C | math4u.vsb.cz

1003082606

Level:

How many of the following inequalities have the same solution set?

\begin{aligned} 2 {(\frac{1}{4})}^{2 x - 1} - {(\frac{1}{2})}^{4 x - 2} - \frac{1}{4} & \leq 0 \\ 2^{4 x + 4} - 15 \cdot 4^{2 x} & \geq 2^{4} \\ 9^{2 x + 1} - 2 \cdot 3^{5} & \geq 3^{4 x + 1} \end{aligned}

3

2

1

0

1003082605

Level:

Solve the following system of two inequalities.

\begin{aligned} {(\frac{1}{2})}^{x + 1} - 3 {(\frac{1}{2})}^{x + 2} + \frac{1}{2} & \geq 0 \\ 4^{x + 2} - 3 \cdot 4^{x + 1} & < 1 \end{aligned}

The system of inequalities has no solution.

x \in (- \infty; \infty)

x \in (- \infty; - 1)

x \in (- \infty; - 1]

1003082603

Level:

How many solutions does the following inequality have?

2^{x - 1} - 2^{x - 3} - 2^{x - 4} \geq 2^{- 4} - 2^{- 3} - 2^{- 2}

Infinitely many solutions

No solution

Exactly one solution

Exactly two solutions

1003064203

Level:

Find the solution of the following inequality.

\sqrt{2^{2 x} - 2^{3 + x}} < 2^{x} - 2^{3}

No solution

x \in (- \infty; 3)

x \in (8; \infty)

x \in [3; \infty)

1003064201

Level:

How many solutions does the following inequality in the set of positive integers have?

16^{x} - 3 \cdot 4^{x} - 4 \leq 0

Exactly one solution

Infinitely many solutions

Exactly two solutions

No solutions

1003029206

Level:

In the hospital,

22

boys and

18

girls were born in one month. Babies were listed in the register by their date of birth. Find the probability that there are at least three boys in the first five places of the register. The results are rounded to four decimal places.

\frac{(\binom{22}{3}) \cdot (\binom{18}{2}) + (\binom{22}{4}) \cdot (\binom{18}{1}) + (\binom{22}{5}) \cdot (\binom{18}{0})}{(\binom{40}{5})} = 0.5982

\frac{(\binom{22}{3}) + (\binom{22}{4}) + (\binom{22}{5})}{(\binom{40}{5})} = 0.0535

\frac{22^{3} \cdot 18^{2} + 22^{4} \cdot 18^{1} + 22^{5} \cdot 18^{0}}{40^{5}} = 0.1252

\frac{(\binom{22}{3}) \cdot (\binom{18}{2}) + (\binom{22}{4}) \cdot (\binom{18}{1}) + (\binom{22}{5}) \cdot (\binom{18}{0})}{40^{5}} = 0.0038

C

1003082606

1003082605

1003082604

1003082603

1003082602

1003082601

1003064203

1003064202

1003064201

1003029206

Events

Akce

Interests

Zajímavosti

About portal

O portálu