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1003029205

Level:

In the hospital,

22

boys and

18

girls were born in one month. Babies were listed in the register by their date of birth. Find the probability that there are two boys and three girls in the first five places of the register. The results are rounded to four decimal places.

\frac{(\binom{22}{2}) \cdot (\binom{18}{3})}{(\binom{40}{5})} = 0.2865

\frac{(\binom{22}{2}) \cdot (\binom{18}{3})}{\frac{40!}{35!}} = 0.0024

\frac{22^{2} \cdot 18^{3}}{40^{5}} = 0.0276

\frac{(\binom{22}{3}) \cdot (\binom{18}{2})}{\frac{40!}{35!}} = 0.0030

1003029204

Level:

A class consists of

50

students including twins, Mark and Martin. For an exam students are randomly divided into two equally sized subgroups. Find the probability that Mark and Martin will be in the same subgroup. The results are rounded to two decimal places.

\frac{(\binom{48}{23}) + (\binom{48}{25})}{(\binom{50}{25})} = 0.49

\frac{(\binom{48}{23})}{(\binom{50}{25})} = 0.24

\frac{2 \cdot (\binom{48}{24})}{(\binom{50}{25})} = 0.51

\frac{(\binom{49}{24})}{(\binom{50}{25})} = 0.50

1003029203

Level:

Three dice are thrown together. Find the probability that three different outcomes are rolled. Results are rounded to two decimal places.

\frac{(\binom{6}{1}) \cdot (\binom{5}{1}) \cdot (\binom{4}{1})}{6^{3}} = 0.56

\frac{(\binom{6}{1}) + (\binom{5}{1}) + (\binom{4}{1})}{6^{3}} = 0.07

\frac{(\binom{6}{6}) \cdot (\binom{6}{5}) \cdot (\binom{6}{4})}{6^{3}} = 0.42

\frac{(\binom{6}{6}) + (\binom{6}{5}) + (\binom{6}{4})}{6^{3}} = 0.10

1003067810

Level:

Find the solution set of the following equation.

| x - 4 | \cdot (x + 4) = 4

{- 2 \sqrt{3}; 2 \sqrt{3}; 2 \sqrt{5}}

{- 4; 4}

{- 2 \sqrt{3}; 2 \sqrt{3}}

{2 \sqrt{3}; 2 \sqrt{5}}

{- 2 \sqrt{5}; - 2 \sqrt{3}; 2 \sqrt{3}; 2 \sqrt{5}}

1103067809

Level:

Given the graphs of the functions

f (x) = \frac{1}{2} x^{2} - 3

and

g (x) = \frac{1}{2} x

, find the solution set of the following equation.

| \frac{1}{2} x^{2} - 3 | = | \frac{1}{2} x |

{- 3; - 2; 2; 3}

{- 2; 3}

{2; 3}

{- \sqrt{6}; - 2; \sqrt{6}; 3}

1003067808

Level:

Find the solution set of the following equation.

- 2 x^{2} + 5 x + 3 = | - 2 x^{2} + 5 x + 3 |

[- \frac{1}{2}; 3]

[- 5; 3]

(- \infty; - \frac{1}{2}] \cup [3; \infty)

(- \infty, - 3] \cup [5, \infty)

1003067807

Level:

Find the solution set of the following equation.

2 x^{2} + 4 x - 30 = | 2 x^{2} + 4 x - 30 |

(- \infty; - 5] \cup [3; \infty)

[- 5; 3]

(- \infty; - 3] \cup [5; \infty)

[- 3; 5]

1003067806

Level:

Find the solution set of the following equation.

| (x - 1) (x + 2) | = 4

{- 3; 2}

{2}

{- 2; 3}

{- 2}

1003067805

Level:

For

x \in [- 3; 5]

find the solution set of the following equation.

| (x + 3) (x - 5) | = 5

{1 - \sqrt{11}; 1 + \sqrt{11}}

{1 - \sqrt{21}; 1 + \sqrt{21}}

{- 3; 5}

{1 - \sqrt{21}; 1 - \sqrt{11}; 1 + \sqrt{11}; 1 + \sqrt{21}}

1003067804

Level:

For

x \in [4; \infty)

choose the correct form of the equation

| - x^{2} + 3 x + 4 | = | - 2 x^{2} + 11 x - 12 |

that does not contain an absolute value.

x^{2} - 3 x - 4 = 2 x^{2} - 11 x + 12

x^{2} - 3 x - 4 = - 2 x^{2} + 11 x - 12

- x^{2} + 3 x + 4 = 2 x^{2} - 11 x + 12

- x^{2} + 3 x + 4 = - 2 x^{2} + 11 x - 12

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