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kati45 [8]
3 years ago
14

A large university accepts 70​% of the students who apply. Of the students the university​ accepts, 45​% actually enroll. If 30

comma 000 students​ apply, how many actually​ enroll?
Mathematics
1 answer:
uysha [10]3 years ago
4 0

Answer: the number of students that actually enroll is 9450

Step-by-step explanation:

The large university accepts 70​% of the students who apply. If 30 comma 000 students​ apply, it means that the total number of students that applied is 30000 and the number of students accepted would be 70/100 × 30000 = 21000

Of the students that the university​ accepts, 45​% actually enroll. This means that the number of students that enrolled would be

45/100 × 21000 = 0.45×21000

= 9450

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Serggg [28]

I assume C has counterclockwise orientation when viewed from above.

By Stokes' theorem,

\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S

so we first compute the curl:

\vec F(x,y,z)=xy\,\vec\imath+yz\,\vec\jmath+xz\,\vec k

\implies\nabla\times\vec F(x,y,z)=-y\,\vec\imath-z\,\vec\jmath-x\,\vec k

Then parameterize S by

\vec r(u,v)=\cos u\sin v\,\vec\imath+\sin u\sin v\,\vec\jmath+\cos^2v\,\vec k

where the z-component is obtained from

1-(\cos u\sin v)^2-(\sin u\sin v)^2=1-\sin^2v=\cos^2v

with 0\le u\le\dfrac\pi2 and 0\le v\le\dfrac\pi2.

Take the normal vector to S to be

\vec r_v\times\vec r_u=2\cos u\cos v\sin^2v\,\vec\imath+\sin u\sin v\sin(2v)\,\vec\jmath+\cos v\sin v\,\vec k

Then the line integral is equal in value to the surface integral,

\displaystyle\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S

=\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}(-\sin u\sin v\,\vec\imath-\cos^2v\,\vec\jmath-\cos u\sin v\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm du\,\mathrm dv

=\displaystyle-\int_0^{\pi/2}\int_0^{\pi/2}\cos v\sin^2v(\cos u+2\cos^2v\sin u+\sin(2u)\sin v)\,\mathrm du\,\mathrm dv=\boxed{-\frac{17}{20}}

6 0
3 years ago
HELP ASAP PLS!!!
viva [34]
4p(x-4)-5
That is my answer I hope I’m right have a merry Christmas
5 0
2 years ago
The steps below show the incomplete solution to find the value of x for the equation
mafiozo [28]
Step 1: 6x - 2x - 5 = -6 + 21 
Step 2: 6x - 2x - 5 = 15 
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The next step would be to add 5 to both sides of the equation. 
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So after the next step you would have 4x = 20 

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7 0
3 years ago
Jason considered two similar televisions at a local electronics store. The generic version was based off the brand name and was
slavikrds [6]

Keywords:

<em>Variables, televisions, generic version, TV brand, dimensions </em>

For this case we have two televisions, one generic version and one brand. We know that the generic version represents \frac {2} {3}the size of the brand. We must define two variables that represent the dimensions of the brand TV, so we have:

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Dimensions of the generic TV:

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By clearing the variables we have:

x = 12 \frac {3} {2} = 18\\y = 24 \frac {3} {2} = 36

Thus, the dimensions of the brand TV are 18 inches by 36 inches

Answer:

 The dimensions of the brand TV are 18 inches by 36 inches

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2 years ago
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blagie [28]

Answer:

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Step-by-step explanation:

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hope it helped you:)

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3 years ago
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