Find how many solutions there are to the given equation that satisfy the given condition.
y1 +y2+y3+y4=27, each yi is a nonnegative integer.

Answers

Answer 1

Answer:

17550 solutions

Step-by-step explanation:

Given that:

y1 +y2+y3+y4=27

where;

(yi  ≥ 0 and yi [tex]\epsilon[/tex] [tex]{\displaystyle \mathbb {Z} }[/tex]  )

The no. of a nonnegative integer determines the number of ways to choose 27 objects from (4) distinct objects with repetition regardless of the order.

i.e

[tex]\bigg(^{27}_{4} \bigg)[/tex]

The number of nonnegative integer solution is [tex]\bigg(^{27}_{4} \bigg)[/tex]

[tex]= \dfrac{27!}{4!(27-4)!}[/tex]

[tex]= \dfrac{27!}{4!(23)!}[/tex]

[tex]= \dfrac{27\times 26\times 25\times 24 \times 23 !}{4\times 3\times 2\times 1(23)!}[/tex]

[tex]= \dfrac{27\times 26\times 25\times 24 }{4\times 3\times 2\times 1}[/tex]

[tex]= \dfrac{421200}{24}[/tex]

= 17550 solutions


Related Questions

It is approximately 32 miles from Dallas to Fort Worth.
Which number sentence could be used to find f, the number
of feet from Dallas to Ft. Worth.


(A) 1760 x 1/32 = f; because the scale factor is 5280
(B) 32 x 1760 = f; because the scale factor is 5280.
(C)5280 x 1/32 = f; because the scale factor is 5280.
(D)32 x 5280 = f; because the scale factor is 5280.

Answers

I believe the answer your looking for is b
My guy in some kind of 7000 level gawk gawk math or sum yo haha

Which of the following sets are disjoint?

a) Men and uncles

b) Aunts and uncles

c) Women and Aunts

d) They are all disjoint ​

Answers

Answer: b) Aunts and uncles

=======================================================

Explanation:

The term "disjoint" is another way of saying "mutually exclusive". If two sets are disjoint, then they have nothing in common. Put another way, if two sets are disjoint, then it's not possible to be part of both sets at the same time.

In this case, it is not possible to be both an aunt and an uncle simultaneously for any one person. So this is why choice B is the answer.

At a shelter, 35% of the dogs are puppies. There are 200 at the shelter. How many are puppies?

Answers

Answer:

Step-by-step explanation:

Percentage of purebred dogs in shelters: 25% Number cats and dogs adopted from shelters each year: 4 million. Percentage of cats euthanized in shelters: 70% Percentage of total shelter intake comprised of cats: Approximately 50% (but in some regions 2/3 of shelter population is cats)

Answer:

70 puppies

Step-by-step explanation:

Find 10% which is 200÷10=20

20*3=60=30%

20÷2=10=5% so 60+10=70 puppies

HELPPPPPPPPPPP APPARENTLY MY ANSWER WAS WRONG ​

Answers

Answer:

d= -12 + 925

Step-by-step explanation:

decrease means negative and Increase means up (positive) so probably that why your answer was wrong

Answer:

d= -12 + 925

Step-by-step explanation:

please answer this :(

Answers

Answer:

X+2 metres. Just use a^+2ab+b^2

What does x = if x multiplied by 7/3 = 1

Answers

Answer:

Step-by-step explanation:

X×7/3 =1

X=3/7

please please please help me i’ll mark brainliest

Answers

Given:

The graph of a function f(x).

To find:

The solution set for f(x)>0 and f(x)≤0.

Solution:

From the given graph it is clear that, the function intersect the x-axis at 3 points, i.e., x=-4, -3 and -2.

The graph is above the x-axis before -4 and between -3 and -2.

So, the solution set for f(x)>0 is [tex](-\infty,-4)\cup (-3,-2)[/tex].

The graph is below the x-axis between -4 and -3; and after -2. For f(x)≤0, those values are in the solution set for which f(x)=0, i.e., x-intercepts. So, we use close brackets in the interval notation.

So, solution set for f(x)≤0 is [tex][-4,-3]\cup [-2,\infty)[/tex].

Select the correct answer from the drop-down
menu.

Answers

Answer:

-30

Step-by-step explanation:

did the test and it is right

Help pls and thank you!

Answers

Answer:

120 such cubes could fit in the prism.

