A word is anything of seven letters of the alphabet(26 letters) (no space in between). Repeated lettersare allowed. How many words are there?

Answer:

A ) i) X control chart : upper limit = 50.475, lower limit = 49.825

    ii) R control chart : upper limit =  1.191, lower limit = 0

Step-by-step explanation:

A) Finding the control limits

grand sample mean = 1253.75 / 25 = 50.15

mean range = 14.08 / 25 = 0.5632

Based on  X control CHART

The upper control limit ( UCL ) =

grand sample mean + A2* mean range ) = 50.15 + 0.577(0.5632) = 50.475

The lower control limit (LCL)=

grand sample mean - A2 *  mean range = 50.15 - 0.577(0.5632) = 49.825

Based on  R control charts

The upper limit = D4 * mean range = 2.114 * 0.5632 = 1.191

The lower control limit = D3 * mean range = 0 * 0.5632 = 0  

B) estimate the process mean and standard deviation

estimated process mean = 50.15 = grand sample mean

standard deviation = mean range / d2  = 0.5632 / 2.326 = 0.2421

note d2 is obtained from control table

Answer: It will  take you about 61 years for you to reach your goal.

Step-by-step explanation:

We will represent this situation by an exponential function. So if you earn 5% yearly then we could represent it by 1.05.So in exponential function we need to find the initial value and the common difference and in this case the common difference is 1.05 and the initial value or amount is 50,000 dollars.

We could represent the whole situation by the equation.

y= [tex]50,000(1.05)^{x}[/tex]  where x is the number of years. so if you aspire to have 1,000,000 in some years then we will put in 1 million dollars for y and solve for x.

1,000,000 = 50,000(1.05)^x   divide both sides by 50,000

20 = (1.05)^x

x= 61.40

Answer:

.

Step-by-step explanation:

Answer:

Measure of angle W + measure of angle Z = 180°

Step-by-step explanation:

The reason is that angles in a straight line add up to 180° and angles at a point add up to 360° (i.e the sum of measure of angles W, X, Y, Z is 360°)

Answer:

D is your answer

Step-by-step explanation:

I have no explanation

Answer: try using sine for this equasion

Step-by-step explanation:

Answer:

C. in five hours Caroline wraps an odd number of packages

Step-by-step explanation:

for A until hours you would multiply 2 by 9 and 2 by 9 is 18 and that's an even number so it's not A.

A eliminated.

for B in 3 hours 3 by 9 is 27 and that's an odd number so B is automatically eliminated.

for C in 5 hours all you would do is multiply the 9 by 5 and 9 by 5 is 45 and 45 is indeed an odd number so C is your answer.

for D 7 by 9 is 63 and 63 is an odd number so we already know that C is the answer but still we got to check and D is wrong because 63 is not an even number.

Answer:

[tex]\boxed{Mean = 34.33}[/tex]

Step-by-step explanation:

Mean = Sum of Observations / No. Of Observations

Mean = (24+18+37+82+17+26)/6

Mean = 206 / 6

Mean = 34.33

Answer:

[tex]2 \times 10 {}^{ - 7} [/tex]

Step-by-step explanation:

[tex] \frac{4 \times 10 {}^{ - 4} }{20 \times 10 {}^{2} } = \frac{0.0004}{2000} = 2 \times 10 {}^{ - 7} [/tex]

Hope this helps ;) ❤❤❤

Answer: a) 0.8708, b) 5714, c) 0.000, d) 0.3830

Step-by-step explanation:

(a)

To find P(Z>-1.13):

Since Z is negative, it lies on left hand side of mid value.

Table of Area Under the Standard Normal Curve gives area = 0.3708

So,

P(Z>-1.13) = 0.5 + 0.3708 = 0.8708

(b)

To find P(Z<0.18):

Since Z is positive, it lies on right hand side of mid value.

Table of Area Under the Standard Normal Curve gives area = 0.0714

So,

P(Z<0.18) = 0.5 + 0.0714 = 0.5714

(c)

To find P(Z>8):

Since Z is positive, it lies on right hand side of mid value.

