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2000018803

Level:

Given the function

f (x) = \frac{5}{x}

, find the function

g

such that the graphs of

f

and

g

are symmetric about the line

y = - x

g (x) = \frac{5}{x}

g (x) = 5 x

g (x) = - \frac{5}{x}

g (x) = - 5 x

2000018802

Level:

Given the function

f (x) = \frac{6}{x}

, evaluate

\frac{f (- 3)}{f (2)}

- \frac{2}{3}

- 6

- \frac{3}{2}

- \frac{1}{6}

2000018801

Level:

Consider a triangle with area of

5 {cm}^{2}

. Find the formula which relates the length of its side

a

to the length of the height

v_{a}

, where

v_{a}

is the height to the side

a

v_{a} = \frac{10}{a}

v_{a} = \frac{5}{a}

v_{a} = 5 a

v_{a} = \frac{5}{2 a}

2010018504

Level:

In the interval

[0^{\circ}; 360^{\circ}]

find the angle coterminal with the angle

900^{\circ}

180^{\circ}

280^{\circ}

220^{\circ}

300^{\circ}

2010018502

Level:

One of the angles

α

β

γ

δ

takes the same position on the unit circle as the angle

A S B

. Which of the angles

α

β

γ

δ

it is?

α = 135^{\circ}

β = - 100^{\circ}

γ = - 315^{\circ}

δ = 210^{\circ}

2000018305

Level:

Consider three matrices

A = (\begin{matrix} 3 & 4 \\ 1 & 2 \end{matrix}), B = (\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}), C = (\begin{matrix} 1 & 0 \\ 1 & 1 \end{matrix}) .

Let

E

denote the identity matrix of order

2

. Then, find

X

, which is the solution to the following equation.

C \cdot (A + X) \cdot B = E

X = (\begin{matrix} - 2 & - 5 \\ - 2 & 0 \end{matrix})

X = (\begin{matrix} - 2 & - 5 \\ 2 & 0 \end{matrix})

X = (\begin{matrix} - 2 & 5 \\ - 2 & 0 \end{matrix})

X = (\begin{matrix} - 2 & 5 \\ 2 & 0 \end{matrix})

2000018303

Level:

Let

E

denote an identity matrix of order

2

and let matrix

M = (\begin{matrix} m & 0 \\ 0 & 2 \end{matrix}) .

Find all the values of

m

so that the equality below holds.

M^{2} - \frac{5}{2} M + E = 0

m = 2

m = \frac{1}{2}

m = \frac{1}{2}

m = 2

m = 2

m = - \frac{1}{2}

2000018302

Level:

Find the matrix

M

so that the equality given below is true.

2 \cdot (\begin{matrix} - 1 & 4 \\ 3 & - 5 \end{matrix}) - M = (\begin{matrix} - 3 & 6 \\ 9 & - 14 \end{matrix})

M = (\begin{matrix} 1 & 2 \\ - 3 & 4 \end{matrix})

M = (\begin{matrix} - 1 & 2 \\ - 3 & 4 \end{matrix})

M = (\begin{matrix} - 1 & - 2 \\ 3 & - 4 \end{matrix})

M = (\begin{matrix} 1 & 2 \\ 3 & - 4 \end{matrix})

2000018301

Level:

Find the matrix

B

, the solution to the equation given below.

(\begin{matrix} 3 & - 1 & 5 \\ 1 & 0 & 3 \end{matrix}) + B = (\begin{matrix} 5 & 0 & 4 \\ 3 & 2 & 1 \end{matrix})

B = (\begin{matrix} 2 & 1 & - 1 \\ 2 & 2 & - 2 \end{matrix})

B = (\begin{matrix} 2 & - 1 & - 1 \\ 2 & 2 & - 2 \end{matrix})

B = (\begin{matrix} 2 & 1 & - 1 \\ 2 & - 2 & - 2 \end{matrix})

B = (\begin{matrix} 2 & 1 & - 1 \\ 2 & 2 & 2 \end{matrix})

2010013606

Level:

In a set of

200

items,

20

are defective. We pick randomly

10

items from this set. First nine items were not defective. Find the probability that the tenth item selected is not defective too. Results are rounded to three decimal places.

\frac{171}{191} ≐ 0.895

\frac{180}{191} ≐ 0.942

\frac{180}{200} ≐ 0.9

\frac{1}{171} ≐ 0.006

A

2000018803

2000018802

2000018801

2010018504

2010018502

2000018305

2000018303

2000018302

2000018301

2010013606

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