Answer: 3060
Step-by-step explanation:
Formula : (r+1)th term of [tex](a+b)^n[/tex] : [tex]T_{r+1}=\ ^nC_r(a)^{n-r}(b)^r[/tex]
To find: Coefficient of [tex]x^{14}y^4[/tex] in the expansion of [tex](x + y)^{18}[/tex].
Let the term in the expansion of [tex](x + y)^{18}[/tex] be [tex]^{18}C_r x^{18-r}y^r=x^{14}y^4[/tex]
[tex]\Rightarrow\ r=4[/tex]
Now, Coefficient = [tex]^{18}C_r=^{18}C_4=\dfrac{18!}{4!14!}[/tex] [[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]]
[tex]=\dfrac{18\times17\times16\times15\times14!}{14!(24)}\\\\=3060[/tex]
Hence, the coefficient of [tex]x^{14}y^4[/tex] in the expansion of [tex](x + y)^{18}[/tex] is 3060 .
Simplify the expression 4(2x - 3)
Answer:
8x - 12
Step-by-step explanation:
4(2x - 3) (use distributive property, see attached)
= (2x)(4) - 3(4)
= 8x - 12
solve the inequality 7(v + 8) ≥ 7v + 1
Answer:
True all for v
Step-by-step explanation:
7(v+8)≥7v+17v+56≥7v+17v+56−7v≥7v+1−7v56≥156−56≥1−560≥−55All real numbers are solutions.
PLEASE HELP The coefficients of the first four terms in the expansion of (a + b) ^5 are a) 1, 3, 5, 7 b) 1, 4, 6, 4 c) 1, 2, 3, 4, 5 d) 1, 5, 10, 10
Answer:
D is the correct answer
Step-by-step explanation:
Fifth row of Pascal pyramid is 1 , 5, 10, 10, 5 , 1
The expansion should always have n + 1 number of terms
Where n is the power
Answer:
answer is D
Step-by-step explanation:
What is the middle term of the product of (x - 4)(x - 3)?
Answer:
- 7x
Step-by-step explanation:
Given
(x - 4)(x - 3)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x - 3) - 4(x - 3) ← distribute both parenthesis
= x² - 3x - 4x + 12 ← collect like terms
= x² - 7x + 12
with middle term = - 7x
Answer:
Step-by-step explanation:
= x(x-3) - 4(x-3)
= x²-3x - 4x + 12
= x² -7x +12
So -7x is the middle term
PLEASE PLEASE HELP WILL MARK BRAINLY
Answer:
The second option (see attached image)
Step-by-step explanation:
You are looking for a box diagram that represents 9 units, and from those, clearly marked sections that contain 3/2 = 1.5 units.The idea is to count how many 1.5 units you have in 9 units.
The in the second diagram you see 9 boxes subdivided in half. Then outlined in red other smaller boxes of length 1.5 units. We can clearly see from the diagram that there are exactly 6 of these smaller 1.5 units red boxes to produce the total 9 unit object.
PLEASE HELPP NOW!!! Question in the photo
Answer:
Step-by-step explanation:
Am I correct in thinking that the question is asking how much of the $4.95 the city of San Francisco receives?
In that case....
Step 1.
$4.95 ÷ 8.25% = $0.60
Step 2.
$0.60 x 2.5% = $1.50
ANSWER =
The city of San Francisco receives 2.5% of the total taxes, equal to $1.50
Hope this helps!
Bluey :)
Select the correct answer. What is the area of the cross section that is parallel to side PQRS in this rectangular box? A. 12 square units B. 16 square units C. 30 square units D. 40 square units
Answer:
12 square units.
Step-by-step explanation:
What is the mean average deviation (MAD) of the data set shown below? Round your answer to the nearest tenth when necessary.
