Answer:
240
Step-by-step explanation:
We need to find the coeffeicent of the binomial expansion of
[tex]( {x}^{3} - 2 {x}^{ - 2} ) {}^{10} [/tex]
Note that
[tex] - 2 {x}^{ - 2} = - \frac{2}{ {x}^{2} } [/tex]
The binomial theorem states that
[tex](x + y) {}^{n} = x {}^{n} y {}^{0} + \binom{n}{1} x {}^{n - 1} y + \binom{n}{2} x {}^{n - 2} y {}^{2} ....... + x {}^{0} y {}^{n} ( \binom{n}{n} )[/tex]
Using this, we let expand our series
[tex]( {x}^{3} - 2 {x}^{ - 2} ) {}^{10} = x {}^{30} + \binom{10}{1} ( {x}^{27} 2 {x}^{ - 2} ) + \binom{10}{2} {x}^{24} 2x {}^{ - 4} + \binom{10}{3} {x}^{21} 2x {}^{ - 6} + \binom{10}{4} {x}^{18} 2x { }^{ - 8} + \binom{10}{5} x {}^{15} 2x {}^{ - 10} + \binom{10}{6} x {}^{12}2 x {}^{ - 12} + \binom{10}{7} x {}^{ 9} 2x {}^{ - 14} + \binom{10}{8} x {}^{ 6} 2x {}^{ - 16} + \binom{10}{9} ( {x}^{3} )2x {}^{ - 18} + 2x {}^{ - 20} [/tex]
[tex] \frac{1}{ {x}^{5} } = x {}^{ - 5} [/tex]
So what term in the series eqaul x^-5.
That term is the 10 choose 7 term.
[tex] \binom{10}{7} {x}^{9} 2x {}^{ - 14} [/tex]
Because
[tex] = \binom{10}{7} 2x {}^{ - 14} {x}^{9} = \binom{10}{7} 2 {x}^{ - 5} [/tex]
So we need to compute 10 choose 7.
That equals
10!/3!(7!)= 10×9×8/6= 720/6=120.
So we get
[tex]120(2) {x}^{ - 5} [/tex]
[tex]240 {x}^{ - 5} [/tex]
So the coeffceint u
is 240
Each pair of shapes below are similar. Solve for each variable. Show all work necessary to justify your answer. 26 11 6 18 X = 21 a = 13 b 11 22
Answer:
x = 21
a= 22
b = 13
Step-by-step explanation:
18 / 6 = 3
3 * 7 =21
20 / 10 = 2
2 * 11 = 22
10 / 20 = 0.5
26 * 0.5 = 13
The price for a gallon of gas is $4.99 how much is it going to cost for 20 gallons ?
Answer:
if one gallon is 4.99, 20 gallons?
write a ratio to make it easier
gallon : price
1 4.99
20 x
cross multiply,
x = 20 × 4.99
x=99.8
helppppppppp meee too simplify this
Answer:
30,976
Step-by-step explanation:
=}.
[tex](11 {}^{3} \times 4 { }^{2} \binom{}{11 {}^{2} } ) {}^{2} [/tex]
=}.
[tex](11 \times 4 {}^{2} ) {}^{2} [/tex]
=}.
[tex]121 \times (4 {}^{2} ) {}^{2} [/tex]
=}.
[tex]121 \times 256[/tex]
=}. 30,976
Answer:
Answer given above
Step-by-step explanation:
11^2 * 4^4
Help!! This is i-ready!!! Will get brainiest!!!
Answer:
C is the answer
Step-by-step explanation:
people who usually volunteers really don't get represented
Harold randomly selected one square tile and one round tile from the sets shown below. what is the probability that harold selected a pink square tile, and either a red or a blue round tile? square tiles: 20 green, 16 pink, 9 red, 10 yellow, 5 blue.round tiles: 5 black, 4 pink, 9 red, 6 blue, 3 yellow, 8 green, 1 white. a. 3/5 b. 14/60 c. 1/9 d. 4/45
The probability that Harold selected a pink square tile, and either a red or a blue round tile is 1/9.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
Considering the selections are independent, their combined probability is the product of the probabilities of the individual events.
