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2 years ago

Find the sample variance and standard deviation of: 21, 12, 3, 9, 11s2=?

Mathematics

1 answer:

olga nikolaevna [1]2 years ago

8 0

Answer:

42. 2

6.496

Step-by-step explanation:

Given the data :

21, 12, 3, 9, 11

Variance :

S² = Σ(x - m)² ÷ (n - 1)

n = sample size = 5

m = sample mean = Σx / n

m = (21 + 12 + 3 + 9 + 11) / 5

m = 11. 2

(21-11.2)² + (12 -11.2)² + (3 - 11.2)² + (9-11.2)²

+ (11-11.2)² / (5 - 1)

S² = 42.2

Standard deviation, s = sqrt(42.2) = 6.496

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3 years ago

What two rational expressions sum to 2x+3/x^2-5x+4

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Answer:

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}$

Step-by-step explanation:

Given the rational expression: $\frac{2x + 3}{x^2 - 5x + 4}$ , to express this in simplified form, we would need to apply the concept of partial fraction.

Step 1: factorise the denominator

$x^2 - 5x + 4$

$x^2 - 4x - x + 4$

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Thus, we now have: $\frac{2x + 3}{(x- 1)(x - 4)}$

Step 2: Apply the concept of Partial Fraction

Let,

$\frac{2x + 3}{(x- 1)(x - 4)}$ = $\frac{A}{x- 1} + \frac{B}{x - 4}$

Multiply both sides by (x - 1)(x - 4)

$\frac{2x + 3}{(x- 1)(x - 4)} * (x - 1)(x - 4)$ = $(\frac{A}{x- 1} + \frac{B}{x - 4}) * (x - 1)(x - 4)$

$2x + 3 = A(x - 4) + B(x - 1)$

Step 3:

Substituting x = 4 in $2x + 3 = A(x - 4) + B(x - 1)$

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$B = \frac{11}{3}$

Substituting x = 1 in $2x + 3 = A(x - 4) + B(x - 1)$

$2(1) + 3 = A(1 - 4) + B(1 - 1)$

$2 + 3 = A(-3) + B(0)$

$5 = -3A$

$\frac{5}{-3} = \frac{-3A}{-3}$

$A = -\frac{5}{3}$

Step 4: Plug in the values of A and B into the original equation in step 2

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$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}$

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