Use hexadecimal number system (base 16) to represent quaternary number 1111222(base4).

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Find the average of the following number sequence: 258,161,56,265,168,63,272,175,70,…,2106,2009,1904,2113,2016,1911.

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30th September 2024 is Monday. Which day of the week will 26th October 2033 be?

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Factorize 𝑥^2 − 12𝑥 − 16𝑦^2 −48𝑦.

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If 𝑚 and 𝑛 are the distinct roots of 𝑥^2 − 11𝑥 + 36 = 0, find the value of 𝑚^3 + 𝑛^3.

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Solve the equation log(base5) (𝑥^2 + 72) + log(base5) 25 − 2log(base5) 𝑥 = 3. (Answer in simplest surd form)

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. Given that 𝑥 is a 3-digit number, find the smallest possible value of 𝑥 such that 𝑥 = 27√x-162

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Given straight line 𝐿 passes through 𝐴(−21,17) and the slope of 𝐿 is 3/7 , find the 𝑦-intercept of 𝐿.

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In ∆𝐴𝐵𝐶,𝐴𝐵=24,𝐴𝐶=45, and 𝐵𝐶=51. Find the value of cos𝐵/cos𝐶 .

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The side lengths of a triangle are 26, 31, and 41. Find the area of this triangle. (Answer in terms of

simplest surd form)

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Determine the number of positive integer(s) 𝑥 such that 𝑥^2<41𝑥−238.

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Miranda randomly picks 7 balls from the bag containing 4 red, 5 green and 6 yellow balls without

replacement. What is the probability that at least 3 of the balls drawn are red?

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Find the number of different way(s) of arranging 5 identical red balls and 9 identical white balls in a row.

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If 𝑥 and 𝑦 are positive integers such that 11𝑥 + 14𝑦 = 1259, find the maximum value of 𝑥 − 𝑦.

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