How many ways are there to put 9 differently colored beads on a $3\times3$ grid if the purple bead and the green bead cannot be adjacent (either horizontally, vertically, or diagonally), and rotations and reflections of the grid are considered the same

Answers

Answer 1

Answer:

20,160

Step-by-step explanation:

The arrangement of the 9 differently colored bead can be presented as follows;

[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]

Where 1 is the purple bead and 2 is the green bead, the number of ways of arrangement where the green bead cannot be adjacent to the green either horizontally, vertically, or diagonally

Placing the purple bead at 1, the location of the green bead = 3, 6, 7, 8, or 9

The number of ways = 5 ways × 7! ways of arranging the other beads

With the purple bead at 2, the location of the green bead = 7, 8, or 9

The number of ways = 3 × 7!

With the purple at 3, we also have 5 × 7! ways

At 4, similar to 2, we have, 3 × 7! ways

At 5, we have, 0 × 7!

At 6, we have 3 × 7!

For 7, 8, and 9, we have, (5 + 3 + 5) × 7!

The total number of ways = (5 + 3 + 5 + 3 + 0 + 3 + 5 + 3 + 5) × 7! ways

However, placing the purple bead at 1, 2, 3, 4, 6, 7, 8, and 9, (8 positions) can be taken as reflection and rotation of each other and can be considered the same

Therefore, the total number of acceptable ways = (5 + 3 + 5 + 3 + 0 + 3 + 5 + 3 + 5) × 7!/8 = 20,160 ways


Related Questions

(3 1/3) (6) What is the answer?

Answers

Answer:

20

Step-by-step explanation:

(6x3=18)  (6x1/3=2)  (18+2=20)

First things first!

Multiply 6 by 3 (18).

Mulitply 6 by 1/3 (2).

Add 18 and 2, and ... *drum roll*, the final answer is 20!

Hope this helps :)

Samuel takes 5 hours to make a table and a chair. He takes 9 hours to make 3 chairs
and a table. How much time does he take to make a table?

Answers

Answer:

3 hours

Step-by-step explanation:

t = time to make a table

c = time to make a chair

t + c = 5

t+3c = 9

Subtract the second equation from the first

t+3c = 9

-(t + c = 5)

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

       2c = 4

Divide by 2

2c/2 = 4/2

c =2

2 hours for the chair

t+c = 5

t+2 = 5

t = 5-2

t = 3hours

Answer:

It takes 3 hours to make a table.

Step-by-step explanation:

Table and chair : 5 hours

Table and 3 chairs : 9 hours

(Table and 3 chairs) - (Table and chair) = (2 chairs)

9 hours - 5 hours = 4 hours

2 chairs : 4 hours / 1 chair : 2 hours

Table and chair : 5 hours

Chair : 2 hours

Table: x hours

5 - 2 = 3

Table : 3 hours

A typical television newscast has three cameras. The center camera directly faces the news anchor’s desk. The other two cameras are both angled 45 degrees away from the center camera. Suppose each camera has a filed if 60 degrees. What is the total angle covered by three cameras? Explain your reasoning.

Answers

5428 7091 6278 63 and none that are changed in a way for us good to have the right ✅✅is 3 and is made of solid rocks mostly basalt and none of the duties should be separated on any basis of the following ratio of a 666you and a volcano of a bone of a bone of a bone of a bone of a bone of a bone of a bone of a bone of a bone of a bone of a bone where

ayudenme pls aaaaaaaaaaaaaaaaaaaaaaaaaaaa

Answers

Answer:

aslo bien jjjjjjj

Step-by-step explanation:

Jillian bought 3 pounds of apples for $3.09 per pound. she then bought 6 pounds of peanuts for $0.87 per pound. How much did Jillian spend all together?

Answers

Answer:

Jillian spent $14.49 altogether.

Step-by-step explanation:

Let a = pounds of apples, p = pounds of peanuts, and t = total cost

t = 3.09a + 0.87p

t = 3.09(3) + 0.87(6)

t = 9.27 + 5.22

t = 14.49

Theorem 8.9 : The line segment joining the mid-points of two sides of a triangle is parallel to the third side.
prove this theorem

Answers

Answer:

The essence of Mathematics lies in its freedom

What is the quotation of 6 and -1/2?

