Q. There are 9 letters having different colors (red, orange, yellow, green, blue, indigo, violet) and 4 boxes each of different shapes (tetrahedron, cube, polyhedron, dodecahedron). How many ways are there to place these 9 letters into the 4 boxes such that each box contains at least 1 letter?

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Q. A card is drawn randomly from a standard deck of cards. Determine the probability that the card drawn is a queen or a heart.

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Q. An integer from 300 through 780, inclusive is to be chosen at random. Find the probability that the number is chosen will have 1 as at least one digit.

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Q. From 1, 2, 3, …, 320 one number is selected at random. Find the probability that it is either a multiple of 7 or a multiple of 3.

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Q. Computation of the discrete logarithm is the basis of the cryptographic system _______

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Q. Solve the logarithmic function of ln(\(\frac{1+5x}{1+3x}\)).

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Q. Determine the logarithmic function of ln(1+5x)⁻⁵.

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Q. Find the value of x: 3 x² aˡᵒᵍᵃˣ = 348?

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Q. Solve for x: log₂(x²-3x)=log₂(5x-15).

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Q. Solve for x the equation 2ˣ⁺³ = 5ˣ⁺².

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Q. Given: log₄ z = B log₂/₃z, for all z > 0. Find the value of constant B.

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Q. Evaluate: 16ˣ – 4ˣ – 9 = 0.

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Q. Transform 54ʸ = n+1 into equivalent a logarithmic expression.

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Q. If logₐ\((\frac{1}{8}) = -\frac{3}{4}\), than what is x?

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Q. The explicit formula for the geometric sequence 3, 15, 75, 375,… is _______

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Q. The third term of a geometric progression with common ratio equal to half the initial term is 81. Determine the 12th term.

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Q. Which of the following series is called the “formal power series”?

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Q. Determine the interval and radius of convergence for the power series: ∞∑ₙ₌₁7ⁿ/n(3x−1)ⁿ⁻¹.

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Q. What is the radius of convergence and interval of convergence for the power series ∞∑ₙ₌₀m!(2x-1)ᵐ?

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Q. Determine the radius of convergence and interval of convergence for the power series: ∞∑ₙ₌₀ (x−7)ⁿ⁺¹/nⁿ.

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