Table of Area Under the Standard Normal Curve gives area = 0.5 nearly

So,

P(Z>8) = 0.5 - 0.5 nearly = 0.0000  

(d)

To find P(| Z | < 0.5)

that is

To find P(-0.5 < Z < 0.5):

Case 1: For Z from - 0.5 to mid value:

Table of Area Under the Standard Normal Curve gives area = 0.1915

Case 2: For Z from mid value to 0.5:

Table of Area Under the Standard Normal Curve gives area = 0.1915

So,

P(| Z | < 0.5) = 2 * 0.1915 = 0.3830

The Probability can be determine using z-Table. The z- table use to determine the area under the standard normal curve for any value between the mean (zero) and any z-score.

(a) The value of [tex]P(z>-1.13)=0.8708[/tex].

(b) The value of  [tex]P(Z < 0.18) = 0.5714[/tex].

(c) The value of [tex]P(Z > 8) = 0.0000[/tex].

(d) The value of [tex]P(| Z | < 0.5) =0.3830[/tex].

Given:

The given condition is [tex]Z\sim N(\mu= 0,\sigma = 1).[/tex]

(a)

Find the value for [tex]P(Z > -1.13)[/tex].

Here Z is less than 1 that means Z is negative. So it will lies it lies on left hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area = 0.3708[/tex].

Now,

[tex]P(Z > -1.13)=0.5 + 0.3708 = 0.8708[/tex]

Thus, the value of [tex]P(z>-1.13)=0.8708[/tex].

(b)

Find the value for [tex]P(Z < 0.18)[/tex].

Here Z is positive. So it will lies it lies on right hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area = 0.0714[/tex].

Now,

[tex]P(Z <0.18)=0.5 + 0.0714 = 0.5714[/tex]

Thus, the value of  [tex]P(Z < 0.18) = 0.5714[/tex].

(c)

Find the value for [tex]P(Z >8)[/tex].

Here Z is positive. So it will lies it lies on right hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area \approx 0.5[/tex].

Now,

[tex]P(Z >8)\approx0.5 - 0.5 = 0.0000[/tex]

Thus, the value of [tex]P(Z > 8) = 0.0000[/tex].

(d)

Find the value for [tex]P(|Z| <0.05)[/tex].

Here Z is mod of Z, it may be positive or negative. Consider the negative value of Z.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area =0.1915[/tex].

Consider the positive  value of Z.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area =0.1915[/tex].

Now,

[tex]P(|Z| <0.5)=2\times 0.1915 = 0.3830[/tex]

Thus, the value of [tex]P(| Z | < 0.5) =0.3830[/tex].

Learn more about z-table here:

https://brainly.com/question/16051105

Answer:

A. This statement A is false.

B. This statement A is false.

C. This statement is true .

Step-by-step explanation:

Determine which of the following statements is true.

From the statements we are being given , we are to determine if the statements are valid to be true or invalid to be false.

SO;

A: If V is a 6-dimensional vector space, then any set of exactly 6 elements in V is automatically a basis for V

This statement A is false.

This is because any set of exactly 6 elements in V is linearly independent vectors of V . Hence, it can't be automatically a basis for V

B. If there exists a set that spans V, then dim V = 3

The statement B is false.

If there exists a set , let say [tex]v_1 ...v_3[/tex], then any set of n vector (i.e number of elements forms the basis of V)  spans V. ∴ dim V < 3

C. If H is a subspace of a finite-dimensional vector space V  then dim H ≤ dim V is a correct option.

This statement is true .

We all know that in a given vector space there is always a basis, it is equally important to understand that there is a cardinality for every basis that exist ,hence the dimension of a vector space is uniquely defined.

SO,

If  H is a subspace of a finite-dimensional vector space V  then dim H ≤ dim V is a correct option.

Answer:

[tex]\boxed{3}[/tex]

Step-by-step explanation:

We can use ratios to solve since the sides are proportional.

[tex]\frac{18}{x} =\frac{48}{8}[/tex]

Cross multiply.

[tex]48x=18 \times 8[/tex]

Divide both sides by 48.

[tex]\frac{48x}{48} = \frac{18 \times 8}{48}[/tex]

[tex]x=3[/tex]

The value of x in the given triangle is 3.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Given are two similar triangles,

Therefore, they have the same ratio of corresponding sides

18/48 = x/8

x = 3

Hence, The value of x in the given triangle is 3.

