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3 years ago

Simplify 3 over quantity of 5 minus 6 i . (1 point)

Mathematics

1 answer:

julsineya [31]3 years ago

5 0

3/(5 - 6i)

To simplify this, we need to multiply both sides by the conjugate of the denominator, which is 5 + 6i

3(5 + 6i)

Distributive property.

15 + 18i

(5 - 6i)(5 + 6i)

25 + 30i - 30i - 36i^2

25 - 36i^2

i^2 = -1

25 + 36

<h3><u>The simplified expression is (15/61) + (18i/61).</u></h3>

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3 years ago

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Answer:

The right answer is:

(a) 0.1456

(b) 18.125, 69.1202, 8.3139

Step-by-step explanation:

Given:

N = 24

n = 5

r = 7

The improperly drilled gearboxes "X".

then,

⇒ $P(X) = \frac{\binom{7}{x} \binom {17}{5-x}}{\binom{24}{5}}$

(a)

P (all gearboxes fit properly) = $P(x=0)$

= $\frac{\binom{7}{0} \binom{17}{5}}{\binom{24}{5}}$

= $0.1456$

(b)

According to the question,

$X = 91+5$

Mean will be:

⇒ $\mu = E(x)$

$=E(91+5)$

$=9E(1)+5$

$=9.\frac{nr}{N}+5$

$=9.\frac{5.7}{24} +5$

$=18.125$

Variance will be:

⇒ $\sigma^2=Var(X)$

$=V(9Y+5)$

$=81.V(Y)$

$=81.n.\frac{r}{N}.\frac{N-r}{N}.\frac{N-n}{N-1}$

$=81.5.\frac{7}{24}.\frac{24-7}{24}.\frac{24-5}{24-1}$

$=69.1202$

Standard deviation will be:

⇒ $\sigma = \sqrt{69.1202}$

$=8.3139$

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