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2 years ago

What is the 8th term of the binomial expansion (x + y)10?

Mathematics

1 answer:

12345 [234]2 years ago

4 0

We can use the Pascal's Triangle to solve this problem. This pascal's triangle is shown in the figure below. To build the triangle, begin with the number 1 at the top, then continue placing numbers below it in a triangular pattern. In this way, each number are the numbers directly above added together. So, the expression:

$(x+y)^{10}$

Can be extended as follows, for n = 10:

$(x+y)^{10}=x^{10}+10x^{9}y+45x^{8}y^2+120x^{7}y^3+210x^{6}y^4+252x^{5}y^5+210x^{4}y^6+120x^{3}y^7+45x^{2}y^8+10xy^9+y^{10}$

So, the 8th term of the binomial expansion is:

$120x^{3}y^7$

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James is the manager at an entertainment arena that draws an average 7,000 patrons per event. Each ticket taker can process 350

Elina [12.6K]

Answer:

No. James didn't have enough ticket takers to process the average number of patrons hat usually attend the events.

He need to hire 2 more ticket taker (i.e 20 ticket takers) in order to process the average number of patrons hat usually attend the events.

Step-by-step explanation:

Given:

Average amount of patron per event= 7000

Each ticket taker can process = 350

Number of ticket takers hired = 18

We need to find the whether he hire enough to process the average number of patrons that usually attend the events.

Solution:

We will find the Average amount of patron ticket takers can process.

Now we can say that

Average amount of patron ticket takers can process is equal to Each ticket taker can process multiplied by Number of ticket takers hired.

framing in equation form we get;

Average amount of patron ticket takers can process = $350 \times 18 = 6300\ patrons$

Hence With the required hires James cannot fully process the patrons usually attending the event.

To find how many ticket takers required we will divide average number of patrons with Each ticket taker can process.

framing in equation form we get;

ticket takers required = $\frac{7000}{350}=20$

hence In order t process the the average number of patrons that usually attend the events James will require 20 ticket takers.

6 0

2 years ago

Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D = {(x, y) |

Bas_tet [7]

Answer:

$M=168k$

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

Step-by-step explanation:

Let's begin with the mass definition in terms of density.

$M=\int\int \rho dA$

Now, we know the limits of the integrals of x and y, and also know that ρ = ky², so we will have:

$M=\int^{9}_{1}\int^{4}_{1}ky^{2} dydx$

Let's solve this integral:

$M=k\int^{9}_{1}\frac{y^{3}}{3}|^{4}_{1}dx$

$M=k\int^{9}_{1}21dx$

$M=21k\int^{9}_{1}dx=21k*x|^{9}_{1}$

So the mass will be:

$M=21k*8=168k$

Now we need to find the x-coordinate of the center of mass.

$\bar{x}=\frac{1}{M}\int\int x*\rho dydx$

$\bar{x}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}x*ky^{2} dydx$

$\bar{x}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}x*y^{2} dydx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*\frac{y^{3}}{3}|^{4}_{1}dx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*21 dx$

$\bar{x}=\frac{21}{168}\frac{x^{2}}{2}|^{9}_{1}$

$\bar{x}=\frac{21}{168}*40=5$

Now we need to find the y-coordinate of the center of mass.

$\bar{y}=\frac{1}{M}\int\int y*\rho dydx$

$\bar{y}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}y*ky^{2} dydx$

$\bar{y}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}y^{3} dydx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{y^{4}}{4}|^{4}_{1}dx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{255}{4}dx$

$\bar{y}=\frac{255}{672}\int^{9}_{1}dx$

$\bar{y}=\frac{255}{672}8=\frac{2040}{672}$

$\bar{y}=\frac{85}{28}$

Therefore the center of mass is:

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

I hope it helps you!

3 0

2 years ago

a ball bounces from a height of 2 metres and returns to 80% of its previous height on each bounce. find the total distance trave

Levart [38]

The solution to the problem is as follows:

We have 2+.8(2) + .8(.8(2)) + .8(.8(.8(2))) + ... =

2( .8^0 + .8^1 + .8^2 + .8^3 + ... ) =

2(.8^n -1) / (.8-1) . As n-->infinity, .8^n-->0 giving us

<span>2(-1)/(-.2) = 2(5) = 10 meters.
</span>

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

5 0

2 years ago

Read 2 more answers

Nico and Albert are finishing up a science project. They measured the length in inches of three insects. They also found the ave

atroni [7]

Answer:

Step-by-step explanation:

Given the length of the bugs as shown;

Lady bug = 3/8

Ant = 1/4

Firefly = 7/8

Honey bee = 0.8

Deer tick = 0.2

Before we arrange the length in ascending order (shortest to longest), we will have to represent them in percentage.

Lady bug = 3/8×100

= 300/8

= 37.5%

Ant = 1/4×100

Ant = 25%

Firefly = 7/8 × 100

Firefly = 87.5%

Honey bee = 0.8×100

Honey bee = 80%

Deer tick = 0.2×100

Deer tick = 20%

On rearranging in ascending order:

20%, 25%, 37.5%, 80%, 87.5%

Based on the insect

Deer tick, Ant, ladybug, honey bee, Firefly

Based on their length:

0.2, 1/4, 3/8, 0.8, 7/8

5 0

2 years ago

Read 2 more answers

Ann took a taxi home from the airport. The taxi fare was \$2.10$2.10dollar sign, 2, point, 10 per mile, and she gave the driver

Studentka2010 [4]

Answer:

$2.10x+5=49.10$

Distance = 21 miles.

Step-by-step explanation:

Let x be the distance in miles between the airport and Ann's home.

We have been given that Ann took a taxi home from the airport. The taxi fare was $2.10 per mile. So fare for x miles will be 2.10x.

We are also told that she gave the driver a tip of $5. Ann paid a total of $49.10. This means that fare of x miles and tip given to driver equals $49.10. We can represent this information in an equation as:

$2.10x+5=49.10$

Now let us solve our equation.

$2.10x=49.10-5$

$2.10x=44.10$

$x=\frac{44.10}{2.10}=21$

Therefore, the equation $2.10x+5=49.10$ represents the distance in miles between the airport and Ann's home and distance between Ann's home and airport in 21 miles.

3 0

2 years ago

Read 2 more answers