For more references on similar triangles, click;

https://brainly.com/question/25882965

#SPJ2

Answer:

The adult ticket costs $18 and the children ticket costs $13.

Step-by-step explanation:

Let the price of the adult ticket be a.

Let the price of the children ticket be c.

Three adults and four children must pay $106. This implies that:

3a + 4c = 106 _______(1)

Two adults and three children must pay $75. This implies that:

2a + 3c = 75 ________(2)

We have two simultaneous equations:

3a + 4c = 106 _____(1)

2a + 3c = 75 ______(2)

Multiply (1) by 2 and (2) by 3 and subtract (1) from (2):

  6a + 9c = 225

- (6a + 8c = 212)

             c = $13

Put this value of c in (2):

2a + 3*13 = 75

2a + 39 = 75

=> 2a = 75 - 39

2a = 36

a = 36/2 = $18

Therefore, the adult ticket costs $18 and the children ticket costs $13.

Answer:

the perimeter of the square is just "(5+2x)(2)+(7+2x)(2)

Step-by-step explanation:

Answer:

2 × 10 + 2 × 14

Step-by-step explanation:

The frame is given to have measurements 2 times that of the photograph's measurements. We also know that the photograph is given by dimensions being 5 inch by 7 inch. Therefore the measurements of the frame should be 5 [tex]*[/tex] 2, which = 10 inches, by 7 [tex]*[/tex] 2 = 14 inches.

So the dimensions of the frame are 10 inch × 14 inch. As the frame is present as a rectangle, the perimeter is given by two times both dimensions together. That would be represented by the expression " 2 × 10 inch + 2 × 14 inch. " In other words you can say that the expression is 2 × 10 + 2 × 14 - the expression that represents the perimeter of the frame.

Answer:

43 mountain climbers have not climbed either mountain.

Step-by-step explanation:

Total number of mountain climbers, i.e. n(U) = 60

Number of mountain climbers who have climbed Mt. Everest, n(E) = 10

Number of mountain climbers who have climbed Mt. Rainier, n(R) = 15

Number of mountain climbers who have climbed both, n(E [tex]\cap[/tex] R) = 15

Using the formula to find number of climbers who have climbed either of the mountains:

[tex]n(A \cup B) = n(A)+n(B)-n(A\cup B )[/tex]

[tex]\therefore n(E \cup R) = n(E)+n(R)-n(E\cup R )\\\Rightarrow n(E \cup R) = 10+15-8 = 17[/tex]

To find, who have not climbed either mountain:

[tex]n(E\cup B)'=n(U) - n(E\cap B)\\\Rightarrow n(E\cup B)'=60 - 17 = \bold{43}[/tex]

So, the answer is:

43 mountain climbers have not climbed either mountain.

Answer:

a. P(0 < z < 3.00) =  0.4987

b. P(0 < z < 1.00) =  0.3414

c. P(0 < z < 2.00) = 0.4773

d. P(0 < z < 0.79) = 0.2852

e. P(-3.00 < z < 0) = 0.4987

f. P(-1.00 < z < 0) = 0.3414

g. P(-1.58 < z < 0) = 0.4429

h. P(-0.79 < z < 0) = 0.2852

Step-by-step explanation:

Find the area under the standard normal probability distribution between the following pairs of​ z-scores.

a. z=0 and z=3.00

From the standard normal distribution tables,

P(Z< 0) = 0.5  and P (Z< 3.00) = 0.9987

Thus;

P(0 < z < 3.00) = 0.9987 - 0.5

P(0 < z < 3.00) =  0.4987

b. b. z=0 and z=1.00

From the standard normal distribution tables,

P(Z< 0) = 0.5  and P (Z< 1.00) = 0.8414

Thus;

P(0 < z < 1.00) = 0.8414 - 0.5

P(0 < z < 1.00) =  0.3414

c. z=0 and z=2.00

From the standard normal distribution tables,

P(Z< 0) = 0.5  and P (Z< 2.00) = 0.9773

Thus;

