y = frac{26 + 2i}{pi} + left(-frac{11 + 31i}{pi}right) x + y = frac{26 + 2i - 11 - 31i}{pi} x + y = frac{15 - 29i}{pi} Therefore, the sum of x and y is frac{15 - 29i}{pi}.

question:If the total pressure in the flask is 6.0 atm at equilibrium, what is the value of the equilibrium constant, Kp, at the same temperature?

answer:Following the same steps as in the original answer: {eq}rm P_{tot} = 6.0 atm {/eq} {eq}rm P_{NH3} = P_{HCl} = dfrac{6.0 atm}{2} = 3.0 atm {/eq} {eq}rm K_p = (3.0 atm)^2 K_p = 9.0 {/eq} Therefore, the equilibrium constant, Kp, is 9.0.

Released under the MIT License.

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