2010020102
Level:
A
An urn contains \(19\) red balls and \(9\) blue balls. Find the minimum number of blue balls that must be added so that the probability of drawing a blue ball is greater than \(0.65\).
\(27\)
\(17\)
\(7\)
\(47\)
A
2010020101
Level:
A
An urn contains \(12\) red balls and \(30\) blue balls. Find the minimum number of red balls that must be added so that the probability of drawing a red ball is greater than \(0.66\).
\(47\)
\(27\)
\(37\)
\(17\)
2100021008
Level:
A
Which of the graphs is the graph of the following function?
\[f(x)=|x+2|+|2x+1|-|x-3|;\quad x\in[-4;1]\]
2110020004
Level:
A
A function \(f\) is given by the formula \(f(x)=-(x-3)^3+3x-12\). Choose the picture that shows a part of the graph of this function.
2110020003
Level:
A
A function \(f\) is given by the formula \(f(x)=(x+3)^3-3x-6\). Choose the picture that shows a part of the graph of this function.
2010020002
Level:
A
A function \(f\) is given by the formula \[f(x)=1-\sqrt{\frac{x^4}{4}-4x^2+16}.\] Choose the true statement about local extrema of this function.
The function has two local maxima and one local minimum.
The function has two local minima and one local maximum.
The function has two local minima and no local maximum.
The function has two local maxima and no local minimum.
2010020001
Level:
A
A function \(f\) is given by the formula
\[f(x)=1+\sqrt{\frac{x^4}{4}-2x^2+4}.\]
Choose the true statement about local extrema of this function.
The function has two local minima and one local maximum.
The function has two local maxima and one local minimum.
The function has two local minima and no local maximum.
The function has two local maxima and no local minimum.
2010013910
Level:
A
Suppose a function is increasing on the interval \([-6;-3]\). Which one of the offered functions has that property?
\(i(x)=-x^4+2x^2-3\)
\(h(x)=\sqrt{x^2+x}+1\)
\(f(x)=\frac{1-x^2}{x}\)
\(g(x)=(x+3)^3-3x-6\)
2010013909
Level:
A
Suppose a function is decreasing on the interval \([-5;-2]\). Which one of the offered functions has that property?
\(h(x)=\frac{x^4}{2}-x^2-1\)
\(f(x)=2-\sqrt{x^2+x}\)
\(g(x)=\frac{x^2+3}{x}\)
\(i(x)=(x+2)^3-x-1\)
2110013904
Level:
A
The pictures show part of graphs of even functions. Choose the picture showing the part of the graph of the function \(f(x)=-\frac4{2+x^2}\).
