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.
\[
\sqrt{-2x^2+x+5}\geq5
\]
\(x\in\emptyset\)
\(x\in[-1;5]\)
\(x\in\left(-\frac12;\frac52\right)\)
\(x\in\mathbb{R}\)
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.
\(0.934\)
\(1.440\)
\(0.506\)
\(0.494\)
9000154806
Level:
B
A man plays a dice game. He rolls one dice three times and to win he needs at least
one number six. However, the dice is not fair. The probability of an even number is
two times bigger than the probability of an odd number. Find the probability that
the man wins. Suppose that all even numbers have equal probability and all odd
numbers also have equal probability. Round your answer to three decimal
places.
\(0.529\)
\(0.471\)
\(0.421\)
\(0.579\)
9000154807
Level:
B
The Robin's band has \(10\)
men and \(5\)
women. From this group they select randomly two fellows to negotiate with the
Sheriff of Nottingham. Find the probability that there will be one man and one
woman in the selected pair. Round your answer to three decimal places.
\(0.476\)
\(0.952\)
\(0.325\)
\(0.675\)