True or false? I need help.

Which best represent the simplified relative frequency of winning 9 out 15 games?

Liula [17]

Answer:

i think the answer is A

Step-by-step explanation:

9/15 simplified is 3/5

3 0

3 years ago

Read 2 more answers

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:

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

Learn more about integration here:

brainly.com/question/27988986

brainly.com/question/27805589

5 0

2 years ago

Will mark brainliest, most likely last one sorry.

Neko [114]

Answer:

Step-by-step explanation:

Rational numbers Irrational numbers

3√25 5.15603418923......

-11/151 √141

____

1.1625

√256

Irrational numbers are numbers that doesn't terminate and doesn't repeat.

Rational numbers are numbers that can be written in p/q form

6 0

3 years ago

Zuhalie needs to rent a racing bike. She is choosing between two rental options. Option A is $50 per month with a $200 down paym

Law Incorporation [45]

Answer:

Step-by-step explanation:

Given:

Option a:

Down payment, Da = $200

Monthly fee, Ma = $50

Option B:

Down payment, Db = $500

Monthly fee, Mb = $25

Monthly fee, M = payment, P/number of months, n

Total cost, Pc = down payment, D + payment, P

Equating both options we have:

500 + 25 × n = 200 + 50 × n

500 + 25n = 200 + 50 n

25n = 300

n = 300/25

= 12 months

At 12 months, both payment options will be the same.

7 0

4 years ago

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A peach pie is divided into eight equal slices

hjlf

There would be 35 calories in each slice of pie. All you have to do is divide the total number of calories (280) by the number of slices (8) and you find out there are 35 calories in each piece

4 0

4 years ago