There is a group of $5$ children, where two of the children are twins. How many ways can I distribute $6$ identical pieces of candy to the children, if the twins must get an equal amount of candy?

Answers

Answer 1

Answer:

50

Step-by-step explanation:

Suppose that the kids get $x_1,x_2,x_3,x_4,x_4$ pieces of candy, respectively (each twin received $x_4$ pieces). Then we seek all quadruples $(x_1,x_2,x_3,x_4)$ satisfying

\[x_1+x_2+x_3+2x_4 = 6.\]We proceed by casework, based on the number of candies the twins receive.

If $x_4 = 0$, then there are 6 candies to distribute to 3 kids. This is like arranging 6 C's and 2 |'s (dividers), so there are $\binom{8}{2} = 28$ possible distributions.

If $x_4 = 1$, there are 4 candies remaining for the other 3 kids, so there are $\binom{6}{2} = 15$ possible distributions.

If $x_4 = 2$, there are 2 candies remaining, so there are $\binom{4}{2} = 6$ possible distributions.

If $x_4 = 3$, there are 0 candies remaining, for 1 possible distribution.

Adding all of these results from the separate cases, there are a total of

\[28 + 15 + 6 + 1 = \boxed{50}\].


Related Questions

i need the volume and surface area

Answers

Answer:

Volume: V≈113.1

Step-by-step explanation:

Solved for sphere

Shape: Sphere

Formula: V=43πr3

Volume: V≈113.1

1: R is the radius meaning calculate the radius to find the volume of a sphere.

2: The correct answer is below for this question.

Answer: V≈113.1

Hope this helps.

Can people help with (5a), (5b), (5c), (6a), and (6b)

Answers

。☆✼★ ━━━━━━━━━━━━━━  ☾  

5a.

8x = 2/3

Divide by 8 on both sides

x = (2/3) / 8

x = 1/12

5b.

1.5 = 2x

Divide by 2 on both sides

x = 1.5 / 2

x = 3/4

5c.

5x = 2/7

Divide both sides by 5

x = (2/7) / 5

x = 2/35

I can't see the other questions. If you type them out, I'll answer them :)

Have A Nice Day ❤    

Stay Brainly! ヅ    

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What is the area of the cross section that is parallel to side PQRS in this rectangular box?

Answers

Answer: Hey, you need to add a photo, once you do so I will edit my answer

Answer:

It's 12 square units

Step-by-step explanation: I got it right on the test :)

Please help me! Help is very needed

Answers

What do you need help for :)


m_1=
O 40
O 130
O 50

Answers

Answer:

The answer would be 50

Step-by-step explanation:

What are the coordinates of the vertex of a parabola whose equation is y−4=2(x+7)2 ?
Question 5 options:
a) (7, -4)
b) (-7, 4)
c) (4, -7)
b) (-4, 7)

Answers

The answer is b) (-7, 4)

The coordinate of the vertex of the parabola y - 4 = 2(x+7)² is (-7,4)

The coordinate of the vertex?

The equation of the parabola is given as:

y - 4 = 2(x+7)²

Add 4 to both sides

y = 2(x+7)² + 4

A parabola is represented as:

y = a(x- h)² + k

Where, the vertex is:

vertex = (h,k)

By comparison, we have:

Vertex = (-7,4)

Hence, the coordinate of the vertex is (-7,4)

Read more about vertex at:

https://brainly.com/question/18797214

#SPJ2

which of the following division sentences does the figure below model
A:1/2 DIVIDED by 1/3
B:1/3 divided by 2
C:2 divided by 3
D:1/2 divided by 1/4

please help I need this answer for my leap test

Answers

dudeeee this is hard. Pick C no balls

what is value of x?
help ASAP pls !!!

Answers

The value of x is 40

Find the domain of the function.

y = [tex]\sqrt{x} + 1[/tex]

Answers

Answer:

[0, infinity)

Step-by-step explanation:

A square root can only use positive numbers, otherwise it becomes imaginary. A function needs to be real to output real values. Therefore, the domain is everything from 0 onwards.

Question 15
Not yet
answered
Find the slope of the line that passes through the pair of points ( ) and (, 5)
Points out of
1.00
P Flag question
Select one:
O a. 19
18
O b.
36
157
O C.-
680
9
O d. 1
Question 16
Find the slope of the line that passes through the pair of points(H, ) and ( 1).
Not yet
answered
Points out of
1.00
Select one:
O a.
18
185
185
Ob.
18
289
Ос.
P Flag question
3,330
O d.
88,434
185
Can you please answer both of these please!!!

