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3 years ago

PLEASE HELP MEEEEE!!! IT's TIMED

Mathematics

2 answers:

Triss [41]3 years ago

5 0

Answer:

x is less than oe equal to 12

andreyandreev [35.5K]3 years ago

3 0

Answer:

x ≤ 15

Step-by-step explanation:

7x - 6 ≤ 3x + 54

Subtract 3x from both sides;

4x - 6 ≤ 54

Add 6 to both sides;

4x ≤ 60

Divide both sides by 4;

x ≤ 15

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Three cards are selected one after the other from a standard deck of 52 cards.

pantera1 [17]

Answer:

$\frac{11}{850}$

Step-by-step explanation:

Let's see

The probability of the first card being a spade is 13/52 (as there's 13 spades in the deck.

The probability for the second card is 12/51 (because there's 12 spades left in 51 cards total).

The probability for the third is - you guessed it! - 11/50

so the total probability is:

$\frac{13}{52} \cdot \frac{12}{51} \cdot \frac{11}{50} = \frac{1}{4} \cdot \frac{4}{17} \cdot \frac{11}{50} = \frac{1}{17} \cdot \frac{11}{50} = \frac{11}{850}$

A more generic solution:

Let's use the binomials to find the solution with combinations:

We need to pick 3 cards out of 13. This can be done in

$\binom{13}{3} = \frac{13!}{3!\cdot10!}$ ways.

And the total number of ways to pick 3 cards out of 52 is:

$\binom{52}{3} = \frac{52!}{3!\cdot 49!}$

So the probability is:

$\frac{ \binom{13}{3} }{ \binom{52}{3} } = \frac{ \frac{13!}{3!\cdot 10!} }{ \frac{52!}{3!\cdot 49!} } = \frac{ \frac{13!}{10!} }{ \frac{52!}{49!} } = \frac{13 \cdot 12 \cdot 11}{52 \cdot 51 \cdot 50}$

Which again brings us to the result computed before.

3 0

3 years ago