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Slav-nsk [51]
3 years ago
6

Factor the GCF: -6x^4y^5 - 15x^3y^2 + 9x^2y^3

Mathematics
1 answer:
natta225 [31]3 years ago
5 0
<span>-6x^4y^5 - 15x^3y^2 + 9x^2y^3

</span>-6x^4y^5 =  -2, 3, x, x, x, x,  y, y, y, y, y
15x^3y^2 =  -5, 3 x, x, x, y, y
9x^2y^3 =    3, 3 x, x, y, y, y

Each group has a 3 in common and each group has 2 x in common and each group has 2 y in common so the GCF = -3x^2y^2

Divide that out and we get 
\frac{-6x^4y^5 - 15x^3y^2 + 9x^2y^3}{-3x^2y^2} =
2x^2y^3 + 5x - 3y
-3x^2y^2(2x^2y^3 + 5x - 3y)

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If there are 52 cards in a deck with four suits (hearts, clubs, diamonds, and spades), how many ways can you select 5 diamonds a
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Answer:

12C5 *(12C3) = 792*220 =174240 ways

Step-by-step explanation:

For this case we know that we have 12 cards of each denomination (hearts, diamonds, clubs and spades) because 12*4= 52

First let's find the number of ways in order to select 5 diamonds. We can use the combinatory formula since the order for this case no matter. The general formula for combinatory is given by:

nCx = \frac{n!}{x! (n-x)!}

So then 12 C5 would be equal to:

12C5 = \frac{12!}{5! (12-5)!}=\frac{12!}{5! 7!} = \frac{12*11*10*9*8*7!}{5! 7!}= \frac{12*11*10*9*8}{5*4*3*2*1}=792

So we have 792 was in order to select 5 diamonds from the total of 12

Now in order to select 3 clubs from the total of 12 we have the following number of ways:

12C3 = \frac{12!}{3! 9!}=\frac{12*11*10*9!}{3! 9!} =\frac{12*11*10}{3*2*1}=220

So then the numbers of ways in order to select 5 diamonds and 3 clubs are:

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3 years ago
A school has two varsity basketball teams. One is the girls' team, and the other is the boys' team. On any given Saturday in Dec
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The probability that either the girls' or boys' team gets a game is 0.85            

Step-by-step explanation:

Step 1:

Let P(G) represent the probability of girls team getting a game and P(B) represent the probability of the boys team getting a game.

P(B ∪ G) represents the probability of either girls and boys team getting a game.

P(B ∩ G) represents the probability of both girls and boys team getting a game.

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It is given that P(G) = 0.8, P(B) = 0.7 and P(B ∩ G) = 0.65

We need to find the probability of either girls or boys team getting a game which is represented by P(B ∪ G)

Step 3:

P(B ∪ G) = P(B) + P(G) - P(B ∩ G)

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Answer:

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