Use the binomial formula to find the coefficient of the q^4 p^17
term in the expansion of (29+p)^21

Answers

Answer 1

Recal the binomial theorem:

[tex]\displaystyle (a+b)^n = \sum_{k=0}^n \binom nk a^{n-k} b^k[/tex]

Then

[tex]\displaystyle (2q+p)^{21} = \sum_{k=0}^{21} \binom{21}k (2q)^{21-k} p^k = \sum_{k=0}^{21} \binom{21}k 2^{21-k} q^{21-k} p^k[/tex]

We get the q⁴p¹⁷ term when k = 17, and its coefficient would be

[tex]\dbinom{21}{17} 2^{21-17} = \dfrac{21!}{17!(21-17)!} 2^4 = \dfrac{21\cdot20\cdot19\cdot18}{4\cdot3\cdot2\cdot1}\cdot2^4 = \boxed{95,760}[/tex]


Related Questions

A restaurant keeps eggs in a rack that has 5 layers each layer has 5 row with 5 eggs in each row

Answers

What are you asking?
5 Layers
5 Rows in each layer
5 in each row
25+25+25+25+25=125

What is 2 hundredths in standard form in fifth grade

Answers

0.02

0._ is tenths and

0.0_ is hundredths

Answer:

Step-by-step explanation:

5th Grade Math 1.2, Place Value of Whole Numbers, Standard Form ... this is the name of the  video. I hope it helps.

Order from greatest to least: 3.008,3.825,3.09,3.18

Answers

Answer:

G: 3.825

3.18

3.09

L: 3.008

Step-by-step explanation:

G is greatest, L is least.

Hope this helps!

Find the surface area! Please I need it quick

Answers

Step-by-step explanation:

We first find the area of a trapezium and rectangular faceFourmula to find the are of a trapezium is:Area=1/2*(B+b)*h =1/2*3.7*1.9 =3.515m²Since every rectangular face is different we gotta find each of them

Area1=4.8*2.1 =10.08 m²Area2=4.8*1.4=6.72m²Area3=4.8*2.3=11.05m²Area4=4.8*1.9=9.12m²

Now we find the area of the whole prismArea=3.515*2+10.08+6.72+11.05+9.12Area=44m²

Sorry my wireless went down!!!Hope this helps and you already know what I would like to get

how to solve this.im stuck in this question for 20 mins. Plzz answer

Answers

Answer:

Find the minimum or maximum value of the function g (I) = -3x^2 - 6x + 5. Describe the domain and range of the function, and where the function is increasing and decreasing. > -1 all real numbers The function The maximum value is I < 0 The domain is and the range is right of I left -1 is increasing to the of I= and decreasing to the 0 12 :: yo y0 :: 8 :: IS-1 :: -1 :: 0 :: I> 0 :: 1 :: 8 :: < 0 :: left :: all real numbers :: y -8 :: y < 8 :: y8​

Step-by-step explanation:

Lin is baking cakes. Each cake needs 34 cup of brown sugar, and Lin uses 412 cups of brown sugar for the entire batch of cakes. How many cakes does Lin bake?

Answers

Answer:

12

Step-by-step explanation:

412 ÷ 34 = 12.1176...

Round down to 12 cakes

If  Each cake needs 34 cup of brown sugar, and Lin uses 412 cups of brown sugar for the entire batch of cakes then Lin can bae 12 cakes.

What is Division?

A division is a process of splitting a specific amount into equal parts.

Given that Lin is baking cakes. Each cake needs 34 cup of brown suga

Lin uses 412 cups of brown sugar for the entire batch of cakes

We need to find the number of cakes Lin bake with 412 cups of brown sugar.

To find this we have to divide 412 by 34 cup.

412/34

Four hundred twelve by thirty four

12.111

Hence, if  Each cake needs 34 cup of brown sugar, and Lin uses 412 cups of brown sugar for the entire batch of cakes then Lin can bae 12 cakes.

To learn more on Division click:

https://brainly.com/question/21416852

#SPJ2

PLS HELP WILL MARK BRAINLIEST!

Answers

Answer:

10 adults

Step-by-step explanation:

Convert 50 kg into pounds:

50*2.2 = 110 lbs

Number of adults the elevator can take:

1200 / 110 = 10 (rounded down)

Answer:

The Elevator can hold 10 adults

Step-by-step explanation:

Step 1- Convert kg to lbs to get 110lbs

Step 2- Divide 1200 (the elevators max compacity) by 110 to get 10

Step 3- The elevator can hold 10 adults

-Rocketgamer360


Daniel is a piano teacher. He charges the same amount, s, for every teaching session. After 19 sessions, he has earned $1,235. How much does Daniel charge for 1 teaching session? Write a division equation.​

Answers

Answer:

£65

Step-by-step explanation:

1235 / 19 = 65

(Meeting character limit)

giving Brainliest to whoever answer both

Answers

A.