Answer:
18
Step-by-step explanation:
to find the MAD you add all of the numbers first 22+19+30+13+17+21+8+15+12+23= 180
then you divide it by how many numbers there are for instance there are 10 because there are 10 pairs of numbers then you divide it by 180 and you get 18
hope it helped :)
Each new triangle shown below has one more dot per side than the previous triangle. What is the total number of dots on the 200th triangle of this sequence? first term has 6 second term has 9 third has 12 PLS HELP WILL MARK BRAINLIEST
Answer: 603 dots
Step-by-step explanation:
Triangle always has 3 sides. Given that
Each new triangle shown below has one more dot per side than the previous triangle. That means if first term has 6 dot, the second term will have 9 dots and third has 12 dots.
The difference between first and the second is the same with the difference between third and the second. That is,
First term a = 6
Difference d = 3
Number of term n = 200
This is arithmetic progression. We can come up with a formula:
Tn = a + ( n - 1 )d
Substitute all the parameters into the formula
Tn = 6 + ( 200 - 1 )×3
Tn = 6 + 199×3
Tn = 6 + 597
Tn = 603 dots
Therefore, the total number of dots on the 200th triangle of this sequence is 603 dots.
In the circle below, O is the center and mĞ= 150°. What is the measure of angle HIG?
Answer:
15°
Step-by-step explanation:
∠GOI=150°
∠HOG=30°
∠HIG=30°/2=15°(Circle angle)
which correctly describes how the graph of the inequality -4 -x >7 is shaded?
A. Above the dashed line
B. Above the solid line
C. Below the solid lime
D. Below the dashed line.
Answer:
b
Step-by-step explanation:
(13 points!) Use the frequency table. Find the probability that a person goes to the movies at least 8 times a month. Round to the nearest thousandth. 0.343 0.165 0.697 0.883
Answer:
0.165
Step-by-step explanation:
8 is more than 7.
So, it will be 123 and 123/747 is .1646586345.
.1646586345 rounded to the nearest thousandth is 0.165
Answer:
0.165
Step-by-step explanation:
TRUST ME 100%
What is the distance from the origin to point A graphed on the complex plane below?
|5|
|13|
9
13
Answer:
√13
Step-by-step explanation:
(-3, -2) (0, 0)
distance √(9 + 4) = √13
The distance from the origin to the point A is [tex]\sqrt{13}[/tex] unit.
What is the formula to measure distance between two points ?
Let, the co-ordinates of two points in 2D plane are [tex](x_{1} ,y_{1} )[/tex] & [tex](x_{2}, y_{2} )[/tex]
Then the distance between this two points be d (say)
Therefore, [tex]d=\sqrt{(x_{2}- x_{1}) ^{2}+ (y_{2} -y_{1} )^{2} }[/tex]
What is the required distance ?The co-ordinate of point A in the graph is (-3, -2)
The co-ordinate of origin is (0, 0)
∴ The distance between (0, 0) & (-3, -2) is = [tex]\sqrt{((-3)-0) ^{2}+ ((-2) -0 )^{2} }[/tex]
= [tex]\sqrt{(-3)^{2}+(-2)^{2} }[/tex]
= [tex]\sqrt{9+4}[/tex]
= [tex]\sqrt{13}[/tex]
Learn more about distance of two points here :
https://brainly.com/question/7243416
#SPJ2
30 points high school geometry question
Answer:
x = 5
Step-by-step explanation:
9/15 = 3/x
x = 5
X would equal 5
I did this test in high school. smh
HELP ME PLZZZZZZ I NEED HELP
Answer:
Tossing two coins once.
Step-by-step explanation:
According to the diagram, there are just two outcomes: either H or T.
The spinner has three outcomes, and the cubes have 6 outcomes each, so we can eliminate the top two options.
If the person were just tossing one coin, the outcomes would be H or T, but there are more outcomes than that, so the diagram represents tossing two coins once.
Hope this helps!
A cube has a side length of 10 inches. Jada says the surface area of the cube is
600 in?, and Noah says the surface area of the cube is 3,600 in?. Remember we
calculate surface area by finding the area of all the surfaces and adding them up.
Here is how each of them reasoned:
Jada's Method:
Noah's Method:
6. 102
6.102
6.100
602
600
3,600
Do you agree with either of them? Explain your reasoning.
