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hram777 [196]
3 years ago
14

Please solve this fast​

Mathematics
2 answers:
Bas_tet [7]3 years ago
7 0

Answer:

you can take common and do it

Step-by-step explanation:

1.

qr - pr \: + qs - psqr−pr+qs−ps

r(q - p) + s(q - p)r(q−p)+s(q−p)

(r + s)(q - p)(r+s)(q−p)

2.

{x}^{2} + y - xy - xx

2

+y−xy−x

{x}^{2} - x - xy + yx

2

−x−xy+y

x(x - 1) - y(x - 1)x(x−1)−y(x−1)

3.

6xy + 6 - 9y - 4x6xy+6−9y−4x

- 4x + 6 + 6xy - 9y−4x+6+6xy−9y

2( - 2x + 3) - 3y( - 2x + 3)2(−2x+3)−3y(−2x+3)

(2 - 3y)( - 2x + 3)(2−3y)(−2x+3)

4.

{x}^{2} - 2ax - 2ab + bxx

2

−2ax−2ab+bx

x(x - 2a) - b(x - 2a)x(x−2a)−b(x−2a)

-(x +b)(2a-x)−(x+b)(2a−x)

5.

axy + bcxy - az - bczaxy+bcxy−az−bcz

xy(a + bc) - z(a + bc)xy(a+bc)−z(a+bc)

(xy - z)(a + bc)(xy−z)(a+bc)

Korolek [52]3 years ago
3 0

Step-by-step explanation:

1.

qr - pr \: + qs - ps

r(q - p) + s(q - p)

(r + s)(q  - p)

2.

{x}^{2}  + y - xy - x

{x}^{2}  -  x - xy + y

x(x - 1) - y(x - 1)

3.

6xy + 6 - 9y - 4x

- 4x + 6 + 6xy - 9y

2( - 2x + 3) - 3y( - 2x + 3)

(2 - 3y)( - 2x + 3)

4.

{x}^{2}  - 2ax - 2ab + bx

x(x - 2a) - b(x - 2a)

-(x +b)(2a-x)

5.

axy + bcxy - az - bcz

xy(a + bc) - z(a  + bc)

(xy  - z)(a + bc)

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Seventy percent of all vehicles examined at a certain emissions inspection station pass the inspection. Assuming that successive
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Answer:

(a) 0.343

(b) 0.657

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Step-by-step explanation:

Let P(a vehicle passing the test) = p

                        p = \frac{70}{100} = 0.7  

Let P(a vehicle not passing the test) = q

                         q = 1 - p

                         q = 1 - 0.7 = 0.3

(a) P(all of the next three vehicles inspected pass) = P(ppp)

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                           = 0.343

(b) P(at least one of the next three inspected fails) = P(qpp or qqp or pqp or pqq or ppq or qpq or qqq)

      = (0.3 × 0.7 × 0.7) + (0.3 × 0.3 × 0.7) + (0.7 × 0.3 × 0.7) + (0.7 × 0.3 × 0.3) + (0.7 × 0.7 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.3)

      = 0.147 + 0.063 + 0.147 + 0.063 + 0.147 + 0.063 + 0.027

      = 0.657

(c) P(exactly one of the next three inspected passes) = P(pqq or qpq or qqp)

                 =  (0.7 × 0.3 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.7)

                 = 0.063 + 0.063 + 0.063

                 = 0.189

(d) P(at most one of the next three vehicles inspected passes) = P(pqq or qpq or qqp or qqq)

                 =  (0.7 × 0.3 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.7) + (0.3 × 0.3 × 0.3)

                 = 0.063 + 0.063 + 0.063 + 0.027

                 = 0.216

(e) Given that at least one of the next 3 vehicles passes inspection, what is the probability that all 3 pass (a conditional probability)?

P(at least one of the next three vehicles inspected passes) = P(ppp or ppq or pqp or qpp or pqq or qpq or qqp)

=  (0.7 × 0.7 × 0.7) + (0.7 × 0.7 × 0.3) + (0.7 × 0.3 × 0.7) + (0.3 × 0.7 × 0.7) + (0.7 × 0.3 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.7)

= 0.343 + 0.147 + 0.147 + 0.147 + 0.063 + 0.063 + 0.063

                  = 0.973  

With the condition that at least one of the next 3 vehicles passes inspection, the probability that all 3 pass is,

                         = \frac{P(all\ of\ the\ next\ three\ vehicles\ inspected\ pass)}{P(at\ least\ one\ of\ the\ next\ three\ vehicles\ inspected\ passes)}

                         = \frac{0.343}{0.973}

                         = 0.353

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The correct answer is B. 130,099.

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