1. Yes
2. No
3. Yes

B.

1. Yes
2. No
3. No

Justine and Kate are training for a race.
At every training session Justine runs x miles and Kate runs 3 more miles than Justine.
In one week, Justine and Kate both train every day.
In the 7 days they run 63 miles in total between them.
How many miles do Justine and Kate each run per day?

Answers

Answer:

Justine runs 3 miles a day and Kate runs 6 miles a day.

Step-by-step explanation:

x = number of miles ran in a day

x(7) + (x+3)(7) = 63

7x + 7x + 21 = 63

14x + 21 = 63

14x = 42

x = 3

3 + 3 = 6

Justine runs 3 miles a day and Kate runs 6 miles a day.

Please help me! :D <3

Answers

Answer:

Well 5 times 1 is 2.5 which can't be and integer

so I looked it up an this is what I got How do you write 2.5 as an integer?

If this is the question, then Integer-Part[2.5] = 2, and the Fractional-Part[2.5] = . 5.

I would put 3 it because 2.5 as a hole number is 3

Step-by-step explanation:

YALL I RLLY DONT KNOW HOW I HAVE 13 OVERDUE ASSIGNMENTS BUT PLEASE HELPING ME JUST ON MATH would make my day....

Answers

Answer:

Should be second option: (-6.5,-3.5)

The actual coordinates are (-6.4,-3.6) but the points are rounded.

Step-by-step explanation:

Since these two lines are both in slope-intercept form, all you have to do is graph them, and what ever point they cross each other at, is the solution to this system of equations. (Hint: you can also go online and search desmos graphing calculator, to see how it's graphed, for additional help).

(I've graphed and labeled them for you above btw⤴⤴⤴)

Hope this helps you :)

HELPPP!!!! Both questions are incredibly confusing to me !!!!!

Answers

Answer:

Step-by-step explanation:

I'm going to start with problem 3. You need to become familar with the kind of tricks teachers play on you.

Problem 3 depends on getting RS = RW.

RT = RT                                    Reflexive property

<STR = <WTR                           A straight line having 1 rt angle  actually has 2

ST = TU                                    They are marked as equal

Triangle STR=Triangle WTR    SAS

RS = RW                                    Corresponding parts of = triangles are =

8x = 6x + 5                                Subtract 6x from both sides

8x -6x = 6x - 6x + 5                   Combine

2x = 5                                         Divide by 2

2x/2 = 5/2

x = 2.5

RU = 6*2.5 + 5

RU = 15 + 5

RU = 20

Now we can play with Question 4.

This question depends on the method used in three, although not entirely.

What you need to know is that W is on RT when you take a ruler and make RT longer. You can put W anywhere as long as it is on RT when it is made longer.

Directions

Make RT longer. Draw down and to your right.

Put a point anywhere on the length starting at T. Label this new point as W. There's your W. It goes anywhere on the part of RT made longer.

Draw UW.

Label UW as 8

Now draw another line from S to W. Guess what? By the methods used in question 3, it's also 8. So SW = 8

TW = TW                        Reflexive

<UTW = STW                 Same reason as in 3. UtW is a right angle

UT = ST                          Given (the marking tells you so.

ΔUTW = ΔSTW              SAS

UW = SW                       Corresponding parts of = triangles are =

SW  = 8

Please help me with this question. I don't think I understand it. Quadratic functions graphing #15-19.

Will pick brainliest answer, thank you :)

Answers

Answer:

15) (1, 1) and (-1, 1)

16) (1, 2) and (-1, 2)

17 (1,1/2) and (-1, 1/2)

18) (1,1/4) and (-1, 1/4)

19) 16 is vertical stretch, 17 and 18 is vertical compressed

Step-by-step explanation:

for qs 15-18 since x is 1 or -1 if you sq 1 or -1 you will always get 1

so y is the "a" value in the equation  y=ax²

for qs 19

y=ax²

so if a>1 -- then vertical stretch

when 0<a<1 -- then vertical compressed

   

someone please help meeeee! I don't know what the solution is!

Answers

Answer:

(2,4)

Step-by-step explanation:

Answer:  

(2,4)

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation

Noah earns $9.65 per hour. How much will he
earn next week if he works 18 hours?

Answers

Answer:

$1215.90

Step-by-step explanation

You take Noah's pay per hour of $9.65 then multiply it by how many hours he works 18. You then take that and multiply it by 7 for the days of the week.

Janelle came to bat 464 times in 131 games. At this rate, how many times should she expect to have at bat in a full season of 162 games?

