Answer:
The fourth term of the expansion is -220 * x^9 * y^3
Step-by-step explanation:
Question:
Find the fourth term in (x-y)^12
Solution:
Notation: "n choose k", or combination of k objects from n objects,
C(n,k) = n! / ( k! (n-k)! )
For example, C(12,4) = 12! / (4! 8!) = 495
Using the binomial expansion formula
(a+b)^n
= C(n,0)a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 + C(n,3)a^(n-3)b^3 + C(n,4)a^(n-4)b^4 +....+C(n,n)b^n
For (x-y)^12, n=12, k=3, a=x, b=-y, and the fourth term is
C(n,3)a^(n-3)b^3
=C(12,3) * x^(12-3) * (-y)^(3)
= 220*x^9*(-y)^3
= -220 * x^9 * y^3
The fourth term in the binomial expansion of ( x - y )¹² is given by the equation A₄ = -220 x⁹y³
What is Binomial Expansion?The general term of the binomial expansion is Tr+1 = nCr x^n-r y^r . Here the coefficient values are found from the pascals triangle or using the combinations formula, and the sum of the exponents of both the terms in the general term is equal to n.
( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ
Given data ,
Let the binomial expansion be represented as A
Now , the value of A is
A = ( x - y )¹² be equation (1)
On simplifying the equation , we get
The fourth term of the binomial expansion is calculated by
A₄ = ⁿC₃ a⁽ⁿ⁻³⁾ b³
Substituting the values in the equation , we get
A₄ = ¹²C₃ x⁽¹²⁻³⁾ ( -y )³
On further simplification , we get
A₄ = ( 12 )! / ( 9 )! 3! x⁹ ( -y )³
A₄ = 12 x 11 x 10 / 2 x 3 x⁹ ( -y) ³
A₄ = -220 x⁹y³
Hence , the fourth term of binomial expansion is -220 x⁹y³
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8. If3:8=c:56, the value of c will be
The scale for the second values is 56/8 = 7
C = 3 x 7 = 21
C= 21
Simplify this God please
Answer:
10
Step-by-step explanation:
[tex] \frac{ \sqrt{75a} + \sqrt{12a} + \sqrt{27a} }{ \sqrt{3a} } \\ \frac{ \sqrt{(25 \times 3)a} + \sqrt{(4 \times 3)a} + \sqrt{(9 \times 3)a} }{ \sqrt{3a} } \\ \frac{ 5\sqrt{3a} + 2 \sqrt{3a} + 3\sqrt{3a} }{ \sqrt{3a} } \\ \frac{(5 + 2 + 3) \sqrt{3a} }{ \sqrt{3a} } = 10[/tex]
Answer: See below
Step-by-step explanation:
My old math notebook had simillar question,hope that help
√75a+√12a-√27a/√3a
=√a(3*25)+√a(3*4)+√a(3*9)/√3a
=√25*√3a+√4*√3a+√9*√3a/√3a
=(5+2+3)√3a/√3a
=5+2+3=10
The product of - 6 and a number x, increased by 23 is – 163. What is
the number?
Answer:
Hope this is correct
Based on the Census, state A has 21 fewer electoral votes for president than state B. If the total number of electoral votes for these two states is 85, find the number for each state
Answer:
state A = 32 votes, state B = 53 votes
Step-by-step explanation:
Let the number of electoral votes for state A be a and state B be b
a = b - 21
a + b = 85
Substituting a for b - 21 in the second equation
2b - 21 = 85
2b = 106
b = 53
Plugging b back in
85 - 53 = 32
g(x) = -10x2+ 490
lesser x=
greater x =
Answer:
Greater x =+ 7
Lesser x = -7
Step-by-step explanation:
G(x) = -10x2+ 490
Let the left side = 0
So we have
0= -10x2+ 490
Solving the above now by allowing the variable with the coefficient of x cross the equal sign.
