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ipn [44]
3 years ago
9

(Second time asking this please help) A multiple choice question has 6 options. What is the percentage of getting the answer cor

rect ? Can you write the answer as a ratio too?
Mathematics
2 answers:
Ainat [17]3 years ago
7 0

Answer:

⅙

Step-by-step explanation:

Out of 6 options, 1 is correct

P(correct) = ⅙

igomit [66]3 years ago
5 0

Answer:

A multiple choice question with 6 options will have a 16.7% chance of getting the answer correct, and a ratio of 1:6.

Step-by-step explanation:

You have a 1 in 6 chance of getting the answer correct, which can be represented with the fraction \frac{1}{6} .

To get a percentage, simply divide the 1 by the 6 and you will get an answer of 0.16666667. Multiply this by 100 and you have your answer.

To get a ratio, convert the fraction to a ratio making the left side of the ratio the numerator (the 1)  and the right side the denominator (the 6).

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Let f be defined by the function f(x) = 1/(x^2+9)
riadik2000 [5.3K]

(a)

\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}

Substitute <em>x</em> = 3 tan(<em>t</em> ) and d<em>x</em> = 3 sec²(<em>t </em>) d<em>t</em> :

\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt

=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}

(b) The series

\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}

converges by comparison to the convergent <em>p</em>-series,

\displaystyle\sum_{n=3}^\infty\frac1{n^2}

(c) The series

\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}

converges absolutely, since

\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}

That is, ∑ (-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ converges absolutely because ∑ |(-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ| = ∑ (<em>n</em> ² + 9)/<em>e</em>ⁿ in turn converges by comparison to a geometric series.

5 0
3 years ago
I need help with this i really dont understand it. :)
nikdorinn [45]

Answer:

see explanation

Step-by-step explanation:

Given 2 sides of a triangle then the third side x is in the range

difference of 2 sides < x < sum of 2 sides

(11)

given 2 sides 2, 6 , then

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(12)

Given 2 sides 4, 12 , then

12 - 4 < x < 12 + 4

8 < x < 16

(13)

Given 2 sides 2, 11 , then

11 - 2 < x < 11 + 2

9 < x < 13

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3 years ago
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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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