P(pink square) = (pink squares) / (squares) = 16/60 = 4/15
P(red or blue round) = (red or blue rounds) / ( rounds) = 15/36
Then, the Total probability
P(E) = (4/15)(15/36)
P(E) = 4/36
P(E) = 1/9
So, the probability that Harold selected a pink square tile, and either a red or a blue round tile is 1/9.
Learn more about probability here;
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Answer:
Harold randomly selected one square tile and one round tile from the sets shown below. What is the probability that Harold selected a pink square tile, and either a red or a blue round tile?
Square tiles: 20 green, 16 pink, 9 red, 10 yellow, 5 blue.Round tiles: 5 black, 4 pink, 9 red, 6 blue, 3 yellow, 8 green, 1 white.
a.
3/5
b.
14/60
c.1/9 <<<CORRECTd.
4/45
Step-by-step explanation:
Edge 2022
Two spheres have a scale factor of 3:8. The smaller sphere has a volume of 54pi cubic meters. Find the volume of the larger sphere. Write your answer in terms of pi.
Answer:
i dont know i tried really hard im not really good at math to be honest once again sorry
Step-by-step explanation:
pleaseeee help me solve for X.
Answer:
x-17.5
Step-by-step explanation:
angles in a triangle add to 180
3x+8+(2x-3)+5x = 180
simplify(collect like terms):
10x + 5 = 180
solve:
10x = 175
x=17.5
johnny is making 30 sundaes with mint, chocolate, and vanilla ice cream. 3 5 of the sundaes are mint ice cream and 1 2 of the remaining sundaes are chocolate. The rest will be vanilla. How many sundaes will be vanilla?
Jack rides in a motorboat against a river current for 36 km. Then he returns to his starting point by floating down river on a raft. Tommy travels 9 hours less on the motorboat than on the raft. Find the speed of the river current if the speed of the motorboat in still water is 15 km/h.
Answer:
3 km/h
Step-by-step explanation:
You want to know the speed of the river current if floating 36 km downstream takes 9 h longer than the trip upstream in a boat with a speed relative to the current of 15 km/h.
TimeThe relation between time, speed, and distance is ...
time = distance / speed
If c represents the speed of the current, then 15-c is the speed upstream. The relation between the travel times is ...
36/(15 -c) = 36/c -9
SolutionMultiplying by c(15-c), we have ...
36c = 36(15 -c) -9(c)(15-c) . . . . . . . multiply by c(15-c)
36c = 540 -36c -135c +9c² . . . . . eliminate parentheses
9c² -207c +540 = 0 . . . . . . . collect terms
c² -23c +60 = 0 . . . . . . . . divide by 9
(c -20)(c -3) = 0 . . . . values that make the factors zero are c=20, c=3
The speed of the current is 3 km/h.
__
Additional comment
The speed of the current cannot be greater than 15 km/h, or the boat could not go upstream. The speed of the current cannot be greater than 4 km/h, or the trip downstream would take less than 9 hours.
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PLS HELP
Lacey has a roll of wrapping paper with 2 3/4 yards remaining. She has six boxes to wrap, each of which requires 3/8 of a yard of paper. Will Lacey have enough wrapping paper left to also wrap a book that requires 1/2 yard of paper? Support your answer by showing your work.
Answer: Yes
Step-by-step explanation:
Step #1: Lacey has 2 3/4 yards of wrapping paper remaining. She has six boxes to wrap, each of which requires 3/8 of a yard of paper. First, you must find the total number of yards of wrapping paper needed for six boxes.
Number of boxes * Number of wrapping paper required for each box
6 x 3/8 = 9/4
Step #2: Subtract the number of yards of wrapping paper remaining by the total number of wrapping for 6 boxes.
2 3/4 - 9/4 = 1/2
Step #3: Determine and solve whether Lacey will have enough wrapping paper left to also wrap a book that requires 1/2 yard of paper. To solve, subtract the remaining amount of wrapping paper by the amount of wrapping required for a book.
