Answers
Answer:
The fifteenth term of the binomial expansion of [tex](a+b)^{20}[/tex] is [tex]38760\cdot a^{6}\cdot b^{14}[/tex].
Step-by-step explanation:
Let be a binomial of the form [tex](a+b)^{n}[/tex], where [tex]a, b\in \mathbb{R}[/tex] and [tex]n\,\in\mathbb{N}^{+}[/tex]. The expansion of this polynomial is defined below:
[tex](a+b)^{n} = \Sigma\limits_{k=0}^{n}\,\frac{n!}{k!\cdot (n-k)!}\cdot (a^{n-k}\cdot b^{k})[/tex] (1)
Where:
[tex]n[/tex] - Number of terms of the expanded polynomial.
[tex]k[/tex] - Index associated to [tex]k[/tex]-th term of the expanded polynomial.
For all [tex]n[/tex]-th binomial, we a sum of [tex]n+1[/tex] terms. If the given binomial has a term of [tex]20[/tex], then we have 21 terms and the fifteenth term of the polynomial corresponds to the [tex]14[/tex]-th term. Then, the fifteenth term of the binomial is:
[tex]c_{14} = \frac{20!}{14!\cdot 6!}\cdot (a^{6}\cdot b^{14})[/tex]
[tex]c_{14} = 38760\cdot a^{6}\cdot b^{14}[/tex]
The fifteenth term of the binomial expansion of [tex](a+b)^{20}[/tex] is [tex]38760\cdot a^{6}\cdot b^{14}[/tex].
Related Questions
Need help so confusing whats the answer
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Answers
Answer:
Volume of the cone V》1570 cm^3
Volume of the hemisphere V》4186.67cm^3
Volume of the entire figure V》5756.67cm^3
hope it helps...
hope it helps...have a great day !!
HELP I WILL MARK YOU GOOD
Answers
Answer:
You have a 2/3 chance
Answer:
2/3
Step-by-step explanation:
when you spin twice you either get a KK, KV, KH, VK, VV, VH, HK, HV, HH.
so the probability of getting a K and a K is 1/3 plus 1/3 to get your answer as 2/3.
PLLLZZ HHEELLPPP! QUESTION IS BELOW!
Answers
Answer:
32°Step-by-step explanation:
The two given angles are complementary, it means they add to 90°Find x:
2x + 10 + x + 8 = 903x + 18 = 903x = 72x = 24Find Y:
m∠Y = x + 8 = 24 + 8 = 32°I need some help on this if possible
Answers
where C is the circumference, d is the diameter and r is the radius.
The diameter of a circle is a line segment that passes through the center of the circle and has its endpoints on the circle. The radius of the circle is a line segment from the center of the circle to a point on the circle. The diameter of a circle is twice the length of its radius.
If you are given the diameter then use the formula C = πd
If you are given the radius then use the formula C = 2πr
Step-by-step explanation:
Find the area of the shaded sector
Answers
Answer:
Step-by-step explanation:
ABCD is a kite. Solve for x.
Answers
If you plug in the value of X as option 2. X equals six. Plug in the value of X which is six into the equation and it should give you the answer 15 equals 15. I typed it in using photo math. Hope this help.
HELP PLS!!
If the sequence 4, 8, 12, 16 continues, what will be the 7th
term?
Answers
Answer:
28
Step-by-step explanation:
In order to find the seventh term in this arithmetic function, you need to find its function; in order to do this, you must first identify the common difference by finding the difference between two consecutive terms:
16 - 12 = 4; the common difference is 4
Now, you need to find the 0th term, which is the 1st term minus the common difference:
4 - 4 = 0
At this point, you can write out the function (where f(n) = [0th term] + [common difference]n:
f(n) = 4n
Finally, you can plug 7 into this function:
f(n) = 4(7)
f(n) = 28, so the 7th term is 28
t/3+9=12 what does this mean in algerba
Answers
Answer:
t=9
Step-by-step explanation:
subtract 9 from both sides
t/3=3
t=9
Eight times the sum of a number and 9 equals 7.