Answer:
I agree with Jada
Step-by-step explanation:
So first you would find the area of one of the faces and it is 100 and then you would multiply the area of one face by 6 because there are 6 faces so you would get 600 inches so Jada would be right
Answer:
Jada is correct in this situation.
Step-by-step explanation: Noah's math is not correct. He goes from 6 times 10^2 to 60^2, which you cannot do. You first must do the exponents (10^2=100) and then multiply it by 6. Jada's method should be similar to that.
795.800.913.789
seven hundred ninety-five billions eight hundred sixty millions, nine hundred thirteen thousands, seven hundred
eighty-nine
seven hundred and ninety-five billion, eight hundred and sixty million, nine hundred and thirteen thousand, seven
hundred and eighty-nine
seven hundred ninety-five billion eight hundred sixty million nine hundred thirteen thousand, seven hundred eighty.
nine
seven hundred ninety-five billion eight hundred six million nine hundred thirteen thousand, seven hundred eighty-nine
Submit
Reset
Answer:
seven hundred ninety-five billion eight hundred million nine hundred thirteen thousand seven hundred eighty-nine
From the set {6, 16, 24}, use substitution to determine which value of x makes the inequality true. 4 + x < 20 A. 16 B. 6 C. none of these D. 24
================================================
Explanation:
In math, the term "substitution" basically means "replace". Keep in mind that x is a placeholder for a number. Think of it as a box we place a number inside.
We have the items {6, 16, 24} to use as replacements for x. We only do one number at a time
Let's try x = 6
4 + x < 20
4 + 6 < 20 ... replace x with 6
10 < 20 ... this is a true statement as 10 is less than 20
So x = 6 is a solution
Let's try x = 16
4+x < 20
4+16 < 20
20 < 20 ... this is false because we can't have a number smaller than itself
Lastly, let's try x = 24
4+x < 20
4+24 < 20
28 < 20 ... also false; 28 is not smaller than 20
We've shown that x = 16 and x = 24 are not solutions. Only x = 6 is a solution from the set {6,16,24}. This is why the answer is choice B.
-----------------
Alternative method:
4+x is the same as x+4. We can add two numbers in any order we want.
x+4 < 20 solves to x < 16 after subtracting 4 from both sides. So the set of solutions is anything smaller than 16. Looking at {6,16,24} we see that the only allowed answer is x = 6.
x = 16 is not a solution because x < 16 would turn into 16 < 16, but again we can't have a number smaller than itself.
ASAP PPL!!!! How many 11-player soccer teams can be formed from 16 total players?
Answer:
1 team............
Step-by-step explanation:
There is only 16 people and there has to be teams of 11 people. The remainder of 16/11 is 1 so.......only one soccer team can be formed.
Hope that helps and maybe earns a brainliest! :)
I NEED THIS ASAP, PLEASE HELP!!!
What is the lower quartile of the data set shown? {20,22,23,24,26,26,28,29,30}
What is the interquartile range of this data set?
{62,63,64,65,67,68,68,68,69,74}
What is the upper quartile of the data set shown?