1/2 - 1/2 = 0
So, yes Lacey will have just enough wrapping paper to also wrap a book that requires 1/2 yard of paper.
I need some help with these math questions.
Answer:
For the first question, D is the correct answer.
For the second question, B is the correct answer.
Step-by-step explanation:
First question:
[tex]5.89 + .61(30) = 24.19[/tex]
[tex]5.89 + .61(35) = 27.24[/tex]
So D is the correct answer.
Second question:
A function is a relation in which each element in the domain corresponds to one and only one element in the range. That said, relations A, C, and D are not functions since in each of these relations, one element in the domain corresponds to two elements in the range. Only relation B is a function.
what should be subtracted from 8p + 5p to get 6a - 5b ?
Answer:
8p+5p
=13p
=6a-5b procesa
the annual income of Sam is $37,368 . what is his monthly income if he earns an equal amount every month
Answer:
[tex]\huge\boxed{\sf \$ 3,114}[/tex]
Step-by-step explanation:
Annual Income of Sam = $37,368
To find the monthly income (given that he earns an equal amount of money every month), we can divide the annual income by 12. (Each year has 12 months)
Monthly Income:
= $37,368 / 12
= $3,114
[tex]\rule[225]{225}{2}[/tex]
10. Membership to gym A is $40 per month
plus a $60 registration fee. Gym B charges
$55 per month and no registration fee.
After how many months will the
membership cost be the same?
efine the variable, write an equation, and solve
look at the screenshot
Answer:
37 is the answer for the first one because 600-45=555/15=37 and 270-15=255/15=17 for the second one.
Question 2 of 5
Which choice describes the shape of the data?
83 84 85 86 87 88 89 90 91 92
A. Symmetric; not bell-shaped
ОО o
B. Not symmetric; not bell-shaped
C. Symmetric, bell-shaped
o
D. Not symmetric, bell-shaped
What is the measure of each angle of a regular 19-gon? If necessary, round to the
nearest tenth.
[tex]\begin{array}{llll} \textit{sum of all interior}\\ \textit{angles in a regular polygon} \end{array}\\\\ n\theta = 180(n-2)~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=19 \end{cases}\implies 19\theta =180(19-2) \\\\\\ 19\theta =180(17)\implies 19\theta =3060\implies \theta =\cfrac{3060}{19}\implies \theta \approx 161.1^o[/tex]
The value of each angle for the given regular polygon is 161.05°.
What is a regular polygon?A regular polygon can be defined as a polygon having all of its sides and angles equal to one another. The expression for each angle of a regular polygon is 180(n - 2)/n.
Suppose each angle of the regular polygon be x.
Since the sum of all the interior angles of a regular polygon with n sides is given as 180(n - 2).
As per the given problem the number of sides n = 19.
Then, the following equation can be written as follows,
19x = 180(19 - 2)
=> 19x = 180 × 17
=> x = (180 × 17)/19
= 161.05
Hence, each angle of the given regular polygon with 19 sides is 161.05°.
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What time would it be if the minute hand rotated by 180 degrees from the current time?
2:30
4:00
3:30
2:15
Answer:
3:30 is the answer
Which of the following is not an exponential function?
Answer:
B. y = 5x-1
Step-by-step explanation:
B. y = 5x-1 is not an exponential function.
What is the mean of the numbers 2,6,7,2,2,9
Answer:
4.67
Step-by-step explanation:
You can get this by adding the numbers together and dividing them the numbers of numbers in data set, or like this
2+6+7+2+2+9=28 Then count how many numbers you added.
2.Divide 28 by how many numbers you counted.
The perimeter of a rectangular field is 322 m.
If the width of the field is 67 m, what is its length?
Answer:
75
Step-by-step explanation:
322 = 2(86) + 2w
322 = 172 + 2w
322-172 = 172 +2w -172
150 = 2w
150/2 = 2w/2
w=75
Order these numbers from least to greatest
Answer:
1. -39/50
2. -0.77777
3. square root of 92
4. 9.73
Chrissy has some ribbon in her craft room. She has 3/8 yards of purple ribbon and 1 yard of green ribbon.
