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Novosadov [1.4K]
3 years ago
5

The model represents the factorization of 2x2+5x+3.

Mathematics
1 answer:
Lapatulllka [165]3 years ago
3 0

Answer:

(2x+3)(x+1)

Step-by-step explanation:

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The sum of 3 consecutive even
aleksandrvk [35]

Answer:

The variable representation is x, x+2 and x+4 for this sequence.

Step-by-step explanation:

Given that:

The sum of 3 consecutive even numbers is 78.

Let,

The first even number is represented by x.

As the numbers are consecutive, thus,

First even number = x

Second even number = x+2

Third even number = x+4

Hence,

The variable representation is x, x+2 and x+4 for this sequence.

7 0
3 years ago
A 5-card hand is dealt from a perfectly shuffled deck. Define the events: A: the hand is a four of a kind (all four cards of one
TiliK225 [7]

In a hand of 5 cards, you want 4 of them to be of the same rank, and the fifth can be any of the remaining 48 cards. So if the rank of the 4-of-a-kind is fixed, there are \binom44\binom{48}1=48 possible hands. To account for any choice of rank, we choose 1 of the 13 possible ranks and multiply this count by \binom{13}1=13. So there are 624 possible hands containing a 4-of-a-kind. Hence A occurs with probability

\dfrac{\binom{13}1\binom44\binom{48}1}{\binom{52}5}=\dfrac{624}{2,598,960}\approx0.00024

There are 4 aces in the deck. If exactly 1 occurs in the hand, the remaining 4 cards can be any of the remaining 48 non-ace cards, contributing \binom41\binom{48}4=778,320 possible hands. Exactly 2 aces are drawn in \binom42\binom{48}3=103,776 hands. And so on. This gives a total of

\displaystyle\sum_{a=1}^4\binom4a\binom{48}{5-a}=886,656

possible hands containing at least 1 ace, and hence B occurs with probability

\dfrac{\sum\limits_{a=1}^4\binom4a\binom{48}{5-a}}{\binom{52}5}=\dfrac{18,472}{54,145}\approx0.3412

The product of these probability is approximately 0.000082.

A and B are independent if the probability of both events occurring simultaneously is the same as the above probability, i.e. P(A\cap B)=P(A)P(B). This happens if

  • the hand has 4 aces and 1 non-ace, or
  • the hand has a non-ace 4-of-a-kind and 1 ace

The above "sub-events" are mutually exclusive and share no overlap. There are 48 possible non-aces to choose from, so the first sub-event consists of 48 possible hands. There are 12 non-ace 4-of-a-kinds and 4 choices of ace for the fifth card, so the second sub-event has a total of 12*4 = 48 possible hands. So A\cap B consists of 96 possible hands, which occurs with probability

\dfrac{96}{\binom{52}5}\approx0.0000369

and so the events A and B are NOT independent.

4 0
3 years ago
Simplify by combining like terms:<br> 3x - 10 + 2 + 6x
olya-2409 [2.1K]

Answer:

9x-8 is the simplified form

7 0
3 years ago
(NEED ASAP) 15 POINTS
yulyashka [42]

Answer:

1 and 2 go in the 2nd area and 3 gos to the 1st and 4th gos to the last one

Step-by-step explanation:

hope this helped!

P.S. can i pls have brainlyist am trying to lv up thx! ;D

6 0
3 years ago
Jackson’s mom limits the amount of time he is allowed to play video games. After Jackson plays for 9minutes, his mom tells him t
jeka94

Answer:

21 minutes

Step-by-step explanation:

30%=9

10%=3

100%-30%=70%

7×10%=70%

3x7=21

=21minutes

5 0
3 years ago
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