P(0 < z < 2.00) = 0.9773 - 0.5

P(0 < z < 2.00) = 0.4773

d.  z=0 and z=0.79

From the standard normal distribution tables,

P(Z< 0) = 0.5  and P (Z< 0.79) = 0.7852

Thus;

P(0 < z < 0.79) = 0.7852- 0.5

P(0 < z < 0.79) = 0.2852

e. z=−3.00 and z=0

From the standard normal distribution tables,

P(Z< -3.00) = 0.0014  and P(Z< 0) = 0.5

Thus;

P(-3.00 < z < 0 ) = 0.5 - 0.0013

P(-3.00 < z < 0) = 0.4987

f. z=−1.00 and z=0

From the standard normal distribution tables,

P(Z< -1.00) = 0.1587  and P(Z< 0) = 0.5

Thus;

P(-1.00 < z < 0 ) = 0.5 -  0.1586

P(-1.00 < z < 0) = 0.3414

g. z=−1.58 and z=0

From the standard normal distribution tables,

P(Z< -1.58) = 0.0571  and P(Z< 0) = 0.5

Thus;

P(-1.58 < z < 0 ) = 0.5 -  0.0571

P(-1.58 < z < 0) = 0.4429

h. z=−0.79 and z=0

From the standard normal distribution tables,

P(Z< -0.79) = 0.2148  and P(Z< 0) = 0.5

Thus;

P(-0.79 < z < 0 ) = 0.5 -  0.2148

P(-0.79 < z < 0) = 0.2852

Answer:

Hello!! :) The answer to your question is 13,728

Steps will be below.

Step-by-step explanation:

So we will subtract 22,403 and 8,675.

When we do that we will get 13,728

To check your answer we have to do the opposite of subtracting which will be adding.

This is how we check our work: the answer we got was 13,728...we have to take that answer and add it to 8,675 which will give us 22,403

(Both of the numbers are from the question)

At the bottom I attached a picture of how I did the subtracting and how I checked my work.

Sorry for my handwriting......if you can’t understand my handwriting, I attached another picture which is more clearer.

ANSWER TO YOUR QUESTION: 13,728

Brainliest would be appreciated! Thank you :3

Hope this helps! :)

Answer:

The answer is 13,728

Step-by-step explanation:

Check your work with addition.

Answer: x=2 y=-2

(2,-2) one solution

Step-by-step explanation:

Solve by substitution

[tex]\begin{bmatrix}x^2+y^2=8\\ y=x-4\end{bmatrix}[/tex]

[tex]\mathrm{Subsititute\:}y=x-4[/tex]

[tex]\begin{bmatrix}x^2+\left(x-4\right)^2=8\end{bmatrix}[/tex]

[tex]2x^2-8x+16=8[/tex]

[tex]\mathrm{Isolate}\:x\:\mathrm{for}\:2x^2-8x+16=8:\quad x=2[/tex]

[tex]\mathrm{For\:}y=x-4[/tex]

[tex]\mathrm{Subsititute\:}x=2[/tex]

[tex]y=2-4[/tex]        [tex]2-4=-2[/tex]

[tex]y=-2[/tex]

[tex]The\:solutions\:to\:the\:system\:of\:equations\:are[/tex]

[tex]x=2,\:y=-2[/tex]

Answer:

The volume of the solid is: [tex]\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}[/tex]

Step-by-step explanation:

GIven that :

[tex]y = 2 + sec \ x , -\dfrac{\pi}{3} \leq x \leq \dfrac{\pi}{3} \\ \\ y = 4\\ \\ about \ y \ = 2[/tex]

This implies that the distance between the x-axis and the axis of the rotation = 2 units

The distance between the x-axis and the inner ring is r = (2+sec x) -2

Let R be the outer radius and r be the inner radius

By integration; the volume of the of the solid  can be calculated as follows:

[tex]V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(4-2)^2 - (2+ sec \ x -2)^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(2)^2 - (sec \ x )^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [4 - sec^2 \ x ]dx[/tex]

