Factor x3 ‒ 11x2 ‒ 7x + 77 by grouping. What is the resulting expression?

Mathematics

1 answer:

shepuryov [24]3 years ago

6 0

Answer:

A. $(x^{2}-7)\cdot (x-11)$

Step-by-step explanation:

The third order polynomial is factored herein:

$x^{2}\cdot (x-11) - 7\cdot (x-11)$

$(x^{2}-7)\cdot (x-11)$

Which represents answer A.

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15 workers working 8hrs a day can complete a piece of work in 20 days. In how many days will 10 workers do it,working 6 hrs a da

mel-nik [20]

Answer:

40 days

Step-by-step explanation:

w1*h1*d1=w2*h2*d

15*8*20=10*6*d

2400=60d

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2 years ago

In a home theater system, the probability that the video components need repair within 1 year is 0.02, the probability that the

earnstyle [38]

Answer:

(a) The probability that at least one of these components will need repair within 1 year is 0.0278.

(b) The probability that exactly one of these component will need repair within 1 year is 0.0277.

Step-by-step explanation:

Denote the events as follows:

A = video components need repair within 1 year

B = electronic components need repair within 1 year

C = audio components need repair within 1 year

The information provided is:

P (A) = 0.02

P (B) = 0.007

P (C) = 0.001

The events A, B and C are independent.

(a)

Compute the probability that at least one of these components will need repair within 1 year as follows:

P (At least 1 component needs repair)

= 1 - P (No component needs repair)

$=1-P(A^{c}\cap B^{c}\cap C^{c})\\=1-[P(A^{c})\times P(B^{c})\times P(C^{c})]\\=1-[(1-0.02)\times (1-0.007)\times (1-0.001)]\\=1-0.97216686\\=0.02783314\\\approx 0.0278$

Thus, the probability that at least one of these components will need repair within 1 year is 0.0278.

(b)

Compute the probability that exactly one of these component will need repair within 1 year as follows:

P (Exactly 1 component needs repair)

= P (A or B or C)

$=P(A\cap B^{c}\cap C^{c})+P(A^{c}\cap B\cap C^{c})+P(A^{c}\cap B^{c}\cap C)\\=[0.02\times (1-0.007)\times (1-0.001)]+[(1-0.02)\times 0.007\times (1-0.001)]\\+[(1-0.02)\times (1-0.007)\times 0.001]\\=0.02766642\\\approx 0.0277$