1003024905
Level:
B
Which of the following functions is bounded above?
\( f(x) = -3^{-x} \)
\( f(x) = \left(\frac13\right)^{-x} \)
\( f(x) = 3^x \)
\( f(x) = \left(\frac13\right)^x \)
B
1003024904
Level:
B
Which of the following functions is decreasing?
\( f(x)=\left(\frac15\right)^x \)
\( f(x)=-5^{-x} \)
\( f(x)=\left(\frac15\right)^{-x} \)
\( f(x)=5^x \)
1003024903
Level:
B
Given the function \(f(x)=a\cdot b^x\), where \( a < 0 \) and \( 0 < b < 1 \), find the correct statement.
Function \( f \) is increasing.
Function \( f \) is decreasing.
Function \( f \) is nonincreasing.
Function \( f \) is nondecreasing.
1003024902
Level:
B
Given the function \(f(x)=a\cdot b^x\), where \( a < 0 \) and \( b > 0 \), find the correct statement.
Function \( f \) is bounded above.
Function \( f \) is bounded below.
Function \( f \) is bounded.
Function \( f \) is unbounded.
1003024901
Level:
B
Given the increasing exponential function \(f(x)=a^x\), choose the correct statement about the base \(a\).
\(a > 1\)
\(a=1\)
\(a < 1\)
\( 0 < a < 1 \)
1003020702
Level:
B
Find the solution of the inequality.
\[
\sqrt{3x^2-x+7}\geq2
\]
\(x\in\mathbb{R}\)
\(x\in\emptyset\)
\(x\in\left(-\frac13;\frac73\right)\)
\(x\in\mathbb{R}\setminus\{2\}\)
1003020701
Level:
B
Find the solution of the inequality.
\[
\sqrt{-2x^2+x+5}\geq5
\]
\(x\in\emptyset\)
\(x\in[-1;5]\)
\(x\in\left(-\frac12;\frac52\right)\)
\(x\in\mathbb{R}\)
9000153703
Level:
B
The picture shows a square pyramid. The side of a base square is
\(a = 4\; \mathrm{cm}\) and the height of
the pyramid is \(v = 6\; \mathrm{cm}\).
Find the angle \(\varphi \).
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi }
{2} = \frac{2}
{6}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 36^{\circ }52^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \varphi = \frac{6}
{2\sqrt{2}}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 64^{\circ }46^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi }
{2} = \frac{2}
{2\sqrt{10}}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 35^{\circ }6^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi }
{2} = \frac{2\sqrt{2}}
{6} \mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 50^{\circ }29^{\prime}\)
9000153704
Level:
B
The picture shows a square pyramid. The side of a base square is
\(a = 4\; \mathrm{cm}\) and the height of
the pyramid is \(v = 6\; \mathrm{cm}\).
Find the angle \(\varphi \).
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi }
{2} = \frac{2}
{2\sqrt{10}}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 35^{\circ }6^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \varphi = \frac{6}
{2\sqrt{2}}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 64^{\circ }46^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi }
{2} = \frac{2}
{6}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 36^{\circ }52^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi }
{2} = \frac{2\sqrt{2}}
{6} \mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 50^{\circ }29^{\prime}\)
9000154803
Level:
B
The probability that Robin Hood hits the target is
\(0.83\). The same
probability is \(0.61\)
for Robin's fellow, Little John. Both Robin and John shot on the wolf. Find the
probability that they will hit the wolf. Round your answer to three decimal places.
\(0.934\)
\(1.440\)
\(0.506\)
\(0.494\)