{7,8,8,9,10,12,13,15,16}
Answer: 22.5 ; 5 ; 14
Step-by-step explanation:
Given the dataset:
{20,22,23,24,26,26,28,29,30}
The lower quartile (Q1) = 1/4(n + 1)th term
Where n = number of observations, n = 9
Q1 = 1/4 (9 + 1)th term
Q1 = 1/4(10) = 2.5
We average the 2nd and 3rd term:
(22 + 23) / 2
45 / 2 = 22.5
B) The interquartile range(IQR) of the dataset :
{62,63,64,65,67,68,68,68,69,74}
IQR = Q3 - Q1
The lower quartile (Q1) = 1/4(n + 1)th term
Where n = number of observations, n = 10
Q1 = 1/4 (10 + 1)th term
Q1 = 1/4(11) = 2.75 term
We take the average of the 2nd and 3rd term:
(63 + 64) / 2
45 / 2 = 63.5
The upper quartile (Q3) = 3/4(n + 1)th term
Where n = number of observations, n = 10
Q3 = 3/4 (10 + 1)th term
Q3 = 3/4(11) = 8.25 term
We take the average of the 8th and 9th term:
(68 + 69) / 2
137 / 2 = 68.5
IQR = Q3 - Q1
IQR = 68.5 - 63.5
IQR = 5
C) give the dataset :
{7,8,8,9,10,12,13,15,16}
The upper quartile (Q3) = 3/4(n + 1)th term
Where n = number of observations, n = 9
Q3 = 3/4 (9 + 1)th term
Q3 = 3/4(10) = 7.5 term
We take the average of the 7th and 8th term:
(13 + 15) / 2
28 / 2 = 14
The table shows the number of minutes Garrett practiced his trombone each week in one month. Week Number of Minutes Practiced 1 190 2 163 3 327 4 205 What is the mean number of minutes Garrett practiced his trombone each week? A. 197.5 B. 177 C. 245 D. 221.25
Answer:
[tex]\bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]
The reason is because we assume that each week have the same weight and replacing we got:
[tex]\bar X= \frac{190+163+327+205}{4}= 221.25[/tex]
And the best option would be:
D. 221.25
Step-by-step explanation:
For this case we have the following data given
Week 1 2 3 4
Minutes 190 163 327 205
For this case we can find the mean with the following formula:
[tex]\bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]
The reason is because we assume that each week have the same weight and replacing we got:
[tex]\bar X= \frac{190+163+327+205}{4}= 221.25[/tex]
And the best option would be:
D. 221.25
Complete the point-slope equation of the line through (1,3) (5,1) y-3=?
Answer:
[tex]\huge\boxed{y-3=-\frac{1}{2}(x-1)}[/tex]
Step-by-step explanation:
Point-slope is:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]m-\text{This represents the slope.}\\\\(x_1,y_1)-\text{This represents the point used in the equation.}[/tex]
Our goal:We have to complete the point-slope equation of the line through (1,3) (5,1).
--------------------------------------------------------
We have a incomplete equation of the line.
[tex]y-3=m(x-x_1)[/tex]
We need to find the slope of the line, and the value of [tex]x_1[/tex].
--------------------------------------------------------
Finding 'x1':It seems that the value of 3 was used to be [tex]y_1[/tex]. This means that the point [tex](1,3)[/tex] was used for the equation. This means that [tex]x_1[/tex] would have to be 1.
Finding Slope:Slope is rise over run.
[tex]m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}[/tex]
We are given the points (1,3) and (5,1).
[tex]m=\frac{1-3}{5-1}=\frac{-2}{4}=\frac{-1}{2}=\boxed{-\frac{1}{2}}[/tex]
The slope is one-half.
--------------------------------------------------------
We now have enough information to complete the point-slope equation.
[tex]{\left \{ {{x_1=1} \atop {m=-\frac{1}{2} }} \right.}\\\\y-3=m(x-x_1)\rightarrow\boxed{y-3=-\frac{1}{2}(x-1)}[/tex]
Our final equation is:
[tex]y-3=-\frac{1}{2}(x-1)[/tex]
Hi. Please i need help with this question.
Please show workings.
Answer:
A =176 m^2
Step-by-step explanation:
The area of the floor is length times width
A = lw
A = 16* 11
A =176 m^2
Answer:
176 cm^2
Step-by-step explanation:
Given:
length=16m
width=11m
height=9m
We don't use the height in calculating since we are looking for the area of a rectangular carpet.
Required:
a=?
Formula:
a=l*w
whereas l is length and w is width
Solution:
a=l*w
a=16cm*11cm
a=176cm^2
A shortcut to find the answer:
16*11=1,1+6,6=176
Hope this helps ;) ❤❤❤
Find the measure of d.
Answer:
50°
Step-by-step explanation:
Recall that an inscribed angle is half the arc length. Since Angle A measures 50°, this means that the arc length of BC (the intercepted arc) is 100°.
