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nalin [4]
3 years ago
11

Suppose that IQ scores have a bell-shaped distribution with a mean of 104 and a standard deviation of 17. Using the empirical ru

le, what percentage of IQ scores are between 87 and 121
Mathematics
1 answer:
Shalnov [3]3 years ago
4 0

Answer:

By the Empirical Rule, 68% of IQ scores are between 87 and 121

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 104

Standard deviation = 17

Using the empirical rule, what percentage of IQ scores are between 87 and 121

87 = 104 - 1*17

So 87 is one standard deviation below the mean

121 = 104 + 1*17

So 121 is one standard deviation above the mean

By the Empirical Rule, 68% of IQ scores are between 87 and 121

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(a) Find an angle between 0 and 2π that is coterminal with −19π10.
Katarina [22]

Answer:

\dfrac{\pi}{10}.

Step-by-step explanation:

All coterminal angles of an angle \theta are defined as

\theta +2n\pi or \theta + n360^{\circ}

where, n is an integer.

The given angle is

\theta=-\dfrac{19\pi}{10}

So, all coterminal angles of an angle \theta are

-\dfrac{19\pi}{10}+2n\pi

For n=1,

\Rightarrow -\dfrac{19\pi}{10}+2(1)\pi

\Rightarrow -\dfrac{19\pi}{10}+2\pi

\Rightarrow \dfrac{-19\pi+20\pi}{10}

\Rightarrow \dfrac{1\pi}{10}

Since,  \dfrac{\pi}{10}  between 0 and 2π, therefore,  the required coterminal angle is \dfrac{\pi}{10}.

6 0
2 years ago
Find the area of the composite figure to the nearest hundredth.
Lyrx [107]

Answer:

745.31

Step-by-step explanation:

1.  12.5^2 * 2 = 312.5

2. (3,14 * 156,25)/2 = 245.31

3.  (30 * 12.5)/2 = 187.5

4. 187.5 + 245.31 + 312.5 = 745.31

4 0
3 years ago
∫(cosx) / (sin²x) dx
kirza4 [7]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2822772

_______________


Evaluate the indefinite integral:

\mathsf{\displaystyle\int\! \frac{cos\,x}{sin^2\,x}\,dx}\\\\\\
=\mathsf{\displaystyle\int\! \frac{1}{(sin\,x)^2}\cdot cos\,x\,dx\qquad\quad(i)}


Make the following substitution:

\mathsf{sin\,x=u\quad\Rightarrow\quad cos\,x\,dx=du}


and then, the integral (i) becomes

=\mathsf{\displaystyle\int\! \frac{1}{u^2}\,du}\\\\\\
=\mathsf{\displaystyle\int\! u^{-2}\,du}


Integrate it by applying the power rule:

\mathsf{=\dfrac{u^{-2+1}}{-2+1}+C}\\\\\\
\mathsf{=\dfrac{u^{-1}}{-1}+C}\\\\\\
\mathsf{=-\,\dfrac{1}{u}+C}


Now, substitute back for u = sin x, so the result is given in terms of x:

\mathsf{=-\,\dfrac{1}{sin\,x}+C}\\\\\\
\mathsf{=-\,csc\,x+C}


\therefore~~\boxed{\begin{array}{c}\mathsf{\displaystyle\int\! \frac{cos\,x}{sin^2\,x}\,dx=-\,csc\,x+C} \end{array}}\qquad\quad\checkmark


I hope this helps. =)


Tags:  <em>indefinite integral substitution trigonometric trig function sine cosine cosecant sin cos csc differential integral calculus</em>

5 0
3 years ago
Natalie just rented an apartment for $900 a month. She was told that the rent will increase 5.5% each year. About how much will
belka [17]
$1246. 

<span>This is a guess, though.</span>
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3 years ago
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Sometimes it’s alright . It’s awful when some one robs you of points by writing a b.s answer
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