Let tk be the number of ways to choose k beads from a drawer that contains 10 red beads, 8 blue beads, and 11 green beads. Find the generating function for the sequence {tk} 29 k = 0. Do not find a formula for tk.

Answers

Answer 1

Answer:

[tex]\mathbf{G(x) = (1 + x)^{29}}[/tex]

Step-by-step explanation:

From the given information;

The total number of beads  = 10 + 8 + 11 = 29

To choose k beads out 29 beads, let assume that [tex]t_k[/tex] be the no. such that:

[tex]t_k = ( ^{29}_{k}) \ \ \ where; k =0,1,2,3,....,29[/tex]

The sequence [tex]\{ t_k\}^{29}_{k=0} = (^{29}_{k})[/tex]

The generating function for [tex]\{ a_k \}^n_{k=0}[/tex] is:

[tex]G(x) = a_o +a_1x +a_2x^2 +...+a_nx^n[/tex]

[tex]G(x) = \sum \limits ^{n}_{k=0} \ a_k x^k[/tex]

For the sequence above;

[tex]G(x) = \sum \limits ^{29}_{k =0 } (^{29}_{k}) x^k[/tex]

By applying binomial series [tex](1+x)^n = \sum \limits ^n_{k=0} ( ^n_k) x^k[/tex]

Thus:

[tex]\mathbf{G(x) = (1 + x)^{29}}[/tex]


Related Questions

how many rectangles from 18 square boxes

Answers

Answer:

9 rectangles

Step-by-step explanation:

two squares form a rectangle.

18 ÷ 2 = 9

Player 1 and player 2 are running laps around a field. Player 1 runs 1 lap every 4 ​minutes, while player 2 runs 1 lap every 15 minutes. If player 1 and player 2 begin their run at the same time and location on the​ field, in how many minutes will they meet to begin their next lap​ together?

Answers

Answer:

15 min

Step-by-step explanation:

if it takes Player 1 one min he will meet player two at there second lap after 15 min

If player 1 and player 2 begin their run at the same time and location on the​ field, In 60 minutes will they meet to begin their next lap​ together.

What is LCM?

The LCM of any two is the value that is evenly divisible by the two given numbers.

Given,

Player 1 and player 2 are running laps around a field

Player 1 runs 1 lap every 4 ​minutes,

player 2 runs 1 lap every 15 minutes

We need to find  in how many minutes will they meet to begin their next lap​ together

We need to find the LCM of 4 and 15 to find the answer

4: 4, 8,12,16, 20,24,28,32,36,40,44,48,52,56,60

15: 15,30,45,60

The least common multiple of 4 and 15 is 60.

The two players meet at the same point after 60 minutes.

Hence If player 1 and player 2 begin their run at the same time and location on the​ field, In 60 minutes will they meet to begin their next lap​ together.

To learn more on LCM click:

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Luisa's restaurant bill comes to $85.50, and she leaves a 18% tip. What is Luisa's total
restaurant bill?

Answers

Answer:

85.50+15.39=100.89 dollars

Step-by-step explanation:

First, you calculate the tip cost, which is 15.39. Then you add that to the bill which gives you your total :D

PLEASE HEL0 :( 20 points!

Answers

Answer:

a c b and f

Step-by-step explanation:

Given g(x) = (x - 3)2 and h(x) = 2x + 1, which of the following is (g.h)(5)?
(A) 35
(B) 38
(C) 44
(D) 45

Answers

Answer:

B

Step-by-step explanation:

What is 18 percent of 210?

Answers

Answer:

WN=37.8

Step-by-step explanation:

WN=18%*210

WN=0.18*210

WN=37.8

Which expression represents the following calculation?
"Add 2 and 10, then multiply by 3, then add 9."

Answers

Answer:

I think it's...

[(2 + 10) × 3] + 9

Henry is making a corn grits recipe that calls for 14 cup of corn grits for every 12 cup of water.
How much water will he need if he uses 112 cups of corn grits?

Answers

Answer:

2 cups of water

Step-by-step explanation:

Help plz! Will give brainliest!

Answers

Answer: the answer is d god bless you and plz can i have brainliest i only need 1 more

Step-by-step explanation:

Answer:

D sqrt 72

Step-by-step explanation:

The answer is not A because 8.89 = sqrt 79 and that is too high

The answer is not B because 9.06 = sqrt 82

The answer is not C because 7.94 = sqrt 63

The answer is D 8.49 = sqrt 72 and that is perfect.

Muffins are sold in packages of 18. Select the expressions that can represent the total number of muffins in p packages of muffins.
A. 18 + p
B. 18 × p
C. 18 – p
D. 18 ÷ p
E. 18p

Answers

i would say that the answer is e

I will give brainliest
Jared is going to plant 20 small plants around the edge of a circular garden that is 8 feet in diameter. If he spaces the plants evenly, how much distance will be between the plants?
25.12 feet
12.56 feet
2.5 feet
1.26 feet

Answers

Answer:

2.5 feet

Step-by-step explanation:

20/8=2.5

IF ANY ONE NEEDS HELP WITH ANY KIND OF WORK ILL DO IF FOR A BIT OF CASH I GRADUATED COLLEGE I KNOW WHAT I'M DOING step by step

Answers

oh really?? how much?

rename the fraction 2/5 using tenths and hundredths​

Answers

Answer:

20/50

Step-by-step explanation:

i think

What is the location of Point A

Answers

Answer:

Wheres the rest of the question

Step-by-step explanation:

Answer:

You need to show the picture so we can help you with all due respect

Step-by-step explanation:

There is a proportional relationship between time in hours and time in days.