[tex]V = \pi [4x - tan \ x]^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) - 4(-\dfrac{\pi}{3})+ tan (-\dfrac{\pi}{3})] \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) + 4(\dfrac{\pi}{3})- tan (\dfrac{\pi}{3})] \\ \\ \\ V = \pi [8(\dfrac{\pi}{3}) - 2 \ tan (\dfrac{\pi}{3}) ][/tex]

[tex]\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}[/tex]

Answer: Regression line equation:  [tex]\hat{y}=-1.008x+39.1704[/tex]

Step-by-step explanation:

Equation of least-squares regression line for predicting y :

[tex]\hat{y}=b_1x+b_o[/tex]

, where [tex]\text{Slope} (b_1)=r\dfrac{s_y}{s_x}[/tex] ,  [tex]\text{intercept}(b_0)=\bar{y}-b_1\bar{x}[/tex]

Given: [tex]\bar{x}=8.8,\ s_x=1.5,\ s_y=1.8,\ \bar{y}=30.3,\ r=-0.84[/tex]

Then,

[tex]b_1=(-0.84)\dfrac{ 1.8}{ 1.5}\\\\\Rightarrow\ b_1=-1.008[/tex]

Now,

[tex]b_0=30.3-(-1.008)(8.8)=30.3+8.8704\\\\\Rightarrow\ b_0=39.1704[/tex]

Then, Regression line equation:  [tex]\hat{y}=-1.008x+39.1704[/tex]

Answer:

Let E be the event that the first marble selected is green. Let F be the event that the second marble selected is green. A box contains 20 blue marbles, 16 green marbles and 14 red marbles P(F/E)=15/49 because if the first marble selected is green there are 49 in total and 15 are green. I think this is it.

Step-by-step explanation:

Answer: A) 15

Step-by-step explanation:

Because of Pythagorean Theorem, 9^2+12^2=BC^2.  Thus, 81+144=BC^2.  Thus, 225=BC^2.  Thus, 15=BC.

Hope it helps, and ask if you want further clarification <3

Answer:

The answer is option A.

Step-by-step explanation:

Using the properties of logarithms

that's

[tex] log(x) - log(y) = log( \frac{x}{y} ) [/tex]

log 2 - log 14 is

[tex] log(2) - log(14) = log( \frac{2}{14} ) [/tex]

Simplify

We have the final answer as

[tex] log( \frac{1}{7} ) [/tex]

Hope this helps you

Answer:

log ( 1/7)

Step-by-step explanation:

log2-log14

We know that log ( a/b) = log a - log b

log (2 /14)

log ( 1/7)

Answer:

c ≤ -9

Step-by-step explanation:

c / -3 ≥ 3

c ≤ -9

Remember, we flip the sign of the inequality by multiplying / dividing by a negative number.

Answer:

c ≤ -9

Step-by-step explanation:

c / -3 ≥ 3

c ≤ -9

Answer:

the difference between the estimator and the population parameter grows smaller as the sample size grows larger.

Step-by-step explanation:

In Statistics, an estimator is a statistical value or quantity, which is used to estimate a parameter.

Generally, parameters are the determinants of the probability distribution. Thus, to determine a normal distribution we would use the parameters, mean and variance of the population.

An estimator is said to be consistent if the difference between the estimator and the population parameter grows smaller as the sample size grows larger. This simply means that, for an estimator to be consistent it must have both a small bias and small variance.

Also, note that the bias of an estimator (b) that estimates a parameter (p) is given by; [tex]E(b) - p[\tex]

Hence, an unbiased estimator is an estimator that has an expected value that is equal to the parameter i.e the value of its bias is equal to zero (0).

A sample variance is an unbiased estimator of the population variance while the sample mean is an unbiased estimator of the population mean.

Generally, a consistent estimator in statistics is one which gives values that are close enough to the exact value in a population.

Answer:

[tex]\boxed{Option \ B}[/tex]

Step-by-step explanation:

In the triangle,

Hypotenuse = 13

Opposite = Perpendicular = 5

Adjacent = Base = 12

Now,

Cos B = [tex]\frac{Adjacent}{Hypotenuse}[/tex]

Cos B = 12/13

If the triangle is just like in the attached file!