Step-by-step explanation:

Volume of prism = length × breadth × height

[tex] = \frac{5}{3} \times \frac{4}{3 } \times 2[/tex]

[tex] = \frac{40}{9} cm {}^{3} [/tex]

___________________________________

Volume of cube = a³

[tex] = ( \frac{1} {3}) {}^{3} [/tex]

[tex] = \frac{ {1}^{3} }{ {3}^{3} } [/tex]

[tex] = \frac{1}{27} cm {}^{ 3} [/tex]

____________________________________

[tex] \frac{40}{9} \div \frac{1}{27} [/tex]

[tex] \frac{40}{9} \times 27[/tex]

[tex]40 \times 3[/tex]

120

Help me pls this is due tomorrow at 8:00 am

Answers

Answer:

it would be what they said

Step-by-step explanation:

so sorry i need 50 pts

Answer:

Oh this is easy 24

Step-by-step explanation:

2x4=8x3=24

help im stressing and crying

Answers

the answers should be
1-$280
2-6
I’m so sorry that your upset math makes me cry sometimes too but you just need to push through, and I know it seems hard but I’m sure your a really amazing person and you can do anything you set your mind to!

Now for your answers the answer to the first one is $440

And the second one is 9 times

I hope this helps you!

Can you help find which are functions?

Answers

Answer:

A and C are Functions

Step-by-step explanation:

They pass the vertical line test.

The way you know if a set of coordinates are not a function is if they have multiple points that have the same Y value.

Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams, with the following results:
Mean Grade Standard Deviation
Professor 1 79.3 22.4
Professor 2 82.1 12.0
What is the alternate hypothesis?

Answers

Answer:

Alternative hypothesis:

[tex]\mathbf{H_a = \sigma_1^2 \ne \sigma_2^2}[/tex]

Step-by-step explanation:

Given that:

Sample 1:

Sample size [tex]n_1[/tex] = 10

Sample mean  [tex]\overline x_1[/tex] = 79.3

Standard deviation [tex]\sigma_1[/tex] = 22.4

Sample 2:

Sample size [tex]n_2[/tex] = 10

Sample mean  [tex]\overline x_2[/tex] = 82.1

Standard deviation [tex]\sigma_2[/tex] = 12.0

To find the alternative hypothesis.

The null and alternative hypothesis can be computed as follows:

Null hypothesis:

[tex]\mathbf{H_o = \sigma_1^2 = \sigma_2^2}[/tex]

Alternative hypothesis:

[tex]\mathbf{H_a = \sigma_1^2 \ne \sigma_2^2}[/tex]

Since, alternative hypothesis is ≠, it shows that it is a two tailed test.

Which operation should be done first in the
expression shown below?
3-5+4 + 2 x 6

Answers

Answer:

2x6

Step-by-step explanation:

Answer:

Do multiplications first, then simplify the equation from left to right. Therefore, your answer should be 18.

Step-by-step explanation:

3 - 5 + 4 + 2 × 6

= 3 - 5 + 4 + 12

= 2 + 4 + 12

= 6 + 12

= 18

Please help with this math question thank you!

Answers

I believe the correct answer is c.

The diagram shows a round fountain surrounded by a circular path. The radius of the fountain is v7 yards, and the distance from the center of
the fountain to the outer edge of the path is 56 yards.
The estimated area of the fountain is
square yards, and the estimated area of the path is square yards
Can someone please help me!!!

Answers

Answer:

The first drop down box, I'm pretty sure its the second one

Step-by-step explanation:

Answer:

The guy up there is right so the answer, first one is 147.58 and the second one is 28.26

Step-by-step explanation:

Olivia is using 160 quilt squares to make a red, yellow, and blue quilt. If 25% of the quilt squares are red and 30% are yellow, how many quilt squares are blue?

Answers

Answer:

72 blue quilt squares

Step-by-step explanation:

Total number of quilt squares = 160

Percentage of no. of red quilt squares = 25%

Percentage of no. of yellow quilt squares = 30%

So, percentage of no. of blue quilt squares = 100 - (25 + 30) = 45%

No. of blue quilt squares = [tex]\frac{45}{100} *160=\frac{45*160}{100} = \frac{7200}{100} =72[/tex]

I really need to know what a dependent variable is. Can anyone explain better that google?

Answers

Answer:

A variable that depends on one or more other variables. For equations such as y = 3x – 2, the dependent variable is y. The value of y depends on the value chosen for x. Usually the dependent variable is isolated on one side of an equation.