Answers

The rate at which she bats is an illustration of ratio and proportions

She's expected to bat 574 times in 162 games

In 131 games, she bat 464 times

Represent this as a ratio

[tex]\mathbf{Ratio = 131 : 464}[/tex]

Let the number of times she bat in 162 games be represented with x.

So, the ratio is represented as:

[tex]\mathbf{Ratio = 162 : x}[/tex]

Equate both ratios

[tex]\mathbf{162 : x = 131 : 464}[/tex]

Express as fractions

[tex]\mathbf{\frac{x}{162 }= \frac{464}{131 }}[/tex]

Multiply both sides by 162

[tex]\mathbf{x= \frac{464}{131 } \times 162}[/tex]

Multiply

[tex]\mathbf{x= \frac{75168}{131 } }[/tex]

Divide

[tex]\mathbf{x= 574}[/tex]

Hence, she's expected to bat 574 times in 162 games

Read more about ratios and proportions at:

https://brainly.com/question/7810782

Find the value of h and k.

Answers

Answer:

  h = 6, k = 6.5

Step-by-step explanation:

The segment marked h is half the length of the one marked 3h-6.

  2h = 3h -6

  6 = h . . . . . . . add 6-2h

__

The segment marked k is half the length of the one marked 2h+1.

  2k = 2(6) +1

  k = 13/2 = 6.5 . . . . divide by 2

The values of h and k are 6 and 6.5, respectively.

if g(x)=x^2+2x, find g(-6)

Answers

Answer:

-6/2+2×(-6)

-3+(-12)

-3-12

-15

find the lowest common multiple of: 10 ,15 and 18​

Answers

Answer:

90

Step-by-step explanation:

a drink in japan costs 374 yen. The exchange rate is £1 = 189 yen. What is the cost in pounds

Answers

Answer:

Roughly £2

Step-by-step explanation:

multiply the echange rate by 2 , its 378Yen

find meh x pls 10 points Uwu
−5/6=−1/4−7/10x

Answers

answer is 5/6

Step-by-step explanation:

multiplying by 60, we get,

50=15+42x

we can simplify it, 42x= 35,or x=5/6

X=-5/6
Gotta find a LCD then times both asides by it then solve!

What is the slope of the line?
y-4=-7(x-6)

Answers

Answer:  −7

Step-by-step explanation:

use a point on the number line to represent a number ot whose absulute vaue is?

Answers

Answer:

A

Step-by-step explanation:

Please anyone I’m desperate

Answers

Answer:

the answer is B) 12a+6b

Step-by-step explanation:

3+9=12 so 3a+9a=12a,

7-1=6 so 7b-(1)b=6b

Step-by-step explanation:

calm down ! just breathe.

these are totally simple additions and one also very simple subtraction to make.

you know that you can combine terms based on the same variable, right ?

3a + 9a = 12a

7b - b = 6b

the result is then

12a + 6b, so B is the right answer.

this bases already on the same principle of actual numbers.

2×3 + 5×3 = 7×3 because this is also

(2 + 5) × 3

or

6×5 + 6×3 = 6×8 because this is also

6 × (5 + 3)

or

7×8 - 4×8 = 3×8 because this is also

(7 - 4) × 8

and so on.

Given a circle with radius 5cm and using π=3.14 calculate it's circumference (I will make you Brainliest)​

Answers

Answer:

Circumference = 31.4 feet

Area= 78.5 sq. feet.

Step-by-step explanation:

brainliest please?????

what is the answer ?????​

Answers

As the second decimal place is 4. According to round of law the number less than 5 decreases. SO, THE answer is 1.04Benny weight = 48 ; David weight = 60.

Difference = 60 - 48 = 12

Percentage = [tex] \frac{12}{60} \times 100 = \frac{12}{3} \times 5 = 4 \times 5 = 20\% \\ [/tex]

Calculate the frequency of a wave with a speed of 250m/s and a wavelength of 50m.


HELPPPPPPPPPPPPPPPPPPPPPPPP PLS

Answers

Answer:

formulas

frequency=speed/wavelength

f=250/50

f=50hz

what is 400x800 do any one knows

Answers

Answer:

Step-by-step explanation:

320000 is your answer


- take off the zeros
-4x8= 32
-add the zeros back on
Answer=320,000

A piano teacher gives lessons that are each Three-fourths hour long. How many piano lessons can the teacher fit into a 12-hour work day? Assume no breaks are taken in the 12 hour period.
6
9
11
16

Answers

Answer:

26.6666666667

Step-by-step explanation:

3/4 of a hour is 45 minutes 12 ÷ by 0.45 would equal 26.6666666667

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