Chrissy has a total of 3 yards of ribbon.
How many yards of Chrissy's ribbon are neither purple nor green?
The number of Chrissy's ribbon which are neither purple nor green is 1 5/8 yards
How to calculate Chrissy's ribbon which are neither purple nor green?Purple ribbon = 3/8 yardsGreen ribbon = 1 yardTotal yards of ribbon = 3 yardsRibbon which is neither purple nor green = Total - (purple + green)
= 3 - (3/8 + 1)
= 3 - (1 3/8)
= 3 - 11/8
= (24-11) / 8
= 13/8
= 1 5/8 yards.
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pls help!! 15 points!
A trapezoidal prism undergoes a dilation. The surface area of the pre-image is 35 m2. The surface area of the image is 315 m². The height of the pre-image is 5.8 m. What is the height of the image? Enter your answer as a decimal in the box m
When trapezoidal prism undergoes a dilation, the size of the prism changes
The height of the image is 52.2 meters
How to determine the height of the image?The given parameters are:
A1 = 35 m²
A2 = 315 m²
H1 = 5.8 m
To calculate the height of the image, we make use of the following equivalent ratio
A1 : H1 = A2 : H2
So, we have:
35 : 5.8 = 315 : H
Express as fractions
35/5.8 = 315/H
Make H the subject
H = 315 * 5.8/35
Evaluate the product
H = 52.2
Hence, the height of the image is 52.2 meters
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Answer:
17.4
Step-by-step explanation:
Write an expression for the cost per person if five friends share the cost of a dinner equally.
Answer:
Let c=cost of dinner, 5=the # of people, and P=the cost of person
P=C/5
b. P = (1000)/5
P = 200
Step-by-step explanation:
convert 4 hours into minutes
helpp ASAP
Answer: 240 minutes
Step-by-step
60 times 4 hour = 240 minutes
An equation is shown.
3m • 3 = 3-2
What are the possible values for m and n?
Answer:
n=3m+5
n−2m=3
\hboxsubstitute3m+5forninthesecondequation:
3m+5−2m=3
m+5=3
m=3−5
m=−2
n=3m+5
n=3×(−2)+5
n=−6+5
n=−1
(m,n)=(−2,−1)
The answer is C.
15 of 15 Find the size of the final unknown interior angle in a polygon whose other interior angles are: 162°, 115°, 125°, 148° and 105°.
answer ?
Answer: 147 Degrees
Step-by-step explanation
The size of the final unknown interior angle in a polygon is 147 degrees.
Given that,
The other interior angles are 162°, 115°, 120°, 148° and 85°.
We assume that there is an equation (2n - 4) 90.
Here n be 7.
Based on the above information, the calculation is as follows:
= (2n - 4) 90
= ((2) (7) - 4) 90
= 10 (90)
= 900
Now the size of the unknown interior angle is
= 900-(162+125+148+105+98+115)
= 900 - 753
= 147°
Therefore we can conclude that the size of the final unknown interior angle in a polygon is 147 degrees.
Carley can mow the lawn in 5 hours. When Carley and her dad work together, they can do it in 2
hours. How long does it take Carley's dad to mow the lawn?
The time it will take Carley's dad to mow the lawn is 3.3 hours.
What is rate?Rate is the ratio between two related quantities in different units. Therefore,
The rate Carley do the lawn = 1 / 5
When they work together they do it the 1 / 2 rate.
Therefore,
let
the hours it takes Carley dad = x hours . Therefore,
1 / 5 + 1 / x = 1 / 2
x + 5/ 5x = 1 / 2
cross multiply
2(x + 5) = 5x
2x + 10 = 5x
10 = 5x - 2x
10 = 3x
x = 10 / 3
x = 3.3 hours
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I have to turn a bunch of these questions tomorrow so pleade help
Answer:
21,42/2,-(42/-2)
Step-by-step explanation:
please mark me as brainlest