A. What is the constant of proportionality?

B. what equation describes this relationship?

Answers

Of the proportional relationship between time in hours and time in days, we have that:

a) The constant of proportionality is 24.

b) The equation is [tex]h = 24d[/tex].

What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

[tex]y = kx[/tex]

In which k is the constant of proportionality.

Item a:

A day has 24 hours, hence the constant of proportionality is 24.

Item b:

Considering the time in hours as the output and the time in days as the input, the equation is:

[tex]h = 24d[/tex]

You can learn more about proportional relationships at https://brainly.com/question/25815502

80 POINTS NEED HELP FOR A BIG GRADE:
Reflect what you have learned about the personality traits and viewpoints of the person you select and adopt this persons perspective as though you were seeing the world through his or her eyes.
Includes: Use first-person pronouns
Includes: A viewpoint and tone that idealistically reflects how this individual would see and experience the subject matter he or she writes about.

Then you will rewrite a entry from Tuesday, July 13, 1943 or Friday, October 29, 1943.

Answers

Yesterday afternoon, Anne asked me to allow her to use the little table in our shared room twice a week in the afternoons, from four o’clock till half past five. Probably because nearly every other spot in the home is taken. It may have been a reasonable request but she is but a child, a child with no respect for her elders, I need that desk. So I told her no just no, and that bad-tempered child refused to be put off like that. I tried to send her away, telling her that “I have to work too, if I can’t work in the afternoons, then there is no time left for me at all. I must finish my task, otherwise I’ve started it all for nothing. Anyway, you don’t work seriously at anything. Your mythology, now just what kind of work is that, knitting and reading are not work either. I am at the table and shall stay there” Her reply was:

  “Mr. Dussel, I do work seriously and there is nowhere else for me to work in the afternoons. I beg of you to kindly reconsider my request.”  

  With these words the offended Anne turned her back on this very learned doctor, Ignoring me completely. She looked as though she was seething with rage. She will probably go run to her father and tell him how horrible her roommate is. That insulinant child!  

   Later that day the girl came to me after the dishes were done and started more unneeded drama telling me “Mr. Dussel, I don’t suppose you see any point in discussing the matter anymore, but I must ask you to do so” How relentless! I could not just let her get away with this” Maybe if I tried just playing nice she would be put in her place, so I put on my best smile a replied. “I am always, and at all times, prepared to discuss this matter, but it has already been settled.”

   She kept on talking about how unfair I was saying “When you first came here we arranged that this room should be for both of us; if we were to divide it fairly, you would have the morning and I all the afternoon! But I don’t even ask that much, and I think my two afternoons are really perfectly reasonable.” At this I jumped up outraged feeling as though someone stuck a needle in me. How dare she the ungrateful child! “You can’t talk about your rights here at all. And Where am I to go then? I shall ask Mr. Van Daan whether he will build a little compartment in the attic, then I can go and sit there. I simply can’t work anywhere. With you one always gets in trouble. If your sister Margot, who after all has more reason to ask such a thing, would have come to me with the same questions, I should not think of refusing, but you…” She attempted to show emotion on her face but I could tell she was hurt but I continued “But you one simply can’t talk to you. You are so outrageously selfish, as long as you get what you want, you don’t mind pushing everyone else to one side, I’ve never seen such a child. But after all, I suppose I shall be obliged to give you your own way, because I shall be told later on that Anne Frank failed her exam because Mr. Dussel would not give up the table for her.”

  At one moment she looked as though she wanted to smack me. When I had finally stopped talking and left the room I could hear her rush away, probably to run to her father whining about how horrible I am.

I was right, her father came to me when I was about to take my turn in the bathroom. We talked for nearly two hours about if Anne deserved to sit at the table. Me and Mr. Frank had already had this discussion before and he had agreed with me, but now because of the wretched child we had to have the whole conversation again. That little brat spoke to me as if I was an intruder who tried to monopolize everything, but of course her father made her out to be a perfect angel who just spoke her mind nicely.

 I finally gave in and allowed her to use the table twice a week. I don’t see that girl ever maturing and acting like a young lady.

   

Wish me luck dealing with that girl, Dussel

Can anyone solve this? If so tell me and make sure u know what ur doing please

Answers

Answer:

-2

Step-by-step explanation:

To find the slope of a line, you need to find the [tex]\frac{rise}{run}[/tex] between two points. I will be using the points (-3, 2) and (-1, -2).

