In how many ways can 5 distinct books be arranged on a single shelf?

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What is the domain of the real-valued function $f (x) = 2 x - 6$ ?
What is the exact value of $sin (15 0^{\circ})$ ?
If $lo g_{2} (x) + lo g_{2} (x - 2) = 3$ , what is the real solution for $x$ ?
What is the derivative $f^{'} (x)$ of the polynomial function $f (x) = 4 x^{3} - 5 x^{2} + 7 x - 9$ evaluated at $x = 1$ ?
What is the value of the definite integral $\int_{0}^{3} (2 x + 1) d x$ ?
Two vectors are given in component form as $u = ⟨ 3, - 4 ⟩$ and $v = ⟨ 4, 3 ⟩$ . What is their dot product…