1. -12

2. -1/12

3. 1/12

4. 12

Answers

Answer: Option 2: -1/12

Explanation

= -1/2÷6

= -1/2×1/6

= -1/12

Must click thanks and mark brainliest

Х
49°
x=
degrees
PLEAIEJEHEHEHDJDJDJDI

Answers

Answer:

Step-by-step explanation:

Exterior equals the sum of opposite interior angles

x = 49 + 90

x = 139°

Find the least common multiple of 4 and 10

Answers

Answer:

LCM of 4 and 10 is 20

Step-by-step explanation:

yes that is the answer

Answer:

Step-by-step explanation:

Factor 4 and 10 into primes

4: 2 * 2

10:2 * 5

Number of 2s = 2 twos

Number of 5s = 1 five

LCM of 4 and 10 = 4 * 5 = 20

If 1 angle is four time of another angle in linear pair find the angles. Please do it fast as you can

Answers

Answer:

let the angle be x then other angle is 4x

so,

x + 4x = 180

5x = 180

x = 36

so other angle I.e 4x = 4 × 36 = 144

Let one angle be x

Other angle=4x

Both are linear pair hence their sum will be 180

[tex]\\ \sf \longmapsto x+4x=180[/tex]

[tex]\\ \sf \longmapsto 5x=180[/tex]

[tex]\\ \sf \longmapsto x=\dfrac{180}{5}[/tex]

[tex]\\ \sf \longmapsto x=30[/tex]

[tex]\\ \sf \longmapsto 5x=5(30)=150[/tex]

A. Determine if a given set ie a well-defined or not.


1. the set of all poor people in batangas.
2. the set of books well-liked by my classmate.
3. the set of handsome teachers in your school.
4. the set of whole numbers greater than 8 but less than 20.
5. the set of intelligent students.​

Answers

Answer:

Step-by-step explanation:

1. yes

2. No

3. No

4. Yes

5. I have no idea about this one, but I think its not a well defined set

^ for 5 its well defined. according to g00gle

42 deliveries in 3 hours = deliveries per hour

Answers

Answer:

14 deliveries per hour

Step-by-step explanation:

42/3

14

The person makes 14 deliveries per hour

Answer:

14

Step-by-step explanation:

42 / 3 = 14

What is the sale price of this bed after the discount has been taken off the standard price?

Answers

Answer:

585 is the answer of your question.

Step-by-step explanation:

because formula is

Mp _ d% of mp

You would like to know how effective a diet program is at helping people lose weight. 18 over-weight people are randomly selected to participate in the program. They are weighed before and after the program and the results are listed below. Do these results give evidence that the diet program is effective at the 1% significance level?

Answers

Answer:

There is not enough evidence to support the claim that drug is effective at 1%

Step-by-step explanation:

For this we use the pored test as we have dependent test;

Difference :

10,5,-5,3,-3,4,2,-3,0,10,8,-2,3,-2,5,5,4,0

Hypothesis :

H0 : μd = 0

H0 : μd ≠ 0

The mean of d, dbar = Σd / n = 44 / 18 = 2.44

The standard deviation, Sd = 4.45 (using calculator)

The test statistic, T : dbar / (Sd/√n)

T = 2.44 / (4.45/√18)

T = 2.44 / 1.0488750

T = 2.326

Degree of freedom, df = n - 1 ; 18 - 1 = 17

The Pvalue = 0.0326

α = 0.01

Since Pvalue < α ; we fail to reject H0

A retailer bought 1000 glass tumblers at rs 80 each.50 glass tumblers were broken and he sold the rest at Rs 96 each .find his profit or loss percent​

Answers

Step-by-step explanation:

Soln

Given

Cp of 1 glass tumbler=80.1000

=Rs 80000

Number of broken glass tumbler=50

Number of remaining glass tumbler=1000-50

=950

Sp of one glass tumbler=96

Sp of 950 glass tumbler=96.950

=91200

Now

Sp > Cp so it is profit

Profit%=sp-cp/cp.100

=91200-80000/80000.100

=11200/80000.100

=14%

Answer:

14%profit

Step-by-step explanation:

Cost of 1000 tumblers=1000×80=80,000

50 of them were broken: 1000-50=950

: He sells 950 tumblers of rs.96 each= ( 950×96)

S.P=91200

We can clearly see he gains for rs.11200.

P%=gain/C.P×100

11200×80000×100

=14%

9.
Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 + 2x = 15

A. 3, –5
B. 3.74, 4
C. 4, –4
D. 15, –17

Answers

Answer:

x = 3 , x = -5

Step-by-step explanation:

Given x^2 +2x=15 add 1 to both sides to get:

x^2 + 2x + 1 =16

(x+1)^2 = 16

x + 1 = ± [tex]\sqrt{16}[/tex] = ± 4

x = -1 ± 4

x = 3 or x = -5

find LCM of 60,40 and 90​

Answers

Answer:

Step-by-step explanation:

Prime factorize.