10x²= 490
Dividing by 10
X²= 490/10
X² = 49
Taking the root of both sides
X= √49
X = + 7or -7
Bigger x =+ 7
Smaller x = -7
A worker is paid $2,350 monthly and has $468 withheld from each monthly paycheck. Which of the following is her annual net salary
Answer:
Annual net salary = $22,584
Step-by-step explanation:
Given:
Monthly wage = $2,350
Withheld paycheck = $468
Find:
Annual net salary = ?
Computation:
Total net salary = Monthly wage - Withheld paycheck
Total net salary = $2,350 - $468
Total net salary = $1,882
Annual net salary = Total net salary × 12
Annual net salary = $1,882 × 12
Annual net salary = $22,584
Find the product of LCM and HCF of 3 and 15
Answer:
45
please see the attached picture for full solution
hope it helps
Good luck on your assignment
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
c.
Step-by-step explanation:
2 Points
This graph shows the solutions to the inequalities y> 3x+6 and y<3x - 7
Does the system of inequalities have solutions? If so, which region contains
the solutions?
A
B
С
O A. There are no solutions
B. There are solutions, and they are the points in region C.
O C. There are solutions, and they are the points in region A.
O D. There are solutions, and they are the points in region B.
Answer:
Option (A)
Step-by-step explanation:
Two inequalities have been given as,
y > 3x + 6 --------(1)
y < 3x - 7 ------(2)
Inequality (1) shows the solution area shaded in blue, means all the solutions for the inequality will lie in the blue area.
Similarly, solutions of inequality (2) will lie in red area.
No common area for the inequalities.
Therefore, system of inequalities will have no solution.
Option (A) will be the answer.
E. coli bacteria have a doubling time of 20 minutes. Starting with 30 E. coli bacteria, how many will there be 6 hours later? Group of answer choices 7,864,410 7,864,320 7,864,452 7,864,821
Answer: 7,864,320
Step-by-step explanation:
Because the doubling time is 20 minutes, the bacteria would have gone through binary fission(cell division in bacteria) 18 times after 6hours(6*60/20)
Nt=N0 * 2^n
N0=starting population
n=number of times bacteria divide
So
30*2^18=7,864,320
Choose at random a person aged 20 to 39 years. Ask their age and marital status (never married, married, or widowed/divorced/separated). Offered is the probability model for 12 possible answers. Age in years 20 – 24 25 – 29 30 – 34 35 – 39 Never married 0.227 0.156 0.089 0.054 Married 0.027 0.086 0.137 0.148 Widowed/divorced/separated 0.006 0.015 0.022 0.033 (a) Is this a legitimate finite probability model? Select the correct description. No. This is not a legitimate finite probability model because each probability is between 0 and 1 , and all sum to 1 . Yes. This is a legitimate finite probability model because each probability is between 0 and 1 , and all sum to 1 . Yes. This is a legitimate finite probability model because the probabilities are all greater than 0 and do not sum to 1 . No. This is not a legitimate finite probability model because the probabilities are all greater than 0 and do not sum to 1 . (b) What is the probability that the person chosen is a 20 ‑ to 24 ‑ year‑old who is married? (Enter your answer rounded to three decimal places.) P(20‑ to 24‑year‑old who is married)= (c) What is the probability that the person chosen is 20 – 24 years old? (Enter your answer rounded to three decimal places.) P(20–24 year old)= (d) What is the probability that the person chosen is married? (Enter your answer rounded to three decimal places.) P(married)=
Answer:
(a)(B)Yes. This is a legitimate finite probability model because each probability is between 0 and 1 , and all sum to 1 .
