Ask question

Ask question

All categories

3 years ago

8

How many ways are there to select 25 books from a collection of 27 books? i am just studying today

1 answer:

laiz [17]3 years ago

4 0

notice, this will just be a Permutation.

$\bf _nP_r=\cfrac{n!}{(n-r)!}\qquad \qquad \stackrel{\textit{25 books off a total of 27}}{_{27}P_{25}=\cfrac{27!}{(27-25)!}} \\\\\\ _{27}P_{25}=\cfrac{27!}{2!}\implies 5444434725209176080384000000$

you can always check your calculator also for a [ ₙPᵣ ] button.

You might be interested in

You don't have a driver's license yet, so you have to walk to the store. You can walk 1.5 miles in 24 minutes. If it

stich3 [128]

2,000 that how long it is

3 0

3 years ago

If the radius of a circle is 10 feet, how long is the arc subtended by an angle measuring 81°?

mihalych1998 [28]

Circumference of entire circle = 2 * PI * 10
circumference of entire circle = <span> <span> <span> 62.832 feet
81 degrees is (9/40) of a circle
62.832 * </span></span></span><span>(9/40) = </span> <span> <span> <span> 14.1372 </span> </span> </span>

Source:
http://www.1728.org/radians.htm

4 0

3 years ago

The product of 8 and the sum of a number x and 3

Olin [163]

Answer:

8(x+3)

Step-by-step explanation:

thats the answer

7 0

3 years ago

Read 2 more answers

Evaluate using integration by parts

PolarNik [594]

Rather than carrying out IBP several times, let's establish a more general result. Let

$I(n)=\displaystyle\int x^ne^x\,\mathrm dx$

One round of IBP, setting

$u=x^n\implies\mathrm du=nx^{n-1}\,\mathrm dx$

$\mathrm dv=e^x\,\mathrm dx\implies v=e^x$

gives

$\displaystyle I(n)=x^ne^x-n\int x^{n-1}e^x\,\mathrm dx$

$I(n)=x^ne^x-nI(n-1)$

This is called a power-reduction formula. We could try solving for $I(n)$ explicitly, but no need. $n=5$ is small enough to just expand $I(5)$ as much as we need to.

$I(5)=x^5e^x-5I(4)$

$I(5)=x^5e^x-5(x^4e^x-4I(3))=(x-5)x^4e^x+20I(3)$

$I(5)=(x-5)x^4e^x+20(x^3e^x-3I(2))=(x^2-5x+20)x^3e^x-60I(2)$

$I(5)=(x^2-5x+20)x^3e^x-60(x^2e^x-2I(1))=(x^3-5x^2+20x-60)x^2e^x+120I(1)$

$I(5)=(x^3-5x^2+20x-60)x^2e^x+120(xe^x-I(0))$

Finally,

$I(0)=\displaystyle\int e^x\,\mathrm dx=e^x+C$

so we end up with

$I(5)=(x^4-5x^3+20x^2-60x+120)xe^x-120e^x+C$

$I(5)=(x^5-5x^4+20x^3-60x^2+120x-120)e^x+C$

and the antiderivative is

$\displaystyle\int2x^5e^x\,\mathrm dx=(2x^5-10x^4+40x^3-120x^2+240x-240)e^x+C$

8 0

3 years ago

A slug travels 3 centimeters in 3 seconds. A snail travels 6 centimeters in 6 seconds. Both travel at constant speeds. Mai says,

ollegr [7]

Answer:

Mai is wrong since both travel the same distance in the same amount of seconds

Step-by-step explanation:

3 centimeters in 3 seconds is 1 centimeter a second for the slug

6 centimeters in 6 seconds is 1 centimeter a second for the snail

so both travel the same distance

5 0

3 years ago

Read 2 more answers