1003019402 Level: CIdentify which of the given functions is neither even nor odd.\( h(x) = \frac{x^3-7}{2x^2} \)\( f(x) = \frac{x^2+3}{3x^4} \)\( g(x) = \frac{5x^2-6}{x} \)\( m(x) = \frac{x^3}{2x^2+5} \)
1003019401 Level: CIdentify which of the given functions is even.\( m(x)=\frac{x^4-3}{x^2} \)\( h(x)=\frac{x^3+2}{x^2} \)\( g(x)=\frac{x^2}{x+1} \)\( f(x)=\frac{x^3}{x^2-5} \)
1003025504 Level: CFind the range of the function \( f(x)=\Bigl|\left(\frac13\right)^x-1\Bigr|\).\( [ 0,\infty) \)\( ( 0,\infty) \)\( (-1,\infty) \)\( [ -1,\infty) \)
1003025503 Level: CFind the domain of the function \( f(x)=\sqrt{3^x}\).\( (-\infty,\infty) \)\( (0,\infty) \)\( [0,\infty) \)\( (-\infty,0) \)
1103025502 Level: CIdentify a possible graph of the function \( f(x)=\Bigl|\left(\frac12\right)^x-1\Bigr|\).
1003020901 Level: CLet there be vectors: \(\vec{a}=(1,3,-1)\), \(\vec{b}=(0,3,1)\), \(\vec{c}=(-1,2,2)\). Find \(\vec{a}\times\vec{b}\) and \(\left(\vec{a}\times\vec{b}\right)\cdot\vec{c}\).\(\vec{a}\times\vec{b}=(6,-1,3), \left(\vec{a}\times\vec{b}\right)\cdot\vec{c}=-2\)\(\vec{a}\times\vec{b}=8, \left(\vec{a}\times\vec{b}\right)\cdot\vec{c}=(-8,16,16)\)\(\vec{a}\times\vec{b}=(-6,1,-3), \left(\vec{a}\times\vec{b}\right)\cdot\vec{c}=2\)\(\vec{a}\times\vec{b}=\sqrt{46}, \left(\vec{a}\times\vec{b}\right)\cdot\vec{c}=2\)
9000153901 Level: CFind the number of ways how to distribute \(8\) identical balls among \(5\) persons so that each of them gets at least one ball.\(\left({7\above 0.0pt 3}\right) = 35\)\(5^{3} = 125\)\(\left({12\above 0.0pt 5} \right) = 792\)\(\left({12\above 0.0pt 8} \right) = 495\)
9000153902 Level: CFind the number of ways how to distribute \(8\) identical balls among \(5\) persons.\(\left({12\above 0.0pt 8} \right) = 495\)\(5^{8} = 390625\)\(\left({8\above 0.0pt 5}\right) = 56\)\(\left({12\above 0.0pt 5} \right) = 792\)
9000153905 Level: CFind the number of ways how to distribute \(5\) identical balls among \(8\) persons.\(\left({12\above 0.0pt 5} \right) = 792\)\(8^{5} = 32768\)\(\left({12\above 0.0pt 8} \right) = 495\)\(\frac{8!} {3!} = 6720\)