Answers
Answer:
8(x+9)=7
comment if you need anything else like solving for x
Which of these statements is true? Sin 18° = cos 72°, sin 55° = cos 55°, sing 72° = cos 18°c both a and c
Answers
Answer:
Sin 18° = cos 72° and sin 72° = cos 18°
Step-by-step explanation:
According to trigonometry identity;
sin Ф = cos(90 - Ф)
for Sin 18° = cos 72
Ф = 18°
Substitute into the expression
sin Ф = cos(90 - Ф)
sin 18 = cos(90 - 18)
Sin 18 = cos 72
Hence the statement id true
For sin 72° = cos 18
Ф = 72°
Substitute into the expression
sin Ф = cos(90 - Ф)
sin 72 = cos(90 - 72)
Sin 72 = cos 18
Hence this statement too is correct
The two correct statements are Sin 18° = cos 72° and sin 72° = cos 18°
The determinant of the matrix
Answers
Answer:57
Step-by-step explanation:
(7 x 9) - (-3 x -2) = 57
simplify (2x)^1/3 times (2x)^4/3
Answers
Answer:
2x^5/3
Step-by-step explanation:
Answer:
32x small 5
9 32x small 5 over 9
Step-by-step explanation:
A manager records the number of projects employees complete in one month. If the manager wants to summarize the data, which two statements are true?
The manager should use a measure of center to summarize how many projects the employees that complete the least projects complete.
The manager should use a measure of center to summarize how the number of projects employees complete differs.
The manager should use a measure of center to summarize the typical number of projects an employee completes.
The manager should use a measure of variability to summarize how the number of projects employees complete differs.
The manager should use a measure of variability to summarize the typical number of projects an employee completes.
Answers
Answer:
The manager should use a measure of center to summarize how many projects the employees that complete the least projects complete.
Step-by-step explanation:
Rob can mop a warehouse in 10 hours. Maria can mop the same warehouse in 11 hours. Find how long it would take them if they worked together.
Answers
Answer:
It would take them [tex]\frac{110}{21}[/tex] or approximately 5.24 hours together
Step-by-step explanation:
Use the algebra work formula, [tex]\frac{1}{tb}[/tex] = [tex]\frac{1}{t1}[/tex] + [tex]\frac{1}{t2}[/tex], where tb is the time together, t1 is the time of one person individually, and t2 is the time of the other person.
Plug in 10 and 11:
[tex]\frac{1}{tb}[/tex] = [tex]\frac{1}{t1}[/tex] + [tex]\frac{1}{t2}[/tex]
[tex]\frac{1}{tb}[/tex] = [tex]\frac{1}{10}[/tex] + [tex]\frac{1}{11}[/tex]
Find the common denominator, then add the fractions together:
[tex]\frac{1}{tb}[/tex] = [tex]\frac{11}{110}[/tex] + [tex]\frac{10}{110}[/tex]
[tex]\frac{1}{tb}[/tex] = [tex]\frac{21}{110}[/tex]
Cross multiply and solve for tb:
110 = 21tb
5.24 = tb
So, it would take them [tex]\frac{110}{21}[/tex] or approximately 5.24 hours together
Un sure on this if someone could answer would be great !
Answers
Answer:
x= 5/2 x= (±sqrt13)/2
Step-by-step explanation:
PLEASE HELP THIS IS DUE SOON <33
Find the least possible measure of the third side of a triangle with the given side lengths if the missing measure is a whole number. The given side lengths are 7 in and 11 in.
Answers
Answer:
5 inches
Step-by-step explanation:
Theorem states that the smaller two sides of a triangle have to be greater than the biggest side.
The least possible answer would be 5 inches.
Help me with this pls
Answers
PLEASE !!! HELP D: lord pls
Answers
Answer:
the answer is 4 have a nice day
go follow my friends on Snap.........
iminmymomscar_v itprettyalex old_creamcheese purplehawk_3000 dlowgetsmoney aj-0218
(15-17) (Purple Hawk_ 3000 is 21)
Answers
Answer:
i got you
Step-by-step explanation:
Answer: OK
Step-by-step explanation:
OK
Use the figure at the right to name the following.
8. a pair of supplementary angles
9. a pair of complementary angles
10. a pair of vertical angles
Answers
Answer:
Supplementary: AKB and BKG
Complementary: FGE and EGD
Vertical: IJH and KJG
Step-by-step explanation:
The correct options are given below,
Supplementary: AKB and BKG
Complementary: FGE and EGD
Vertical: IJH and KJG
What are lines and angles?Straight lines with little depth or width are present. You will learn about a number of lines, including transversal, intersecting, and perpendicular lines.