Answer:

B) 12/13

Step-by-step explanation:

Answer:

10 termites will destroy 0.000084kg of wood per week

Step-by-step explanation:

Convert milligram to kilogram

1.2mg=(1.2 / 1,000,000)kg

1.2mg=0.0000012kg

1 termite destroys=0.0000012kg per day

10 termites will destroy (per day) =0.0000012×10 termites per day

10 termites in one day will destroy=0.000012kg

There are 7 days in a week

Therefore,

10 termites will destroy=destruction per day × 7 days

=0.000012×7

=0.000084kg per week

Answer:

x = 30

Step-by-step explanation:

1/2(x+6) = 18

Expand brackets or use distributive law.

1/2(x) + 1/2(6) = 18

1/2x + 6/2 = 18

1/2x + 3 = 18

Subtract 3 on both sides.

1/2x + 3 - 3 = 18 - 3

1/2x = 15

Multiply both sides by 2.

(2)1/2x = (2)15

x = 30

Answer:

30

Step-by-step explanation:

Answer:

60 and 87

Step-by-step explanation:

Question 1: The chance of losing would be 100% - 40% = 60%.

Question 2: Again, we just have to do 100% - 13% = 87%.

Answer:

Below

Step-by-step explanation:

First question:

Jade has a 40% chance of winnig wich could be expressed as 2/5

The chance of losing is the remainning pourcentage from 100%

●100-40 =60%

60% is the chance of losing wich could be expressed as 3/5

The sum of 3/5 and 2/5 is 1 so it's true.

■■■■■■■■■■■■■■■■■■■■■■■■■

Same method for the 2nd question:

The person has a 13 % chance of winning.

The chance of losing is 87%

● 100-13 =87

Answer:

[tex]\boxed{x^3+6x^2+9x}[/tex]

Step-by-step explanation:

[tex]x(x+3)(x+3)[/tex]

Resolving the first parenthesis

[tex](x^2+3x) (x+3)[/tex]

Using FOIL

[tex]x^3+3x^2+3x^2+9x[/tex]

Adding like terms

[tex]x^3+6x^2+9x[/tex]

[tex]\text{If } \: a\cdot b \cdot c = 0 \text{ then } a=0 \text{ or } b =0 \text{ or } c=0 \text{ or all of them are equal to zero.}[/tex]

[tex]x(x+3)(x+3) =0[/tex]

[tex]\boxed{x_1 =0}[/tex]

[tex]x_2+3 =0[/tex]

[tex]\boxed{x_2 = -3}[/tex]

[tex]x_3+3 =0[/tex]

[tex]\boxed{x_3 = -3}[/tex]

Answer:

(2x - y)³ = 8x³ - 12x²y + 6xy² - y³

Step-by-step explanation:

Pascal's Theorem uses a set of already known and easily obtainable numbers in the expansion of expressions. The numbers serve as the coefficients of the terms in the expanded expression.

For the expansion of

(a + b)ⁿ

As long as n is positive real integer, we can obtain the coefficients of the terms of the expansion using the Pascal's triangle.

The coefficient of terms are obtained starting from 1 for n = 0.

- For the next coefficients of terms are 1, 1 for n = 1.

- For n = 2, it is 1, 2, 1

- For n = 3, it is 1, 3, 3, 1

The next terms are obtained from the previous one by writing 1 and summing the terms one by one and ending with 1.

So, for n = 4, we have 1, 1+3, 3+3, 3+1, 1 = 1, 4, 6, 4, 1.

The Pascal's triangle is

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

1 9 36 84 126 126 84 36 9 1

The terms can also be obtained from using the binomial theorem and writing the terms from ⁿC₀ all through to ⁿCₙ

So, for n = 3, the coefficients are 1, 3, 3, 1

Then the terms are written such that the sum of the powers of the terms is 3 with one of the terms having the powers reducing from n all through to 0, and the other having its powers go from 0 all through to n

So,

(2x - y)³ = [(1)(2x)³(-y)⁰] + [(3)(2x)²(-y)¹] + [(3)(2x)¹(-y)²] + [(1)(2x)⁰(-y)³]

= (1×8x³×1) + (3×4x²×-y) + (3×2x×y²) + (1×1×-y³)

= 8x³ - 12x²y + 6xy² - y³

Hope this Helps!!!