B

1003019202

Level: 
B
There are fifty apples left on a tree and ten of them have worms. We pick five apples at random. What is the probability that at least one of them is without a worm?
\( 1-\frac{\binom{10}{5}}{\binom{50}{5}}\doteq 0{.}9999 \)
\( 1-\frac{\binom{10}{1}}{\binom{50}{5}}\doteq 1{.}0000 \)
\( 1-\frac{\binom{10}{1}\binom{40}{4}}{\binom{50}{5}}\doteq 0{.}5687 \)
\( 1-\frac{\binom{40}{5}}{\binom{50}{5}}\doteq 0{.}6894\)

1003019303

Level: 
B
Let \( f(x)=|2-x|+|x+1| \). Identify which of the statements is correct.
Function \( f \) has minimum at \( x=-1 \) and at \( x=2 \).
Function \( f \) has minimum at \( x=-1 \) and maximum at \( x=2 \).
Function \( f \) has maximum at \( x=-1 \) and at \( x=2 \).
Function \( f \) has minimum at \( x=3 \).

1003019612

Level: 
B
Identify which of the following relations is correct.
\( 2^7 > 2^2 > 2^{\frac25} > 2^{-\frac25} > 2^{-6} \)
\( 2^{-6} > 2^{-\frac23} > 2^{\frac25} > 2^2 > 2^7 \)
\( 2^{-\frac23} > 2^{-6} > 2^{\frac25} > 2^2 > 2^7 \)
\( 2^{-6} > 2^{-\frac23} > 2^{\frac25} > 2^7 > 2^2 \)

1003019611

Level: 
B
Identify which of the following relations is correct.
\( \left(\frac15\right)^{-6} > \left(\frac15\right)^{-\frac23} > \left(\frac15\right)^{\frac25} > \left(\frac15\right)^2 > \left(\frac15\right)^7 \)
\( \left(\frac15\right)^7 > \left(\frac15\right)^2 > \left(\frac15\right)^{\frac25} > \left(\frac15\right)^{-\frac25} > \left(\frac15\right)^{-6} \)
\( \left(\frac15\right)^{-\frac23} > \left(\frac15\right)^{-6} > \left(\frac15\right)^{\frac25} > \left(\frac15\right)^2 > \left(\frac15\right)^7 \)
\( \left(\frac15\right)^{-6} > \left(\frac15\right)^{-\frac23} > \left(\frac15\right)^{\frac25} > \left(\frac15\right)^7 > \left(\frac15\right)^2 \)