60 = 2 *2 * 3 * 5     = 2² * 3 * 5

40 = 2 * 2 * 2 *5     = 2³ *       5

90 = 2 * 3 * 3 * 5    = 2 * 3² * 5

LCM = 2³ * 3² * 5 = 8 * 9 * 5 = 360

tìm điều kiện xác định để phân thức A=(1/x-2-2x/4-x^2+1/2+x).(2/x-1)

Answers

X diffrent 0 and 1 ok

I will mark you as BRAINLIEST Please help me out here!! ​

Answers

Step-by-step explanation:

C1:

The pattern for this: you add 1/2 every time.

C2:

3, 3 1/2, 4, 4 1/2

C3:

5 1/2

C4:

The 14th

C5:

10

D1:

You add twice as more than you did before, starting at 3.

D2:

48, 96, 192, 384

D3:

192

D4:

The 9th

D5:

384

Hope this all helps.

Answer:

C)

1) As the sequence progresses, each term in the sequence increases by 1/2.    2) 3 ; 3 1/2 ; 4 ; 4 1/2

3) The 10th term in the sequence is 5 1/2.

4) 7 1/2 is the 14th term in the sequence.

5) The 17th term is 9.

D)

1) As the sequence progresses, each term multiplies by 2.

2) 48 ; 98 ; 192 ; 384

3) The 7th term in the sequence is 192.

4) 768 is the 9th term in the sequence.

5) The 8th term in the sequence is 384.

Step-by-step explanation:

FOR C : 1 + 1/2 = 1 1/2, 1 1/2 + 1/2 = 2, 2 + 1/2 = 2 1/2, and so on. This pattern tells me the rule of the sequence. Continue this sequence to answer 1, 2, 3, 4, and 5.

FOR D: 3 x 2 = 6, 6 x 2 = 12, 12 x 2 = 24, and so on.  This pattern tells me the rule of the sequence. Continue this sequence to answer 1, 2, 3, 4, and 5.

any 5
algebraic formulas

Answers

Answer:

a2 – b2 = (a – b)(a + b)

(a + b)2 = a2 + 2ab + b2

a2 + b2 = (a + b)2 – 2ab

(a – b)2 = a2 – 2ab + b2

(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

(a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca

(a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)

(a – b)3 = a3 – 3a2b + 3ab2 – b3 = a3 – b3 – 3ab(a – b)

a3 – b3 = (a – b)(a2 + ab + b2)

a3 + b3 = (a + b)(a2 – ab + b2)

(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4

(a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4

a4 – b4 = (a – b)(a + b)(a2 + b2)

a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4

Answer:

a2 – b2 = (a – b)(a + b)

(a + b)2 = a2 + 2ab + b2

a2 + b2 = (a + b)2 – 2ab

(a – b)2 = a2 – 2ab + b2

(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

(a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca

(a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)

(a – b)3 = a3 – 3a2b + 3ab2 – b3 = a3 – b3 – 3ab(a – b)

a3 – b3 = (a – b)(a2 + ab + b2)

a3 + b3 = (a + b)(a2 – ab + b2)

(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4

(a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4

a4 – b4 = (a – b)(a + b)(a2 + b2)

a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)

factorize = n!+(n-1)!

Answers

Answer:

Hello,

Step-by-step explanation:

n! + (n-1)!

=(n-1)! * n+ (n-1)!

=(n-1)! * (n+1)

Is 6272 a perfect square? If not find the smallest number by which it must be divided so that the product becomes a perfect square.

Answers

Answer:

(2^7)*(7^2)

Step-by-step explanation:

2*2*2*2*2*2*2*7*7=6272where2 is the smallest number by which it becomes a perfect square

URGENT PLS HELP<3 Each person needs to rent a helmet for $5. Write the expression for the total cost for the helmets.

Answers

Answer:

5n

Step-by-step explanation:

cost of one helmet = $5

let 'n' be the number of person that is n=1,2,3,4........

note that the value of n is always a natural number

therefore the expression = 5n

where 5 is the cost one helmet

n is the number of persons

5n is the answer. N is the number. Hope this helps

Complete the tables, and the graph… HELPPP

Answers

Answer:

answer is - 1

Step-by-step explanation:

- x + y = 3

x = 4

- ( - 4 ) + y = 3

4 + y = 3. take 4 to the right

y = 3 - 4

y = - 1

I hope this answers your question.

PLEASE HELP ASAP ON THESE TWO QUESTIONS BLESS YOUR HEART IF YOU HELP ME 9) Look for two points and find the sloope.
10) Plot the given points and find the slope.

