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3 years ago

If (a+b+c) = 5 and ab+bc+ac = 10. Prove that a3+b3+c3 -3abc = -25

Mathematics

1 answer:

maks197457 [2]3 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

Using the identity

(a + b + c)³ = a³ + b³ + c³ + 3 [ (a + b + c)(ab + bc + ac) - abc ], then

5³ = a³ + b³ + c³ + 3(5 × 10) - 3abc, that is

125 = a³ + b³ + c³ + 150 - 3abc, hence

a³ + b³ + c³ - 3abc = 125 - 150 = - 25

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The random variable X~(30,2^2) Find p(X<33) Find p(X>26)

Ostrovityanka [42]

Answer:

i) P(X<33) = 0.9232

ii) P(X>26) = 0.001

Step-by-step explanation:

Step(i):-

Given that the mean of the Population = 30

Given that the standard deviation of the Population = 4

Let 'X' be the Normal distribution

Step(ii):-

Given that the random variable X = 33

$Z = \frac{x-mean}{S.D}$

$Z = \frac{33-30}{2} = 1.5$ >0

P(X<33) = P( Z<1.5)

= 1- P(Z>1.5)

= 1 - ( 0.5 - A(1.5))

= 0.5 + 0.4232

P(X<33) = 0.9232

Step(iii) :-

Given that the random variable X = 26

$Z = \frac{x-mean}{S.D}$

$Z = \frac{33-26}{2} = 3.5$ >0

P(X>26) = P( Z>3.5)

= 0.5 - A(3.5)

= 0.5 - 0.4990

= 0.001

P(X>26) = 0.001

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3 years ago

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bagirrra123 [75]

Answer:

Step-by-step explanation:

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Step-by-step explanation:

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3 years ago

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zmey [24]

Answer:

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Step-by-step explanation:

There are a few things to note when reading an inequality on a number line.

The number line would contain the following:

i. circles: These can be closed or open. Closed circles are denoted by a shaded small circle showing that the point or number shown on the number line is included in the inequality. Open circles are denoted by an unshaded small circle showing that the point or number shown on the number line is not included in the range of inequality.

ii. arrows: An arrow can point to the right or left. When it points to the right, that means the values greater than the number specified on the number line are included in the range. When it points to the left, the values less than the number are included.

From the given number line,

The type of circle is a closed circle since it is shaded. This means that the number pointed at on the number line (-4 in this case) is included in the range.

Also, the arrow is pointing leftwards. This means that values less than the number pointed at (-4 in this case) are included in the range.

Therefore, the inequality should read,

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3 years ago

If (a+b+c) = 5 and ab+bc+ac = 10. Prove that a3+b3+c3 -3abc = -25​

If (a+b+c) = 5 and ab+bc+ac = 10. Prove that a3+b3+c3 -3abc = -25