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    Integer Selection Triangle Probability

    I choose a random integer $ n $ between $ 1 $ and $ 10 $ inclusive. What is the probability that for the $ n $ I chose, there exist no real solutions to the equation $ x(x+5) = -n $? Express your answer as a common fraction.

    • 1
    • 2
    • 3
    • +
    • 4
    • 5
    • 6
    • -
    • 7
    • 8
    • 9
    • $\frac{a}{b}$
    • .
    • 0
    • =
    • %
    • $a^n$
    • $a^{\circ}$
    • $a_n$
    • $\sqrt{}$
    • $\sqrt[n]{}$
    • $\pi$
    • $\ln{}$
    • $\log$
    • $\theta$
    • $\sin{}$
    • $\cos{}$
    • $\tan{}$
    • $($
    • $)$
    • $[$
    • $]$
    • $\cap$
    • $\cup$
    • $,$
    • $\infty$

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