3.2555555 as a fraction

Please help! What is the perimeter of Trapezoid? (ABCD) Answer and explanation please! <3

viktelen [127]

Answer:

are there any numbers around it?

4 0

3 years ago

Calculate the variance of the following set of data. 3, 33, 303, 233, 3, 73, 83, 63

andrew-mc [135]

Answer:

12083.929

Step-by-step explanation:

First step: find the mean of the data.

mean = 3+33+303+233+3+73+83+63

8

= 794

8

= 99.25

Second step: Now we calculate each dog's difference from the Mean.

Example : 3–99.25=96.25

Answer: (-96.25)+(-66.25)+203.75+133.75+(-96.25)+(-26.25)+(-16.25)+(36.25)

Third step: To calculate the Variance, take each difference, square it, and then average the result.

s² = (-96.25)²+(-66.25)²+203.75²+133.75²+(-96.25)²+(-26.25)²+(-16.25)²+(36.25)²

8–1

= 9264.063+4389.063+41514.063+17889.063+9264.063+689.063+264.063+1314.063

7

= 84587.5

7

= 12083.929

Variance Formula:

Variance = s² =Σ(xi− x )²

n−1

4 0

3 years ago

Read 2 more answers

CAN SOMEONE HELP ME!

Georgia [21]

Answer:

26

Step-by-step explanation:

5 × 4 = 20 (rectangle)

8-5 = 3 (triangle)

3×4÷2 = 6

20+6 = 26

4 0

3 years ago

Evaluate the following integral (Calculus 2) Please provide step by step explanation!

Step2247 [10]

Answer:

$\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=-\dfrac{2}{x+1}+\text{C}$

Step-by-step explanation:

Fundamental Theorem of Calculus

$\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))$

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given integral:

$\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x$

Factor the denominator:

$\begin{aligned}\implies x^2+2x+1 & = x^2+x+x+1\\& = x(x+1)+1(x+1)\\& = (x+1)(x+1)\\& = (x+1)^2\end{aligned}$

$\implies \displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=\int \dfrac{2}{(x+1)^2}\:\:\text{d}x$

$\textsf{Apply exponent rule} \quad \dfrac{1}{a^n}=a^{-n}$

$\implies \displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=\int 2(x+1)^{-2}\:\:\text{d}x$

$\boxed{\begin{minipage}{4 cm}\underline{Integrating $ax^n$}\\\\$\displaystyle \int ax^n\:\text{d}x=\dfrac{ax^{n+1}}{n+1}+\text{C}$\end{minipage}}$

Use Integration by Substitution:

$\textsf{Let }u=(x+1) \implies \dfrac{\text{d}u}{\text{d}x}=1 \implies \text{d}x=\text{d}u}$

Therefore:

$\begin{aligned}\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x & = \int 2(x+1)^{-2}\:\:\text{d}x\\\\& = \int 2u^{-2}\:\:\text{d}u\\\\& = \dfrac{2}{-1}u^{-2+1}+\text{C}\\\\& = -2u^{-1}+\text{C}\\\\& = -\dfrac{2}{u}+\text{C}\\\\& = -\dfrac{2}{x+1}+\text{C}\end{aligned}$