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Ymorist [56]
3 years ago
7

Jane has several legal documents to type. Jane completes an average of 7 documents per 15 minutes. Her completion of one documen

t is independent of any other one.
a) Let N be the number of documents Jane completes between 9:00am and 10:00am. What are the distribution, parameter(s), and support of N?
b) Determine the probability that Jane completes 30 documents between 9:00am and 10:00am.
c) What is the probability that Jane completes 58 documents between 2:00pm and 4:00pm.
d) Determine the probability that Jane completes 30 documents between 9:00am and 10:00am and 40 documents between 1:00pm and 2:30pm.
e) What is the standard deviation for the number of documents Jane will complete between 3:00pm and 5:45pm?
f) If Jane is paid at a rate of 1 dollar and 25 cents per document how much can she expect to make for a day in which she has 6 and a half hours of straight typing?

Mathematics
1 answer:
liq [111]3 years ago
8 0

Answer:

Step-by-step explanation:

check the attachments below for step by step solution

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Stells [14]

let's recall that there are 180° in π radians, thus


\bf \begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ -36&x \end{array}\implies \cfrac{180}{-36}=\cfrac{\pi }{x}\implies -5=\cfrac{\pi }{x}\implies x=\cfrac{\pi }{-5}\implies x=-\cfrac{\pi }{5}

4 0
4 years ago
Evaluate the surface integral:S
rjkz [21]
Assuming S does not include the plane z=0, we can parameterize the region in spherical coordinates using

\mathbf r(u,v)=\left\langle3\cos u\sin v,3\sin u\sin v,3\cos v\right\rangle

where 0\le u\le2\pi and 0\le v\le\dfrac\pi/2. We then have

x^2+y^2=9\cos^2u\sin^2v+9\sin^2u\sin^2v=9\sin^2v
(x^2+y^2)=9\sin^2v(3\cos v)=27\sin^2v\cos v

Then the surface integral is equivalent to

\displaystyle\iint_S(x^2+y^2)z\,\mathrm dS=27\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^2v\cos v\left\|\frac{\partial\mathbf r(u,v)}{\partial u}\times \frac{\partial\mathbf r(u,v)}{\partial u}\right\|\,\mathrm dv\,\mathrm du

We have

\dfrac{\partial\mathbf r(u,v)}{\partial u}=\langle-3\sin u\sin v,3\cos u\sin v,0\rangle
\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle3\cos u\cos v,3\sin u\cos v,-3\sin v\rangle
\implies\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle-9\cos u\sin^2v,-9\sin u\sin^2v,-9\cos v\sin v\rangle
\implies\left\|\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}\|=9\sin v

So the surface integral is equivalent to

\displaystyle243\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv\,\mathrm du
=\displaystyle486\pi\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv
=\displaystyle486\pi\int_{w=0}^{w=1}w^3\,\mathrm dw

where w=\sin v\implies\mathrm dw=\cos v\,\mathrm dv.

=\dfrac{243}2\pi w^4\bigg|_{w=0}^{w=1}
=\dfrac{243}2\pi
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SVETLANKA909090 [29]

Answer:

2

Step-by-step explanation:

to find slope use the equation-

y2-y1 / x2 - x1

then plug in your points

13-7 / 6-3

13-7 = 6

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6/3 = 2

hope this helped :)

5 0
3 years ago
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