Answers

Answer:

C: -680/9

B: -185/18

Solve each proportion

Answers

Answer:

2 is 45

3 is 36

Step-by-step explanation:I just know plz mark brainliest

Answer:

25x5/9=x   x=45

Step-by-step explanation:

25x5 (to cross multiply) and then divide by five. or 5x5=25 so 9x5=45

In circle A shown below, the measure of ∠BAD is 148°: Circle A with angle BAD measuring 148 degrees; points B, C, D lie on Circle A. If m Arc BC is 96°, what is m Arc CD ?

Answers

Answer:

52°

Step-by-step explanation:

In the figure attached, Circle A is shown. There we can see that:

∠BC + ∠CD =  ∠BAD

We know that Arc BC measures 96° and arc BAD measures 148°. Replacing this data into the equation and solving for Arc CD, we get:

96° + ∠CD =  148°

∠CD = 148° - 96°

∠CD = 52°

Answer:

The answer is 52

Identify the equivalent expressions of 4(2x + x – 3) – 3x + 3 by substituting x = 2 and x = 3.

Answers

Answer:

9

18

Step-by-step explanation:

x = 2:

4(4 + 2 - 3) - 6 + 3 = 12 - 6 + 3 = 9

x = 3:

4(6 + 3 - 3) - 9 + 3 = 24 - 9 + 3 = 18

Answer:

9x -9

9(x - 1)

4(3x-3) - 3x + 3

Step-by-step explanation:

4(2x + x-3) - 3x + 3

Combine like terms

4(3x-3) - 3x + 3

Distribute

12x -12 -3x+3

Combine like terms

9x -9

Factor out 9

9(x-1)

Question 3 Multiple Choice Worth 4 points)
(07.04A)
If y = 6x - 3, which of the following sets represents possible inputs and outputs of the function represented
ordered pairs?
{(0, 3), (1, -9), (2, -15)}
{(0, -3), (2, 15), (4, 21)}
{0, -3), (2, 9), (4, 21)}
{(0, 3), (-2, 15), (4, 21)}

Answers

Answer:

{0, -3), (2, 9), (4, 21)}

Step-by-step explanation:

if x = 0 ⇒ y = 6x - 3 = 6(0) - 3 = 0 - 3 = -3

if x = 2 ⇒ y = 6x - 3 = 6(2) - 3 = 12 - 3 = 9

if x = 4 ⇒ y = 6x - 3 = 6(4) - 3 = 24 - 3 = 21

30 points for the right answer! Please I need helpies.

a. What should the total of all of the probability be? Show your work.(you need a common denominator)

b. What is the probability of eating no cookies?

c. What is the probability of eating two or fewer cookies?

d. What is the probability of not eating 2 cookies?

Answers

Answer:

a. What should the total of all of the probability be?

it is 100% which is equal to 1

b. What is the probability of eating no cookies?

23% as per table (23% against 0)

c. What is the probability of eating two or fewer cookies?

23% (for 0 )+0.16 (for 1)+16/50 (for 2)= 0.23+0.16+0.32= 0.71 = 71%

d. What is the probability of not eating 2 cookies?

1-16/50= 34/50= 0.68 = 68%

The product of 4 and the difference of x and 3 is 54

Answers

Answer:

x = 16.5

Step-by-step explanation:

the original equation is:        4(x - 3) = 54

first divide both sides by 4:   x - 3 = 13.5

finally add both sides by 3:   x = 16.5

Consider triangle QRS. The legs each have a length of 10 units. What is the length of the hypotenuse of the triangle?

Answers

Answer:

14.14

Step-by-step explanation:

10^2+10^2=x^2

x=square root 200

Answer: 102 units or 14.14 units

Solution,

Hypotenuse=?

Perpendicular=10 units

Base=10 units

Using the Pythagoras theorem,

H^2=p^2+b^2

or,h^2= (10)^2+(10)^2

or,h^2=100+100

or,h^2=200

or,h=200

h=102 or 14.14

Hope it helps..

Good luck on your assignment

What is 72% of 606,738

Answers

Answer:

436,851.36

Step-by-step explanation:

72%/ 606,738= 436,851.36

436851.36 is 72% of 606,738

FOR 15 POINTS Determine whether each given value of h makes the inequality 4h + 13 ≤ −7 true. Select Yes or No for each value.

Answers

Answer:

Yes, no, yes

Step-by-step explanation:

Answer:

Yes,  No, Yes

Step-by-step explanation:

Nicole has a piece of ribbon that is 4 yards long. She cuts off a piece that is 3 feet long and gives it away.
How many inches of ribbon does Nicole have left over?
A
1
B
9
C
36
D
108
can someone help me please​

Answers

Answer:

3 yards

Step-by-step explanation:

you have to convert the yards in to inches

4 yards is 12 ft so minus 3 = 9 ft the convert back to 2 yards :)

Question on attachment below!
Step - by - step work please!

Answers

Answer:

You would need $23.87.

Step-by-step explanation:

Divide $20.46 by 6 which equals $3.41. Multiply $3.41 by 7 and you get $23.87.

Answer:

You would need $23.87

Step-by-step explanation:

Cost for 6 books is 20.46

Finding the unit cost:

the cost of one single book will be amount for 6books ÷ 6

= 20.46 ÷ 6

= 3.41

We need to find the cost of 7 books so now that we know it for one book, we multiply that amount by 7

Therefore,

3.41 x 7

= 23.87 dollars

An isosceles triangle has two angle measurements of 80 and 50 degrees. Could more than one triangle be drawn that fits these conditions? Explain.

Answers

Answer:

Step-by-step explanation:

In an isosceles triangle, the base angles are equal. This also means that two sides of the triangle are equal in length. Since the sum of the angles in a triangle is 180 degrees, it means that the third angle of the given triangle is

180 - (80 + 50) = 50 degrees

Therefore, the base angles of the isosceles triangle are 50 degrees each. For more triangles with these conditions to be drawn, only the lengths of the equal sides can be increased or decreased. This would in turn increase the length of the third side. Therefore, isosceles triangles of the same angles but different sizes can be drawn.

Find the surface area of the cone. Use 3.14 for π explain your answer

Answers

Answer: 151.58 sq inches

Step-by-step explanation:

A=πr(r+√h2+√r2)

The volume V of a rectangular prism of a particular height varies jointly as the
length I and the width w, and V = 224 ft when I = 8ft and w = 4 ft.
Find I when V = 210 ft' and w = 5ft.

Answers

Answer:

    6ft

Step-by-step explanation:

Volume of rectangular prism = l x w x h, where h is height. So, we have to work out the height of the first prism in the following way. 224 divided by ( 8 x 4), which gives 7. So, to find l in the second prism, we have to :

L x W x H = 210

L x 5  x 7 = 210

L x 35 = 210

L = 210 divided by 35 = 6

Georgia is making a square sign for her bedroom door. The length of one side is 9 inches. What is the perimeter of the sign?

Answers

Answer:

36 inches

Step-by-step explanation:

a squares sides all measure the same length so, if one side is 9 inches all 4 of them are 9 inches. perimeter is all sides added up:

the equation would be 9+9+9+9 which would equal 36

What is the length of d?

Answers

For this we have have to use Pythagoras Theorem
11^2 + 13^2 = 121 + 169 = 290
We then Square root 290 which gives us 17.02

DUE RIGHT NOW
TABLE BELOW USED FOR QUESTION (1st pic)

Find the relative frequencies of students by COLUMN for the previous table. Round to the nearest hundredth if necessary. (2nd pic)

Answers

Answer:

                 like fishing    dislike fishing

male         0.62               0.38

female      0.38               0.62

Step-by-step explanation:

To compute column relative frequencies you have to divide the value of each column by the total of each column, as follows:

                 like fishing               dislike fishing

male         35/56 = 0.62            15/39 = 0.38

female      21/56 = 0.38             24/39 = 0.62

2 4 6 = 2


Fill in the blanks

Answers

Answer:

2x4-6

Step-by-step explanation:

2x4 is 8, and 8-6=2. Therefore 2x4-6=2

the answer is 2 x 4 -6

Which is the graph of y = [X] - 2?

Answers

Hope this helps, you should get the app Desmos, it works well for questions like this.

Hartley has two 4-section spinners, each labeled 1-4. She will spin both spinners a total of 96 times. For each pair of numbers where the pointers of the spinners land on, Hartley will subtract the smaller number from the greater number.


How many possible total outcomes are there?

How many times should Hartley spin a difference of 1?

How many times should Hartley spin a difference of 0?

Answers

Answer:

1) Total outcomes of 1 time = 16

2) 36 times

3) 24 times

Step-by-step explanation:

1) Total outcomes

If both spinners are spinning together, and are labelled from 1 to 4, the the outcome are:

{(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4), (4, 1), (4, 2), (4, 3), (4, 4)}

We can count them to find total no. of outcomes

Total outcomes = 16

2) When Difference = 1

Following combinations have a difference of 1

{(1, 2), (2, 1), (2, 3), (3, 2), (3, 4), (4, 3)}

n = 6

Probability of getting such combination is: 6/16

How many times Harvey would get such a combination out of 96 times?

[tex]\frac{6}{16}\cdot96=36[/tex]

3) When Difference = 0

Following combinations have a difference of 0

{(1, 1), (2, 2), (3, 3), (4, 4)}

n=4

Probability of getting such combination is: 4/16

How many times Harvey would get such a combination out of 96 times?

[tex]\frac{4}{16}\cdot96=24[/tex]

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