Arc BC is also representative of Angle D. In other words, the measure of angle D is half of 100°.
Angle D = 50°.
Answer:
d = 50°
Step-by-step explanation:
Inside a circle we can have inscribed angles (angles with the three points on the circle). These angles are half the length of the arc they inscribe.
The arc BC is inscribed by the angle of 50°, so we have:
[tex]50 = mBC/2[/tex]
[tex]mBC = 100\°[/tex]
The angle d inscribes the arc BC, so we have:
[tex]d = mBC/2[/tex]
[tex]d = 100/2[/tex]
[tex]d = 50\°[/tex]
PLEASE HELP AS SOON AS POSSIBLE
Answer:
Picture is down below
Step-by-step explanation:
When you are doing this question you would just graph the points (-4,4) and (4,4) so we would get a width of 8 and you need an area of 8 so the height would just be 1 since the area of a rectangle is l times w. So when you graph it, it would look like this. And the coordinate points would be (-4,4), (4,4), (-4,3),(4,3).
Answer:
Answer is (-4,4), (4,4), (-4,3),(4,3).
Step-by-step explanation:
(-4,4), (4,4), (-4,3),(4,3).
Plz help me I do not understand this Plz show your work 4x-8=16
Answer:
x = 6
Step-by-step explanation:
First, add 8 to both sides.
4x - 8 = 16
4x - 8 + 8 = 16 + 8
4x = 24
Then, divide 4 from each side.
4x ÷ 4 = 24 ÷ 4
x = 6
Hope this helps.
Answer:
x = 6
Step-by-step explanation:
Well to solve for x in,
4x - 8 = 16
We use the commutative property which is the moving of numbers and variables to either side of the equation.
So 4x - 8 = 16
+8 to both sides
4x = 24
Divide 4 by both sides
x = 6
Thus,
x is 6.
Hope this helps :)
Jacqueline. Harry, and Stanley bought a pizza pie to share for dinner. Harry ate
of the pie, and then Jacqueline ate of what was left. After Jacqueline
finished, Stanley ate of what was left of the pic. What fractional part of the
pizza pie was left after Stanley finished eating?
Answer:
1/6
Step-by-step explanation:
Harry 1x1/2=1/2
Jacqueline 1/2x1/2=1/4
Stanley 1/3x1/4=1/12
1-1/2-1/4-1/12=
12/12-6/12-3/12-1/12=
2/12 or 1/6
A plane traveled 5525 miles with the wind in 8.5 hours and 4505 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind. The speed of the plane in still air is _____ (Hours,Miles,Mph) Simplify your answer.
Answer:
The speed of the plane in still air is 590Mph
The speed of the wind is 60Mph
Step-by-step explanation:
Let
s= the speed of the plane in still air
w= the speed of the wind
Flying with the wind:
5525=(s+w)*8.5
5525=8.5s + 8.5w (1)
Flying against the wind:
4505=(s-w)*8.5
4505=8.5s - 8.5w (2)
Add (1) and (2) to eliminate w
5525=8.5s + 8.5w
4505=8.5s - 8.5w
10,030=17s
Divide both sides by 17
10,030/17=17s/17
590=s
s=590Mph
Substitute the value of s into (1)
5525=8.5s + 8.5w
5525=8.5(590) + 8.5w
5525=5,015 + 8.5w
5525-5015=8.5w
510=8.5w
Divide both sides by 8.5
60=w
w=60Mph
The speed of the plane in still air is 590Mph
The speed of the wind is 60Mph
need to the answer ASAP
Answer:
321
Step-by-step explanation:
Write the following decimals as fractions.
Hi there! Hopefully this helps!
-------------------------------------------------------------------------------------------------------
0.77 as a fraction is 77/100.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
0.2904 as a fraction is 2904⁄10000 unsimplified. (Simplified would be 363⁄1250)
Answer:
8a) 0.2904=363/1250
8b) 0.77=77/100
Step-by-step explanation: