Use the Binomial Theorem to find the coefficient of x^3y^2z^5 in (x + y + z)^10.

Answers

Answer 1

Answer:

The coefficient is 2520

Step-by-step explanation:

Given

[tex](x + y + z)^{10[/tex]

Required

The coefficient of [tex]x^3y^2z^5[/tex]

To do this, we make use of:

[tex]k = \frac{n!}{n_1!n_2!....n_m!}[/tex]

Where

[tex]k \to[/tex] coefficient

[tex]n = 10[/tex] the exponent of the given expression

[tex]n_1=3[/tex] -- exponent of x

[tex]n_2=2[/tex] --- exponent of y

[tex]n_3=5[/tex] --- exponent of z

So, we have:

[tex]k = \frac{n!}{n_1!n_2!....n_m!}[/tex]

[tex]k = \frac{10!}{3!2!5!}[/tex]

Expand

[tex]k = \frac{10*9*8*7*6*5!}{3!2!5!}[/tex]

[tex]k = \frac{10*9*8*7*6}{3!2!}[/tex]

[tex]k = \frac{30240}{3!2!}[/tex]

Expand the denominator

[tex]k = \frac{30240}{3*2*1*2*1}[/tex]

[tex]k = \frac{30240}{12}[/tex]

[tex]k = 2520[/tex]


Related Questions

Help!!!!! find the value of x.

Answers

Answer:

x = 48

Step-by-step explanation:

The two angles shown in the diagram are supplementary and add to 180° because they form a straight line. We can set up an equation:

x - 12 + 3x = 180

4x - 12 = 180

4x = 192

x = 48

Answer:

[tex]x=42[/tex] ✔︎

Step-by-step explanation:

∠1 + ∠2=1803x+x-12=1804x-12=1804x=180-124x=168x=42°

∠1= 3x=3×42=126°

∠2=x-12=42-12= 30°

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

hope it helps...

have a great day!!

Write the simplest form of this ratio and its method.

2/3 : 3/2 : 5/8

Answers

Answer:

16 : 36 : 15

Step-by-step explanation:

2/3 : 3/2 : 5/8

multiply each term by the lowest common denominator: 24

16 : 36 : 15

i need help 3x²+7x+3=0

Answers

Answer:

60

Step-by-step explanation:

3x=3 multiplied by 2 which is 3x3=9

so, 9+(7x= 7x7=49) 49+3=61 rounded to 60

-7(6m+ 2) = -308 showing work

Answers

[tex]\sf\purple{m\:=\:7}[/tex] ✅Step-by-step explanation:

[tex] - 7(6m + 2) = - 308 \\ ➪ \: - 42m - 14 = - 308 \\ ➪ \: - 42m \: = - 308 + 14 \\ ➪ \: m = \frac{ - 294}{ - 42} \\ ➪ \: m \: = 7[/tex]

To verify:-

[tex] - 7(6 \times 7 + 2) = - 308 \\ ➵ - \: 7(42 + 2) = - 308 \\ ➵ \: - 7 \times 44 = - 308 \\ ➵ \: - 308 = - 308[/tex]

L. H. S. = R. H. S.

Hence verified.

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

A student measures the volume of a rubber stopper and finds that it is 36ml. The
teacher also measures the stopper and obtains a value of 40 ml. Other students
measure the stopper and it is decided to use 38 ml as the standard value for the
volume of the stopper. What was the student's percentage error? The teachers
error?

Answers

Answer:

the answer should be 5 I guess

HELP WILL GIVE BRAINLIST

Answers

Number 1 and number 3 are the ones that are equivalent

In selecting one card from a deck of cards is obtaining a queen and obtaining a 2 mutually exclusive events?

A: Yes/True
B: No/False

Answers

Answer:

Mutually exclusive is a statistical term describing two or more events that cannot happen simultaneously. It is commonly used to describe a situation where the occurrence of one outcome supersedes the other.

Since in this question, we have selected one card from a deck, and is obtaining a 2 and a queen.

I think the answer for this would be No/False but if i'm wrong, tell me!

what is 103 more than 1000​

Answers

Answer:

Step-by-step explanation:

         We are looking for a new number which is 1000 more than 103.

We will get the new number by adding 1000 to 103.

We write it down as:

103+1000=1103

And finally the solution for: What number is 1000 more than 103?

is 1103 ans

please mark me as brainliest..

please mark me as brainliest

URGENT QUESTION.

The graph represents all solutions to an inequality


Please tell me the answer to this question. It is urgent...

Answers

Answer:

The answer is D. -9 and -3

Step-by-step explanation:

since the graph starts at 1 and goes backwards, it cant be 1. so that rules out A. and B. then it requires the numbers to be negative because if they are a whole number over 1, they don´t fit the inequality. I hope this helps :))

X + 6
for
<1
f(x) =
-5
for
X = 19
X + 4
for
Find f(1)

Answers

Answer:

Step-by-step explanation:

when, for each x in the domain of f, f(x) 6. A function f Skills and Applications 回避回Domain, Range, and Values of a is , 13. Function In Exercises 7-10, use the graph of the function to find the domain and range of f and each function value. 7. (a) f(-1) (b) f(0) 8. (a) f(-1) (b) f(0 15. f(x) 16. f(x) 17. f(x) 18. f(x) 19. f(x 4-2 2 4 6 (c) f(3) (d) f(-1)(c) f(0 (d) f(2) y | y =f(x) 20. f(x 4 2 21. f(x 22. f(x 23. f(a 24. f( 2 回 回Vertical Line Test for Functions In 25. f Exercises 11-14, use the Vertical Line Test to determine whether the graph represents y as a function of x. To print an enlarged copy of Graph the graph, go to MathGraphs.com. 窝 (a) use

3.750 kg and 1.125 kg in simplest form​

Answers

Answer:

3.750 kg + 1.125 kg = 4.875 kg

Answer:

Hello There!!

Step-by-step explanation:

When it is simplest form you add all the like terms together so in this case it is kilograms so 3.750+1.125= 4.87500kg or 4.875kg (It is the same just shorter)

hope this helps,have a great day!!

~Pinky~


Help please! I would really appreciate it!!!

Answers

Answer:

the output is n+5

Step-by-step explanation:

3+5

4+5

8+5

n+5

1) Find the area of  ABC to the nearest square centimeter.

Answers

that is right correct answer

Rewrite in simplest terms: 3g-5(-3g+7)3g−5(−3g+7)

Answers

Answer:

Step-by-step explanation:

Figure JKLM is similar to figure PQRS.
S
J
к
R
Р
M
L
Which proportion must be true for these figures?
QR JK
F
=
QP
LM
QR
RS
=
KL
JK
QR
H
Il
PO
LM
QR
Il
PS
IM
KL

Answers

Answer:

the answer is D

Step-by-step explanation:

i found it in quizzes and Quizlet

The average of 2 3 and what number is 10?
pls help

Answers

i think it’s 5 tbh it’s random

Work out the size of angle p.
97°
64°
р
49°
76

Answers

Answer:

You have not attached a picture of the triangle.

180 degrees complete a triangle so maybe if an angle is given + 90 degrees if its right angle then 90- other angle = angle p.

You would need to see if any other angles given and if not then you would need to see if any straight parallel lines or adjacent or even consecutive angles given if not then angle p could be worked out from a side given.

If its an opposite side and adjacent then we use shift Tan-1  side/side

If its an adjacent side and hypotenuse we use shift Cos-1 side/side

IF its an opposite and hypotenuse given we use shift Sin -1 side/side

need help w this pls guys

Answers

Answer:

B

Step-by-step explanation:

Enter the value of p so that the expression (7 + 4n)3 is equivalent to 3 (4n + p).

I NEED HELPPP

Answers

Answer:

7

Step-by-step explanation:

Makes both expressions exactly identical and equivalent in value.

Please help!! What is (-4r) (-30) - (-8) when r = 8

Answers

Answer:

968

Step-by-step explanation:

just substitute r for 8 and solve!

(-4r) (-30) - (-8) when r = 8

-4(8)×(-30)+8

-32 × -30 +8

960 + 8

968

can someone please help sovle this

Answers

Answer:

3

Step-by-step explanation:

[tex]4x * x = 9 * 4[/tex]

[tex]4x^2 = 36[/tex]

[tex]x^2 = 9[/tex]

[tex]x = 3[/tex]

help me i need help pls

Answers

Answer:

13

Step-by-step explanation:

4x-9=×+12. x=1 plug it in and u get 13

joe paid 14.00 for a board game. this is 70% of the original price. what was the original price?

Answers

Answer:

I'm going to be honest

Step-by-step explanation:

I don't have any clue sorry.

Help me please giving out brainliest!

Answers

Answer:

Your answer is B

Step-by-step explanation:

If you use the division you technically can't use the distributive property, so it could be A. But if you had to use it; I would say the best way to do so it to multiply everything by 1.

What is the rule of 72?​

Answers

Answer:

Brainiest please

Step-by-step explanation:

In finance, the rule of 72, the rule of 70 and the rule of 69.3 are methods for estimating an investment's doubling time. The rule number (e.g., 72) is divided by the interest percentage per period (usually years) to obtain the approximate number of periods required for doubling. Although scientific calculators and spreadsheet programs have functions to find the accurate doubling time, the rules are useful for mental calculations and when only a basic calculator is available.

What is coordinates of point C?

Answers

Answer:

(3,6)

Step-by-step explanation:

Using the midpoint segment formula

M(X, Y) = [(ax1+bx2/2, ay1+by2/2)]

Given (-2 -6) and (4,6) divided in the ratio 1:5

X = 1(-2) + 5(4)/1+5

X = -2+20/6

X = 18/6

X = 3

Similarly

Y = 1(-6)+ 5(6)/1+5

Y = -6+30/6

Y = 24/6

Y = 4

Hence the required coordinate of C is (3,6)

Find the domain and range of the given graph?
HELPPPP PLSS​

Answers

Answer:

The domain would be -3≤x≤2 and the range would be -5≤y≤4

Step-by-step explanation:

The domain is where the x values cover, so since on the graph the points range from having -3 as the x value to 2, x would be anything between or equal to these values.

The domain is where the y values cover, so since on the graph the points range from having -5 as the y value to 4, y would be anything between or equal to these values.

A tennis court has a length of (5x+7) and a width of (3x-3).
What is the area of the tennis court?

Answers

15x^2-15x+21x-21
15x^2+6x-21 is the answer

A recent study revealed that the average weight of babies born in the United States is normally distributed with a mean of 7.5 pounds. This number is lower than recent years and so researchers are interested in determining what factors are associated with lower birth weights. One researcher decides to look at the age of the mother to determine if younger mothers have babies that are significantly heavier or lighter than average. To study this the researcher collects data from 87 babies who were born to mothers between the ages of 16 and 18. Only one baby was measured per mother. Twins and other multiple births were excluded. The average weight for these babies was 7.3 pounds with a standard deviation of .6 pounds.

Which of the following statements is relevant to the assumption of Normality?

a. the standard deviation for young mothers is not expected to be different than the standard deviation in the population
b. only one baby was measured per mother
c. weights of babies are normally distributed in the population
d. the study used a sample that is different than the comparison population and measured weight on a ratio scale

Answers

Answer:

a. the standard deviation for young mothers is not expected to be different than the standard deviation in the population

Step-by-step explanation:

The population mean = μ= 7.5

Sample mean = x`= 7.3

Sample standard deviation= s= 0.6

Sample size = 87

Assuming normality we perform z test

z= x`-u/s/√n

z= 7.3-7.5/0.6/√87

z= -3.11

The critical region for 0.05 for two tailed test is z>+1.96 and Z<-1.96

Since the calculated z= -3.11 falls in the critical region Z<-1.96 we conclude that birth rate is lower in the young mothers.

a. the standard deviation for young mothers is not expected to be different than the standard deviation in the population

Only choice a is correct because when n > 30 the population standard deviation and the sample standard deviation are assumed to be normal

Choice b cannot be the correct option because it is already inferred that only one baby was measured per mother.

Choice C cannot be also the best choice because it is already assumed.

Choice d is totally incorrect.

Which trig ratio? Can you solve this??

Answers

Step-by-step explanation:

There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant and cotangent. These six trigonometric ratios are abbreviated as sin, cos, tan, csc, sec, cot. These are referred to as ratios since they can be expressed in terms of the sides of a right-angled triangle for a specific angle θ.

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