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 \(\left(\overrightarrow{a}\times\overrightarrow{b}\right)\cdot\overrightarrow{c}\).
\(\overrightarrow{a}\times\overrightarrow{b}=(6;-1;3); \left(\overrightarrow{a}\times\overrightarrow{b}\right)\cdot\overrightarrow{c}=-2\)
\(\overrightarrow{a}\times\overrightarrow{b}=8; \left(\overrightarrow{a}\times\overrightarrow{b}\right)\cdot\overrightarrow{c}=(-8,16,16)\)
\(\overrightarrow{a}\times\overrightarrow{b}=(-6;1;-3); \left(\overrightarrow{a}\times\overrightarrow{b}\right)\cdot\overrightarrow{c}=2\)
\(\overrightarrow{a}\times\overrightarrow{b}=\sqrt{46}; \left(\overrightarrow{a}\times\overrightarrow{b}\right)\cdot\overrightarrow{c}=2\)
9000153903
Level:
C
Find the number of ways how to distribute
\(8\) mutually different
balls among \(5\)
persons.
\(5^{8} = 390625\)
\(\frac{8!}
{3!} = 6720\)
\(8^{5} = 32768\)
\(\left({12\above 0.0pt
8} \right) = 495\)
9000154801
Level:
C
There are six money transports through the Sherwood forest. Robin Hood knows
that two of the transports are secured by soldiers. Find the respective probabilities
that if Robin's band attacks two random transports, then none, one and both
transports will be secured by the soldiers.
\(\frac{6}
{15};\, \frac{8}
{15};\, \frac{1}
{15}\)
\(\frac{3}
{9};\, \frac{5}
{9};\, \frac{1}
{9}\)
\(\frac{1}
{3};\, \frac{2}
{3};\, \frac{2}
{3}\)
\(\frac{1}
{2};\, \frac{1}
{4};\, \frac{1}
{4}\)
9000154802
Level:
C
Three hundred soldiers know details related to the weapon transport to Nottingham. The probability that a soldier betrays the sheriff and tells the details to Robin Hood is \(0.01\)
. This probability is fixed for all soldiers. Robin tries to find out the details on the transport by asking each soldier. Find the probability that Robin will find out details (i.e. at least one soldier tells the secret to Robin). Round your answer to three decimal places.
\(0.951\)
\(0.049\)
\(0.827\)
\(0.173\)
9000154804
Level:
C
Robin Hood wants to have \(6\)
children with his love Maid Marian. Find the probability that they will have
\(2\) girls
and \(4\)
boys. The probability that one child will be a girl is
\(48.79\%\) and the probability
of a boy is \(51.21\%\).
Round your answer to three decimal places.
\(0.246\)
\(0.222\)
\(0.015\)
\(0.016\)