All categories

3 years ago

What is the central limit theorem?

1 answer:

3 0

°°°In mathematical terms, the central limit theorem is the theory of statistical regularity that under general conditions the average data observed over time tends to be distributed as a normal distribution.

↑ ↑ ↑ Hope this helps! :D

You might be interested in

Here’s another one thank u all for helping me. I really appreciate it!

nikdorinn [45]

Answer:

628 feet..............

6 0

3 years ago

. Evaluate each of the following without using a calculator. Show all steps clearly. - 5^2

Verizon [17]

Answer:

Step-by-step explanation:

-5^2 expanded is -5 x -5

- two negatives equal a positive

-visual representation of 5 x 5

O O O O O

7 0

2 years ago

Let f(x) = 1/x^2 (a) Use the definition of the derivatve to find f'(x). (b) Find the equation of the tangent line at x=2

Verdich [7]

Answer:

(a) $f'(x)=-\frac{2}{x^3}$

(b) $y=-0.25x+0.75$

Step-by-step explanation:

The given function is

$f(x)=\frac{1}{x^2}$ .... (1)

According to the first principle of the derivative,

$f'(x)=lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{\frac{1}{(x+h)^2}-\frac{1}{x^2}}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{\frac{x^2-(x+h)^2}{x^2(x+h)^2}}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{x^2-x^2-2xh-h^2}{hx^2(x+h)^2}$

$f'(x)=lim_{h\rightarrow 0}\frac{-2xh-h^2}{hx^2(x+h)^2}$

$f'(x)=lim_{h\rightarrow 0}\frac{-h(2x+h)}{hx^2(x+h)^2}$

Cancel out common factors.

$f'(x)=lim_{h\rightarrow 0}\frac{-(2x+h)}{x^2(x+h)^2}$

By applying limit, we get

$f'(x)=\frac{-(2x+0)}{x^2(x+0)^2}$

$f'(x)=\frac{-2x)}{x^4}$

$f'(x)=\frac{-2)}{x^3}$ .... (2)

Therefore $f'(x)=-\frac{2}{x^3}$ .

(b)

Put x=2, to find the y-coordinate of point of tangency.

$f(x)=\frac{1}{2^2}=\frac{1}{4}=0.25$

The coordinates of point of tangency are (2,0.25).

The slope of tangent at x=2 is

$m=(\frac{dy}{dx})_{x=2}=f'(x)_{x=2}$

Substitute x=2 in equation 2.

$f'(2)=\frac{-2}{(2)^3}=\frac{-2}{8}=\frac{-1}{4}=-0.25$

The slope of the tangent line at x=2 is -0.25.

The slope of tangent is -0.25 and the tangent passes through the point (2,0.25).

Using point slope form the equation of tangent is

$y-y_1=m(x-x_1)$

$y-0.25=-0.25(x-2)$

$y-0.25=-0.25x+0.5$

$y=-0.25x+0.5+0.25$

$y=-0.25x+0.75$

Therefore the equation of the tangent line at x=2 is y=-0.25x+0.75.

5 0

3 years ago

The length of a rectangle is 2 cm longer than its width if the perimetier of the rectangle is 44cm, find its area

Natasha2012 [34]

L=w+2 and 2w+2l=44

substitute equation for length in perimeter equation

2w+2(w+2)=44
2w+2w+4=44
4w+4=44
4w=40
w=10

substitute width into length equation to get length

l=10+2
l=12

a=lw
a=12*10
a=120 cm^2

7 0

3 years ago

Whats 600 divied by 300

kolbaska11 [484]

Answer:

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers