1003019401
Level:
C
Identify which of the given functions is even.
\( m(x)=\frac{x^4-3}{x^2} \)
\( h(x)=\frac{x^3+2}{x^2} \)
\( g(x)=\frac{x^2}{x+1} \)
\( f(x)=\frac{x^3}{x^2-5} \)
C
1003025504
Level:
C
Find the range of the function \( f(x)=\Bigl|\left(\frac13\right)^x-1\Bigr|\).
\( [ 0;\infty) \)
\( ( 0;\infty) \)
\( (-1;\infty) \)
\( [ -1;\infty) \)
1003025503
Level:
C
Find the domain of the function \( f(x)=\sqrt{3^x}\).
\( (-\infty;\infty) \)
\( (0;\infty) \)
\( [0;\infty) \)
\( (-\infty;0) \)
1103025502
Level:
C
Identify a possible graph of the function \( f(x)=\Bigl|\left(\frac12\right)^x-1\Bigr|\).
1103025501
Level:
C
Identify a possible graph of the function \( f(x)= 2^{|x|}-1\).
1003020901
Level:
C
Let there be vectors: \(\overrightarrow{a}=(1;3;-1)\), \(\overrightarrow{b}=(0;3;1)\), \(\overrightarrow{c}=(-1;2;2)\). Find \(\overrightarrow{a}\times\overrightarrow{b}\) and \(\left(\overrightarrow{a}\times\overrightarrow{b}\right)\cdot\overrightarrow{c}\).
\(\overrightarrow{a}\times\overrightarrow{b}=(6;-1;3); \left(\overrightarrow{a}\times\overrightarrow{b}\right)\cdot\overrightarrow{c}=-2\)
\(\overrightarrow{a}\times\overrightarrow{b}=8; \left(\overrightarrow{a}\times\overrightarrow{b}\right)\cdot\overrightarrow{c}=(-8,16,16)\)
\(\overrightarrow{a}\times\overrightarrow{b}=(-6;1;-3); \left(\overrightarrow{a}\times\overrightarrow{b}\right)\cdot\overrightarrow{c}=2\)
\(\overrightarrow{a}\times\overrightarrow{b}=\sqrt{46}; \left(\overrightarrow{a}\times\overrightarrow{b}\right)\cdot\overrightarrow{c}=2\)
9000154805
Level:
C
A boy plays Monopoly game. He is in the jail and has to roll three times a pair of
dices. To escape from the jail he needs the number six on both dices. Find the
probability that he succeeds to escape the jail. Round your answer to three decimal
places.
\(0.081\)
\(0.919\)
\(0.028\)
\(0.095\)
9000154809
Level:
C
The soldiers play a card game with a pack of
\(32\) cards.
Find the probability that there is at least one ace among three randomly selected
cards. (There are four aces in the pack.) Round your answer to two decimal places.
\(0.34\)
\(0.66\)
\(0.57\)
\(0.43\)
9000153901
Level:
C
Find 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:
C
Find the number of ways how to distribute
\(8\) identical
balls among \(5\)
persons.
\(\left({12\above 0.0pt
8} \right) = 495\)
\(5^{8} = 390625\)
\(\left({8\above 0.0pt
5}\right) = 56\)
\(\left({12\above 0.0pt
5} \right) = 792\)