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maxonik [38]
3 years ago
7

A bag contains 17 cards numbered 1 through 17 . a card is randomly chosen from the bag. what is the probability that the card ha

s an even number on it? write your answer as a fraction in simplest form.
Mathematics
2 answers:
SVETLANKA909090 [29]3 years ago
7 0

Probability of choosing a card that has an even number on it = \frac{8}{17}

<em><u>Explanation </u></em>

<u>Cards:</u> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

There are total 17 cards and we are choosing only one card randomly which has even number on it.

<em>The even number cards are: </em>2 4 6 8 10 12 14 16

That means there are total 8 even number cards.

So, Probability of choosing a card that has an even number on it = \frac{8}{17}

Strike441 [17]3 years ago
6 0
Solution:

Even number:
2, 4, 6, 8, 10, 12, 14, 16
TOTAL: 8

Therefore,
Probability = 8/17
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Answer:

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

Step-by-step explanation:

<u>Fundamental Theorem of Calculus</u>

\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 <u>constant of integration</u>.

<u>Given integral</u>:

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

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\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

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Use <u>Integration by Substitution</u>:

\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

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