A figure called an angle is one in which two rays originate from the same point. In this area, you could also encounter contrasting and related viewpoints.
Given that there are different lines crossing each other at different angles. The value of the different angles can be named as,
A pair of supplementary angles: AKB and BKG
A pair of complementary angles: FGE and EGD
A pair of vertical angles: IJH and KJG
To know more about lines and angles follow
https://brainly.com/question/25770607
#SPJ2
Describe in your own words how graphing equations can help find the
solution to a system of equations?
Answers
Answer:
i think that if u can please redo this question it might help
What decimal is equivalent to 13/20?
Answers
Answer: 0.65
13/20 as a decimal is 0.65.
Rename 5/6 and 14/15 using the least common denominator.
Answers
Answer:
25/30 and 28/30
Step-by-step explanation:
1. To find the least common denominator, you need to find the least common multiple of the two denominators which are 6 and 15. Prime factorization of these numbers gives:
6 = 2 x 3
15 = 5 x 3
A number that would evenly divide both 6 and 15 must contain 2 x 3 x 5 which is 30.
Thus 30 is the least common denominator.
2. Now we need to somehow change both fractions to make them have a denominator of 30. To do this we can multiply by fractions with same numerator and denominator since that would be like multiplying by 1.
So, 5/6 x 5/5 = 25/30
And 14/15 x 2/2 = 28/30
Answer:
25/30 and 28/30
Step-by-step explanation:
answer for the plato mastery test
find x. round your answer to the nearest tenth
Answers
tan:opposite/adjacent
tan(x)=32/21
tan^-1(32/21)=x
x=56.7
A3-inch candle burns down in 5 hours. How far has it burned after 8
hours? Use the dropdown menu to state your answer as a decimal, mixed
number, or improper fraction.
Answers
Answer:Assuming a 3-inch diameter, pillar candles of 3, 4 and 6 inches in height will burn for 45, 60 and 75 hours, respectively. Three-inch Party Lite pillar candles will burn 30-35 hours; 5-inch, 65 to 70 hours; and 7-inch, 90 to 95 hours. The three-wick 6-by-5-inch candles burn for more than 100 hours.
Step-by-step explanation:
Find the 11th term in the geometric sequence: 4, 6, 9,....
Answers
Answer:
A11 = 230.66015625
Step-by-step explanation:
hi!
the first thing that you have to do when solving for the 11th term in a geometric sequence is to find the common ratio!
I did this by dividing 6/4 = 3/2 (I did multiply this by 6 to test if it was correct, and it was)
the next thing you can do is use this formula:
An = A1*r^(n-1)
An = the nth term of the sequence
A1 = the first term in the sequence
r = common ratio
n = the number of term that you are solving for
A11 = 4*(3/2)^(11-1)
A11 = 4*(3/2)^10
A11 = 230.66015625
how do you take pictures of your work
Answers
Answer:
You take a regular photo of your question on your device and upload it when your asking a question on brainly!
Step-by-step explanation:
Hope I helped!
Given that
[tex]2 {}^{x} = 0.125[/tex]
Find x
Answers
ln(2^x)=ln(.125)
Xln(2)=ln(.125)
X=ln(.125)/ln(2)
X=-3
ALTERNATIVE ROUTE:
You know that 0.125 is equal to 1/8
And 1/2^3 is also equal to 1/8
So since you need the reciprocal to match it the exponent is a negative
Answer:
x = -3.
Step-by-step explanation:
2^x = 0.125
Taking logs:
x ln 2 = ln 0.125
x = ln 0.125 / ln 2
x = -3
The sum of two numbers is 10. The difference between three times the first number and twice the second number is 20. Find the two numbers.
Sample question text with
and
Answers
Answer:
one number x= 16
other number y = 4
what is -1 3/10 + -3.8
Answers
Answer:
answer
Step-by-step explanation:
=convert 3.8 into mixed number
=3 4/5
=1 3/10+3 4/5
=5.1 in mixed fraction
=5 1/10
if i got it wrong i am seriously sorry!