(b)P(20‑ to 24‑year‑old who is married)=0.027
(c)P(20–24 year old)=0.26
(d)P(married)=0.398
Step-by-step explanation:
Given the probability model below:
[tex]\left\begin{array}{|c|c|c|c|c|}$Age in years& 20 - 24& 25 - 29& 30 - 34& 35 - 39\\$Never married& 0.227& 0.156& 0.089& 0.054\\ $Married &0.027& 0.086& 0.137& 0.148\\$Widowed/divorced/separated &0.006 &0.015& 0.022& 0.033\end{array}\right\\[/tex]
(a)
Adding the probability for each row, we obtain: 0.227+0.156+0.089+0.054=0.5260.027+0.086+0.137+0.148=0.3980.006+0.015+0.022+0.033=0.0760.526+0.398+0.076=1
Therefore this is a legitimate finite probability model because each probability is between 0 and 1 , and all sum to 1 .
(b) The probability that the person chosen is a 20‑24-year‑old who is married
P(20‑ to 24‑year‑old who is married)=0.027
(c)Probability that the person chosen is 20 – 24 years old
P(20–24 year old)=0.227+0.027+0.006=0.26
(d)Probability that the person chosen is married
P(married)=0.027+0.086+0.137+0.148=0.398Natalie is scuba diving in the ocean. She starts 30 feet below sea level. She then dives down another 20 feet. From there, she goes up 15 feet. Which equation shows Natalie's current level?
Answer:
35
Step-by-step explanation:
30+20=50
50-15=35
(Brainliest helps)
Answer:
Answer on imagine math ;)
Find the volume of a rectangular prism if the length is 2x, the width 4x^2, and the height is 2x^2+x+7
Answer:
V=16x^5+8x^4+56x^3.
Step-by-step explanation:
The volume of the rectangular prism is V=16x^5+8x^4+56x^3.
Formula for rectangle prism: V=whl
Formula: L*W*H
Answer: V=16x^5+8x^4+56x^3
Hope this helps.
Suppose you have been on the train for at least 5 hours. A passenger
says that the trip to Fairbanks takes 10 hours. Write an inequality
that describes in how many more hours h the train will reach
Fairbanks.
Answer:
[tex]h \leq 5[/tex]
Step-by-step explanation:
Time already spent on the train is at least 5 hours
Since the trip to Fairbanks take 10 hours, we have that, the sum of the number of hours left, h and the time already spent will be equal to 10.
[tex]t+h=10\\$Since the time for which the passenger has been on the train \geq 5\\5+h \leq 10\\h \leq 10-5\\$The inequality that describes in how many more hours, h the train will reach Fairbanks, therefore, is:\\h \leq 5[/tex]
Find the gradient of the line y+2x= -1
BONUS: Find the y-intercept of the line 2y=10x-10
Given points (r1, u1 ) and (r2, u2) in polar coordinates, obtain a general formula for the distance between them. Simplify it as much as possible using the identity cos2 u 1 sin2 u 5 1. Hint: Write the expressions for the two points in Cartesian coordinates and substitute into the usual distance formula.
Answer:
[tex]d=\sqrt{r_1^2+r_2^2-2r_1r_2\cos(u_2-u_1)}[/tex]
Step-by-step explanation:
The Law of Cosines gives an immediate result. No translation to Cartesian coordinates is necessary. That law makes use of the angle between the vectors, u2-u1
[tex]d^2=r_1^2+r_2^2-2r_1r_2\cos(u_2-u_1)\\\\\boxed{d=\sqrt{r_1^2+r_2^2-2r_1r_2\cos(u_2-u_1)}}[/tex]
Eight men and eight women have six tickets in one row to the theater. In how many ways can they sit if the first person in the row is a woman and the people alternate woman, man, woman, man and so on?
Answer:
As there are six seats in a row and the first person in the row is a woman and the people alternate woman, men, the possibility is
W
M
W
M
W
M
in that order.
Now as we four women, three seats for women can be filled in
X
4
P
3
=
24
ways
and similarly as we four men, three seats for men can be filled in
X
4
P
3
=
24
ways
Hence, total
24
×
24
=
576
permutations.
Step-by-step explanation:
When AE = 7, EC= 14, CB= 24, what is ED?