Answers

Answer:

the two points are (-3,-3

Step-by-step explanation:

You must first check if the line is a straight line two the you check the intersection of the two points and the write it

please help I will give brainly, please and thank u :D

Answers

1 . the answer is wrong . correct answer is 3,531.33

2. I would give you suggestions that you need to work on your calculations skills

Put the equation in standard form: Ax+By=C

Equation: 2y= ⅓x - 1​

Answers

Answer:

I answered your question . Hope this helps.

Given three different prime numbers [tex]p_1 \ \ ; \ \ p_2[/tex] and [tex]p_3[/tex] satisfy equation [tex]p_1+p_2+p_3=202[/tex] . Find the maximum value of

[tex]\pmb {p_1 \times p_2\times p_3=?}[/tex]

Answers

Answer:

19982

Step-by-step explanation:

As we know all primes but 2 are odd numbers.

It means sum of any 3 primes not including 2 is odd.

Since we have sum of 202, one of our primes is 2.

Sum of the other two primes is 200.

In order to have maximum value of p*(200 - p) these two numbers must be closer to each other. So we are looking for two primes around 100.

We can test all primes less than 200:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, and 199

The 3 primes with max product are:

2, 97, 103

The value is:

2*97*103 = 19982

*NEED AN ANSWER ASAP* Find x+y given the angle measures in trapezoid EFGH below.

Answers

Answer: x + y = 150

Explanation

y - 65 = 110

y = 110 + 65 (Alternate Interior)

y = 175

y - 65 = 110

∠FGH = 70

70+55+x+45+110 = 360 (sum of angles of a quadilateral is 360)

x + 280 = 360

x = 360 - 280

x = 80

So

x + y = 70 + 80

= 150

Must click thanks and mark brainliest

Look at this sphere:
If the radius is doubled, then which of the following statements about its surface area will be true?

Answers

In the equation for surface area the radius is squared ( r^2)

If the radius is doubled, the radius would be 2^2 more which equals 4

The surface area would be 4 times the old surface area.

Other Questions
what can be the basis for the division of a country in Federal structure give the introduction to each of them ? dch l lt min trung vit nam sang ting anh Could someone answer this for me pleasee Again I am here with privious questionI have post this question last time also but no one answers. So can you solve this. I need it.I will support your account Christian randomly selects students from his grade to rate a math test as easy, moderate, or difficult. Of the students he surveyed, 13 said the test was easy, 11 rated it as moderate, and 3 found it difficult. Assuming that all students took the same test, how many of the 162 total students in Christians grade would probably rate the test something other than easy?A. 27B. 78C. 84D. 126 What is the equation of a parabola that has a vertical axis passes through the point (-1,3) and has its vertex (3,2) comparative and superlative:1. My sister __________ (old) than me2. This t-shirt is _________ (bad) than that t-shirt. What are oromo's cultural values? state the laws of reflection answer this now please :) What is the opportunity cost in this scenario?Mikael has saved $4,000 for his to trip to Brazil. He has calculated that his total transportation expenses will be $1,000. The hotel will cost himanother $1,500. He will spend about $500 on food. He plans on spending the remaining $1,000 for sightseeing and buying souvenirs.While booking his plane ticket, he realizes that the price has gone up. His total transportation expenses will go up by $200. He realizes that hecannot cancel his hotel reservation. He also doesn't want to go cheap on food. Finally, he decides to give up visiting the popular Ouro Pretoduring his stay in Brazil. Parallel Wires: Two long, parallel wires carry currents of different magnitudes. If the current in one of the wires is doubled and the current in the other wire is halved, what happens to the magnitude of the magnetic force that each wire exerts on the other? How tall is the table? 40% of 1000 pls answer and ill mark you brainliest Which of the following is true because of the Associative Law of Addition?A. 1000 + 2000 + 6 = 3006B. (1000) + 2000 + 6 = 1000 + (2000) + 6C. 1000 + 2000 + 6 = 2000 + 1000 + 6D. 1000 + (2000 + 6) = (1000 + 2000) + 6 Which whole number property is represented?(8 2) 6 = 8 (2 6) 1. Consider Smith's connection to each character. What motives might have influencedSmith's portrayal of his fellow colonists?2. How does the map on page 4 help you understand John Smith and the events he narrates?Support your answer with features and details from the map.3.Smith's accounts are filled with details that suggest he is a hero, but if you read closely, hereveals that he was severely criticized for the way he performed. Highlight and reread lines72-90 and record the conflicting information in the chart below: What accusations is hedefending himself against? I need to know how to find the area and to simplify it Equilibrium is when the concentration is the same throughout an entire system. Explain how a cell reaches equilibrium in all three types of solutions (hypertonic, hypotonic, and isotonic). How did France's activity in the Americas differ from that of Spain?