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4 years ago

Compute the standard deviation for the set of data. 2, 4, 6, 8, 10

2 answers:

6 0

$\sigma$ - standard deviation
m - mean
$\sigma= \sqrt{ \frac{1}{n} \sum_{i=1}^{n} (x_i-m)^2} 
\\m= \frac{2+4+6+8+10}{5}= \frac{30}{5} =6 \\ \\ \sigma= \sqrt{ \frac{1}{5} \sum_{i=1}^{5} (x_i-6)^2} 
\\= \sqrt{ \frac{1}{5} [ (2-6)^2+(4-6)^2+(6-6)^2+(8-6)^2+(10-6)^2]} 
\\= \sqrt{ \frac{1}{5} [ 16+4+0+4+16]} 
\\= \sqrt{ \frac{1}{5} \times 40} 
\\= \sqrt{ \frac{1}{5} \times 40} 
\\=2\sqrt{2}$

balu736 [363]4 years ago

4 0

6 is the correct anwser

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In a survey of 200 employees of a company regarding their 401(k) investments, the following data were obtained.

marysya [2.9K]

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Step-by-step explanation:

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3 years ago

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

Anni [7]

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

$x^2 - 5x + 4$

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

$(x^2 - 4x) - (x + 4)$

$x(x - 4) - 1(x - 4)$

$(x- 1)(x - 4)$

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

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

$8 + 3 = A(0) + B(3)$

$11 = 3B$

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

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

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

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

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

7 0

3 years ago

The sum of 7 angles of a decagon is 1170°. The 3 sides are equal to each other. Calculate the size of the other 3 angles.

7nadin3 [17]

Answer:

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5 0

3 years ago

Read 2 more answers

ANSWER CORRECTLY AND ILL MARK YOU AS THE BRAINLIEST

lana66690 [7]

Answer:

2/3

Step-by-step explanation:

im pretty sure that's the answer

6 0

3 years ago

Read 2 more answers

A right square pyramid with base edges of length $8\sqrt{2}$ units each and slant edges of length 10 units each is cut by a plan

seropon [69]

Answer:

32 $unit^{3}$

Step-by-step explanation:

Given:

The slant length 10 units
A right square pyramid with base edges of length 8 $\sqrt{2}$

Now we use Pythagoras to get the slant height in the middle of each triangle:

$\sqrt{10^{2 - (4\sqrt{2} ^{2} }) }$ = $\sqrt{100 - 32}$ = $\sqrt{68}$ units

One again, you can use Pythagoras again to get the perpendicular height of the entire pyramid.

$\sqrt{68-(4\sqrt{2} ^{2} )}$ = $\sqrt{68 - 32}$ = 6 units.

Because slant edges of length 10 units each is cut by a plane that is parallel to its base and 3 units above its base. So we have the other dementions of the small right square pyramid:

The height 3 units
A right square pyramid with base edges of length 4 $\sqrt{2}$

So the volume of it is:

V = 1/3 *3* 4 $\sqrt{2}$

= 32 $unit^{3}$

5 0

4 years ago