Answer:
ED = 8
Step-by-step explanation:
AC = 21 which means AE is 1/3 of the length of AC.
So, ED must also be 1/3 of the length of BC.
1/3 x 24 = 8
PLEASE HELP!!! Two towns are 1100 miles apart. A group of hikers starts from each town and walks down the trail toward each other. They meet after a total hiking time of 240 hours. If one group travels one half mile per hour slower than the other group, find the rate of each group.
Answer:
2.54 miles/hr
2.04 miles/hr
Step-by-step explanation:
Given: Distance between the two towns = 1100 miles
Difference between speeds = [tex]\frac{1}{2}[/tex] miles/hr
Total time when they meet = 240 hours
To find:
Let distance traveled by first group = [tex]x[/tex] miles.
Now, the distance traveled by second group = (1100-[tex]x[/tex]) miles/hr
The relation between Speed, Time and Distance is given as:
[tex]\text{Speed =} \dfrac{\text{Distance}}{\text{Time}}[/tex]
Let speed of first group = [tex]S_1[/tex]
[tex]S_1 = \dfrac{x}{240}[/tex]
Let speed of second group = [tex]S_2[/tex]
[tex]S_2 = \dfrac{1100-x}{240}[/tex]
As per question, [tex]S_1[/tex] = [tex]S_2[/tex] + [tex]\frac{1}{2}[/tex]
[tex]\dfrac{x}{240} = \dfrac{1100-x}{240} + \dfrac{1}{2}\\\Rightarrow \dfrac{x}{240} - \dfrac{1100-x}{240} = \dfrac{1}{2}\\\Rightarrow \dfrac{x-1100+x}{240} = \dfrac{1}{2}\\\Rightarrow 2x - 1100 = 120\\\Rightarrow 2x = 1220\\\Rightarrow x = 610 ft[/tex]
Now,
[tex]S_1 = \dfrac{x}{240}[/tex]
Putting value of [tex]x[/tex]:
[tex]S_1 = \dfrac{610}{240}\\\Rightarrow S_1 = 2.54\ miles/hr[/tex]
Similarly, putting value of [tex]x[/tex] in [tex]S_2[/tex]:
[tex]S_2 = \dfrac{1100-610}{240}\\\Rightarrow S_2=\dfrac{490}{240}\\\Rightarrow S_2 = 2.04\ miles/hr[/tex]
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A. [tex]G(x) = x^2+7[/tex]
Step-by-step explanation:
To shift the function F(x), seven units upwards, there needs to be a 7 being added. Based on this, only "A," is correct.
A house and a lot are apprised at $212,400.If the value of the house is four times the value of the lot, how much is house worth?
simplificar A=4x2-6x2+7x2-20x2+19x2
Answer:
4x²
Step-by-step explanation:
Your equation is 4x² - 6x² + 7x² - 20x² + 19x².
Since they all have the same variable, simply combine them all to find your answer.
4x² - 6x² + 7x² - 20x² + 19x²
-2x² + 7x² - 20x² + 19x²
5x² - 20x² + 19x²
-15x² + 19x²
4x²
If a rock falls from a height of 43 meters on Earth, the height H (in meters) after x seconds is approximately Upper H (x )equals 43 minus 4.9 x squared . (a) What is the height of the rock when xequals1.6 seconds? The height of the rock when xequals1.6 seconds is nothing meters.
Answer:
2.96 seconds
Step-by-step explanation:
Let H(x) = zero and solve for "x".
43 - 4.9x² = 0
4.9x²=43
x²=8.77
x=2.96
therefore, approximately when x=2.96seconds, the rock strike the ground.
The Statue of Liberty in New York stands on top of a foundation and a pedestal. The statue, including foundation and pedestal, measures about 305 feet from the ground to the top of the statue’s torch. The statue herself stands 151 feet. What is the height of the foundation and pedestal?