[tex]\frac{rise}{run}[/tex] = [tex]\frac{-2-2}{-1-(-3)}[/tex]

     = [tex]\frac{-2-2}{-1+3}[/tex]

     = [tex]\frac{-4}{2}[/tex]

     = -2

"Individuals, cultures, societies, and the world change through times of conflict and cooperation."
The statement above exemplifies the era of global expansion and encounter. What other word also reflects this theme?
Technology
Trade
Monopoly
Hegemony

Answers

I would say hegemony
Hegemony because it encompasses dominance in which cultures typically dominate over one another creating a popular culture.

-26=b-13
Plz answer I’m a month late on this test

Answers

Answer:

B = -13

Step-by-step explanation:

Add 13 to both sides

- 13 = b

A wizard-in-training has 300 grams of 20% liquid-gold solution. He wishes to drain some and replace it with an 80% solution, so that he gets 300 grams of 35% solution. How many grams should the wizard drain and replace with 80% solution?

Answers

Answer:

it would take 4 grams. I hope this helps

Answer:

75 grams! hope this helps :3

Can someone help me with this please

Answers

Answer:

teal, red, purple are the correct answers

A contractor is building a tower shaped like a tall
rectangular prism. He is told that the dimensions
of the tower must be 50 ft x 80 ft x 250 ft. The
building is to have 20 floors with a 2.5 ft tall
portion between each floor and for the roof. What
is the volume of each floor of the building?
A. 40,000 ft3
B. 49.500 ft
C. 50,000 ft
D. 60,000 ft

Answers

Answer: I put 50,000 ft^3

Step-by-step explanation: You have to multiply 50, 80, 250 then divide by 20 because you’re looking for the floors only and not the roof and floor

What is 25% of 92?

Pls help thank you so much

Answers

Answer: 23

Hope that helps!

Answer:

23 :)

Step-by-step explanation:

A motorboat moves across a lake at a constant speed. When it begins, it is 48
km from the shore. After 10 minutes, it is 18 km from the shore. Which
function describes the motorboat's distance from the shore?
O A. y = 10x+48
B. y=-3x + 48
O c. y=-10x + 48
O D. y = 3x + 48

Answers

Answer:

b

Step-by-step explanation:

The function describes the motorboat's distance from the shore is y=-3x + 48. So, the correct option is B.

What is the function?

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Given that, a motorboat moves across a lake at a constant speed.

Let x be the number of minutes and y be the total distance.

When it begins, it is 48 km from the shore.

Now, (x₁, y₁) =(0, 48)

After 10 minutes, it is 18 km from the shore.

So, (x₂, y₂) =(10, 18)

We know that, Slope(m) =(y₂-y₁)/(x₂-x₁)

= (18-48)/(10-0)

= -30/10

= -3

Substitute, (x, y)=(0, 48) and m=-3 in y=mx+c, we get

48=-3(0)+c

c=48

Substitute, c=48 and m=-3 in y=mx+c, we get

y=-3x+48

Therefore, option B is the correct answer.

To learn more about the function visit:

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-8+12 divided by 2 + (-14)

Answers

Answer:

-16

Step-by-step explanation:

Answer:

the answer is negitive 12 or -12

4(a+3) - 7 = 6a -21 aaaaaaaaaaaaaaaaaa

Answers

Answer:

a=13

Step-by-step explanation:

4a+12-7=6a-21

combine like terms

4a+5=6a-21

sub 4a from each side

5=2a-21

add 21 to each side

26=2a

divide each side by 2

a=13

Answer:

:)

Step-by-step explanation:

a=13

Sam mows a ¼ of a lawn in ½ of an hour. At this rate, how long will it take him to finish one lawn?

Answers

Answer:

Two hours

Step-by-step explanation:

1/4 = 1/2

2/4 = 1

3/4 = 1 1/2

4/4 = 2

2 hours if he mows 1/4 im 1/2 then 2/4 would be 1 hour then 3/4 would be 1 1/2 hour then 4/4 would be 2 hours so ur answer is 2 hours

You earn 18n dollars. How much do you earn for mowing 3 lawns? 9 lawns?

Answers

Answer:

I am confused but my best guess would be you would earn 54$ for 3 lawns and 162 for 9

Step-by-step explanation:

You multiply 3 x 18 and 9 x 18

Im sorry if im wrong but i dont know what you were asking

Find the greatest common factor of 6 and 35

Answers

Answer:

6

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

State the property that justifies the statement: If 4x + 9 = 15 and X=2y + 1,
then 4(2y+1) + 9 = 15.
Distributive Property
Multiplication Property of Equality
Transitive Property of Equality
Substitution Property of Equality

Answers

Answer:

Substitution property of equality

Step-by-step explanation:

Given

[tex]4x + 9 = 15[/tex] and [tex]x = 2y + 1[/tex]

Then

[tex]4(2y + 1) + 9 = 15[/tex]

Required

State the property

From the list of options, (d) answers the question.

This is so because:

Substitution property of equality states that

If [tex]a = b[/tex] then [tex]b = a[/tex]

In other words, both can replace one another.

So if [tex]x = 2y + 1[/tex], then 2y + 1 can be substituted for x in [tex]4x + 9 = 15[/tex]

So:

[tex]4x + 9 = 15[/tex]  becomes

[tex]4(2y + 1) + 9 = 15[/tex]

Hence, it is substitution property of equality

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