Express this number in scientific notation.

Which of the following is a factor of 1331x3 − 8y3?

Cloud [144]

Answer:

The factor is 11x - 2y ⇒ 2nd answer

Step-by-step explanation:

* Lets explain how to factorize the difference of two cubes

- If we want to factorize x³ - y³

- The binomial x³ - y³ is different of two cubes, because x³ is cube x

and y³ is cube y

- The difference of two cubes has two factors one two two terms and

the other is three terms

- To factorize it we find the ∛x³ and ∛y³

→ ∛x³ = x and ∛y³ = y

→ Then the first factor is (x - y)

→ We find the second factor from the first factor

→ square x

→ square y

→ Multiply x and y and put them between x² and y² with opposite sign

of the first factor

→ The second factor is (x² + xy + y²)

* Lets do the same with 1331x³ - 8y³

∵ $\sqrt[3]{1331x^{3}}=11x$

∵ $\sqrt[3]{8y^{3}}=2y$

∴ The first factor is (11x - 2y)

∵ (11x)² = 121x²

∵ (2y)² = 4y²

∵ 11x × 2y = 22xy

∵ The sign of first factor is (-)

∴ The second factor is (121x² + 22xy + 4y²)

∴ <em>The factor is 11x - 2y </em>

5 0

3 years ago

Read 2 more answers

If f(x) = |x| + 9 and g(x) = –6, which describes the value of (f + g)(x)?

Kryger [21]

(f+g) (x)= f(x) + g(f)

= IxI + 9 + (-6)

= IxI + 9 - 6

= IxI + 3

(f + g)(x) = IxI + 3

6 0

3 years ago

ANSWER PLS I WILL GIVE YOU BRAINERLEST AND 5 STARS AND A THANKS PROMISE

uysha [10]

Answer:

the value is k=

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

The number of pages that Rick can write varies directly with the amount of the time that he spends writing. He can write 5 pages

Gnesinka [82]

Step-by-step explanation:

How many pages can Rick write in 8 hours

= 5 pages / 1/4 hour

= 20 pages / hour

= 20 × 8 / 8 hours

= 160 pages / 8 hours

So, Rick can write 160 pages in 8 hours

3 0

3 years ago

At a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A3). Of those c

grandymaker [24]

Answer:

a.)

P( A₂ ∩ B ) = P(B | A₂) × P(A₂)

P( A₂ ∩ B ) = 0.40 × 0.35

P( A₂ ∩ B ) = 0.14

b.)

P(B) = P( A₁ ∩ B ) + P( A₂ ∩ B ) + P( A₃ ∩ B )

P(B) = 0.08 + 0.14 + 0.125

P(B) = 0.345

c.)

For regular gas:

P(A₁ | B) = P( A₁ ∩ B ) / P(B)

P(A₁ | B) = 0.08 / 0.345

P(A₁ | B) = 0.232

For plus gas:

P(A₂ | B) = P( A₂ ∩ B ) / P(B)

P(A₂ | B) = 0.14 / 0.345

P(A₂ | B) = 0.406

For premium gas:

P(A₃ | B) = P( A₃ ∩ B ) / P(B)

P(A₃ | B) = 0.125 / 0.345

P(A₃ | B) = 0.362

Step-by-step explanation:

We are given the following information

40% of the customers use regular gas (A2)

P(A₁) = 0.40

35% use plus gas (A2)

P(A₂) = 0.35

25% use premium (A3)

P(A₃) = 0.25

Of those customers using regular gas, only 20% fill their tanks (event B).

P(B | A₁) = 0.20

Of those customers using plus, 40% fill their tanks

P(B | A₂) = 0.40

Whereas of those using premium, 50% fill their tanks.

P(B | A₃) = 0.5

a) What is the probability that the next customer will request plus gas and fill their tank?

We are asked to find P(A₂ ∩ B) = ?

Recall that Multiplicative law of probability is given by

P( A₂ ∩ B ) = P(B | A₂) × P(A₂)

P( A₂ ∩ B ) = 0.40 × 0.35

P( A₂ ∩ B ) = 0.14

b) What is the probability that the next customer fills the tank?

We are asked to find P(B) = ?

P(B) = P( A₁ ∩ B ) + P( A₂ ∩ B ) + P( A₃ ∩ B )

P( A₂ ∩ B ) is already calculated, we need to calculate

P( A₁ ∩ B ) and P( A₃ ∩ B )

So,

P( A₁ ∩ B ) = P(B | A₁) × P(A₁)

P( A₁ ∩ B ) = 0.20 × 0.40

P( A₁ ∩ B ) = 0.08

P( A₃ ∩ B ) = P(B | A₃) × P(A₃)

P( A₃ ∩ B ) = 0.50 × 0.25

P( A₃ ∩ B ) = 0.125

Finally,

P(B) = P( A₁ ∩ B ) + P( A₂ ∩ B ) + P( A₃ ∩ B )

P(B) = 0.08 + 0.14 + 0.125

P(B) = 0.345

c) If the next customer fills the tank, what is the probability that the regular gas is requested? Plus? Premium

For regular gas:

P(A₁ | B) = P( A₁ ∩ B ) / P(B)

P(A₁ | B) = 0.08 / 0.345

P(A₁ | B) = 0.232

For plus gas:

P(A₂ | B) = P( A₂ ∩ B ) / P(B)

P(A₂ | B) = 0.14 / 0.345

P(A₂ | B) = 0.406

For premium gas:

P(A₃ | B) = P( A₃ ∩ B ) / P(B)

P(A₃ | B) = 0.125 / 0.345

P(A₃ | B) = 0.362

5 0

4 years ago