1003067808
Level:
C
Find the solution set of the following equation.
\[ -2 x^2+ 5 x + 3 =\left|-2 x^2+ 5 x + 3\right| \]
\( \left[-\frac12;3\right] \)
\( [-5;3] \)
\( \left(-\infty;-\frac12\right]\cup[3;\infty) \)
\( (-\infty,-3]\cup[5,\infty) \)
C
1003067807
Level:
C
Find the solution set of the following equation.
\[ 2x^2+ 4x - 30=\left|2 x^2+ 4 x - 30\right| \]
\( (-\infty;-5]\cup[3;\infty) \)
\( [-5;3] \)
\( (-\infty;-3]\cup[5;\infty) \)
\( [-3;5] \)
1003067806
Level:
C
Find the solution set of the following equation.
\[ |(x-1)(x+2)|=4 \]
\( \{ -3; 2 \} \)
\( \{ 2 \} \)
\( \{ -2; 3 \} \)
\( \{ -2 \} \)
1003067805
Level:
C
For \( x\in[-3;5] \) find the solution set of the following equation.
\[ \left|(x+3)(x-5)\right|=5 \]
\( \left\{ 1-\sqrt{11};1+\sqrt{11} \right\} \)
\( \left\{ 1-\sqrt{21};1+\sqrt{21} \right\} \)
\( \{ -3; 5 \} \)
\( \left\{1-\sqrt{21}; 1-\sqrt{11};1+\sqrt{11};1+\sqrt{21} \right\} \)
1003067804
Level:
C
For \( x\in[4;\infty) \) choose the correct form of the equation
\[ \left|-x^2+3x+4\right|=\left|-2 x^2+ 11 x - 12\right| \]
that does not contain an absolute value.
\( x^2-3x-4=2x^2-11x+12 \)
\( x^2-3x-4=-2x^2+11x-12 \)
\(-x^2+3x+4=2x^2-11x+12 \)
\( -x^2+3x+4=-2x^2+11x-12 \)
1003067803
Level:
C
For \( x\in(1;2) \) choose the correct form of the equation
\[ \left|2x^2-5x-7\right|=\left|x^2-3x+1\right| \]
that does not contain an absolute value.
\( -2x^2+5x+7=-x^2+3x-1 \)
\( 2x^2-5x-7=-x^2+3x-1 \)
\( 2x^2+5x+7=x^2-3x+1 \)
\( -2x^2+5x+7=x^2-3x+1 \)
1003067802
Level:
C
For \( x\in (-\infty;3) \) choose the correct form of the equation
\[ \left|x^2- 9 x + 20\right|=1 \]
that does not contain an absolute value.
\( x^2-9x+20=1 \)
\( -x^2+9x-20=1 \)
\( x^2-9x+20=-1 \)
\( x^2+9x-20=1 \)
1103067801
Level:
C
Given the graph of the function \( f(x)=x^2 + 2x - 4 \), find the solution set of the following equation.
\[ \left|x^2 + 2x - 4\right|= 4 \]
\( \{ -4; -2; 0 ; 2 \} \)
\( \{ -4; 2 \} \)
\( \{ -4; 0; 2 \} \)
\( \left\{ -1-\sqrt5;-1+ \sqrt5 \right\} \)
1003041603
Level:
C
There are \( 30 \) students in a class, of them are \( 14 \) girls and the rest are boys. The teacher selects two students for weekly routine help. If selection is done at random, what is the probability that these students are not two girls? Round the result to two decimal places.
\( \frac{\binom{16}2+\binom{16}1\cdot\binom{14}1}{\binom{30}2}\doteq 0{.}79 \)
\( \frac{\binom{16}2}{\binom{30}2}\doteq 0{.}28 \)
\( \frac{\binom{14}2}{\binom{30}2}\doteq 0{.}21 \)
\( \frac{\binom{16}1\cdot\binom{14}1}{\binom{30}2}\doteq 0{.}51 \)
1003041602
Level:
C
A box contains \( 50 \) transistors and \( 4 \) of them are lower quality. From all transistors \( 5 \) are selected at random for inspection. What is the probability that of lower quality is at most one of the selected transistors? Round the result to two decimal places.
\( \frac{\binom{46}5 + \binom{46}4\cdot\binom41}{\binom{50}5}\doteq 0{.}96 \)
\( \frac{\frac{46!}{41!}+\frac{46!}{42!}}{\frac{50!}{45!}}\doteq 0{.}66 \)
\( \frac{\binom{46}5 + \binom{46}4}{\binom{50}5}\doteq 0{.}72 \)
\( \frac{\frac{46!}{41!}+\frac{46!}{42!}\cdot \frac{4!}{3!}}{\frac{50!}{45!}}\doteq 0{.}71 \)