Answer:
The answer is 154 ft.
Step-by-step explanation:
You would take the total height (305) and subtract is by the actual statue(151) to get your answer.
305-151=154
Answer:
154
Step-by-step explanation:
According to www.whitehouse.gov, the government had about $2.1 trillion in receipts and $2.8 trillion in outlays (expenses) for 2013. Does this represent a surplus or a deficit? What was the ratio of the government's expenses to it's receipts for 2013? Express this as a decimal rounded to the thousandths place.
Answer:
The ratio of the government's expenses to it's receipts for 2013 is 1.3333333 trillion
Step-by-step explanation:
According to the given data we have the following:
Receipt=$2.1 trillion
Expenses=$2.8 trillion
Hence, it represent a decifit of $2.8 trillion-$2.1 trillion=$0.7 trillion
Therefore, to calculate the the ratio of the government's expenses to it's receipts for 2013 we would have to use the following formula:
ratio of the government's expenses to it's receipts=$2.8 trillion/$2.1 trillion
ratio of the government's expenses to it's receipts=1.3333333 trillion
The ratio of the government's expenses to it's receipts for 2013 is 1.3333333 trillion
solve the expression x + 3 = 7
Answer:
x=4
Step-by-step explanation:
think of the equation like this: you have to do the inverse(opposite) operations so for adding you would subtract it. So for the adding 3 you would subtract it from both sides of the equation and get X=4
help me in this question
who can solve everything the fastest
Answer:
Step-by-step explanation:
1. 90
2. 42,49
3. 2860
4. 13cm
5. 16-5=11
6. Sector
7. 1 whole no. 1 divided by 5
8. 7 and 4
9. 3/9
10.57.8
11. 19:20pm
12.
Could someone give me the answer to this.
Answer:
B =33.69
Step-by-step explanation:
Since this is a right triangle, we can us trig functions
tan B = opposite side/ adj side
tan B = 6/9
Take the inverse tan of each side
tan ^ -1 tan B = tan ^-1 (6/9)
B =33.69006753
To the nearest hundredth
B =33.69
Answer:
33.69°
Step-by-step explanation:
From Trigonometry identity;
Tan<B = 6/9 = 2/3 [opposite/adjacent]
B = Tan^{-1} 2/3
=33.69°
What is the product?
(x - 3)(2x2 - 5x + 1)
N
273 - 2 + 16x + 3
2x3 - 11X2 + 16x + 3
O 2x3 - 11x2 + 16x - 3
O 2x3 - x2 + 16x - 3
The right answer is of option C
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Answer:
[tex] = 2 {x}^{3} - 11 {x}^{2} + 16x - 3 \\ [/tex]
Step-by-step explanation:
[tex](x - 3)(2 {x}^{2} - 5x + 1) \\ x(2 {x}^{2} - 5x + 1) - 3(2 {x}^{2} - 5x + 1) \\ 2 {x}^{3} - 5 {x}^{2} + x - 6 {x}^{2} + 15x - 3 \\ = 2 {x}^{3} - 11 {x}^{2} + 16x - 3[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Create an expression that fits all of the following conditions: There are exactly four terms. Exactly two of the terms are like terms. At least one term is an integer. Simplify the expression that you created.
Answer:
The expression created is: [tex]3x^2+3x+8x-7[/tex]
Simplified, we obtain : [tex]3x^2+11x-7[/tex]
Step-by-step explanation:
We are to create an expression that satisfies the following conditions
There are exactly four terms. Exactly two of the terms are like terms. At least one term is an integer.Let the two like terms be 3x and 8x
Let the integer term = -7
Let the other term [tex]=3x^2[/tex]
Our written expression is therefore:
[tex]3x^2+3x+8x-7[/tex]
We simplify the expression by solving the like terms for a single term
[tex]3x+8x=11x\\$Therefore\\3x^2+3x+8x-7=3x^2+11x-7[/tex]