Step-by-step explanation:

PLS HELP PLS THE LAST QUESTION I ASKED PLSSSSS

Answers

Answer:

Okay nvm I have found it here is your graph I don't what type of graph you need so i will provide you with 2 of my choosings

Step-by-step explanation:

X3.1.PS-7
Question
A local little league has a total of 60 players, of whom 40% are right-handed. How many
right-handed players are there?

Answers

24 right-handed players

What is 4501/5 equaled to?

Answers

My answer~

900.2 or 900 1/5

My Step-by-step explanation~basically just divide

4501 ÷ 5

=

900.2

then convert to fraction or leave as is

900 1/5

-------------------------------------------------------------------------------------------------

Answer:

It would be 900.2

hope this hepled!  :)


[tex] \frac{1}{ax} - \frac{1}{bx} = 1[/tex]
can someone ease explain how this is possible. right now I have tried everything from the back of my head and nothing seems to work. Thanks!​

Answers

Answer:

x= 1/a-1/b

Step-by-step explanation:

use math.way

The answer to your question is 1 because:

'ax' and 'bx' have no values, they are missing numbers.

We have to cancel out one 1, and our answer is 1.

Carry on Learning!

A fruit stand has to decide what to charge for thier produce. They need $10 for 4 apples

Answers

Answer:

$10 = 4x

Step-by-step explanation:

The "x" would represent how much the apples would cost. So next you would divide both sides by 4x and then it would leave you with 2/5.

multipy (2c-1) (7c-5)

Answers

Answer:

2.8 or 2 4/5

Step-by-step explanation:

2c*7c= 14c

1*5= 5

14c/5=

Answer:

14c^2 - 17c + 5

Step-by-step explanation:

hope to get a brainliest hope you the bsat on it have a good day:)

A dressmaker has 75 yards of lace . It takes 1 1/2 yards of lace to decorate one pocket . How many pockets can she decorate with the lace she has

Answers

Answer:

50 pockets

Step-by-step explanation:

Given

[tex]Total = 75\ yd[/tex]

[tex]Pocket = 1\frac{1}{2}yd[/tex]

Required

Determine the number of pockets

To calculate the required , we make use of:

[tex]Pockets = \frac{75yd}{1\frac{1}{2}yd}}[/tex]

[tex]Pockets = \frac{75}{1\frac{1}{2}}}[/tex]

Convert the denominator to decimal

[tex]Pockets = \frac{75}{1.5}[/tex]

[tex]Pockets = 50[/tex]

Hence, she can lace 50 minutes

Does the table below represent a proportional relationship?
х
2
3
4
5
y
6
7
8
9
O A. Yes, because all the ratios of y to x are equal to 2.
OB. No, because all the numbers are positive.
O C. Yes, because all the ratios of yto x are equal to 3.
OD. No, because all the ratios of yto x are not equal.

Answers

Answer:

The answer is C. Hope it helps :)

Answer:

I think C Will help...

What is the most profound problem in maths?
No answer needed, just take the points.

Answers

Answer:

SWEEEET!!

Step-by-step explanation:

:D

Answer:thx so much I needed them

Step-by-step explanation:

a owner increases the rent office house by 5% at end of each year if current its rent is ₹2500pm how much will be the rent after two years​

Answers

Answer:

2950$

Step-by-step explanation:

2500×5%=125$

125×2=250$

2500+250=3960$

Review the following information about vectors q and r.

q = ⟨–4, 1⟩

r = ⟨a, 3⟩

7(q + r) = ⟨–35, 28⟩

What is the value of a?

–31
–7
–5
–1

Answers

Answer:

D) -1

Step-by-step explanation:

got it right on edge :)

Vector addition is done by addition of the components

The value of a is -1

a = –1

Reason:

The given parameters are;

q = <-4, 1>

r = <a, 3>

7·(q + r) = <-35, 28>

Required:

The value of a

Solution;

By vector addition of the components of q, and r, we have;

q + r = <-4 + a, 1 + 3> = <-4 + a, 4>

q + r =  <(-4 + a),    4>

By plugging in the value of q + r from the above step, we have;

7·(q + r) = <7 ×(-4 + a), 7 × 4> distribution property

7·(q + r)  = <-35, 28> Given

Therefore, by comparison of components, we have;

7 ×(-4 + a) = -35

[tex]-4 + a = -\dfrac{35}{7} = -5[/tex]

a = -5 + 4 = -1

a = –1

The correct option for the value of a is –1

Learn more here:

https://brainly.com/question/2927458

Type the decimal equivalent of 6 9/20 .

Answers

Answer:

6.45

Step-by-step explanation:

The person on top is correct.

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