I bet the sum you're referring to is supposed to be
[tex]\displaystyle \sum_{r=0}^{20} r^2 \times {}^{20}C_r[/tex]
or equivalently,
[tex]\displaystyle \sum_{r=0}^{20} r^2 \binom{20}r[/tex]
where [tex]\binom nk = \frac{n!}{k!(n-k)!}[/tex] is the binomial coefficient.
Recall the binomial series,
[tex](1+x)^\alpha = \displaystyle \sum_{r=0}^\infty \binom\alpha r x^r[/tex]
which is valid for |x| < 1. (Note that if r > α, the binomial coefficient is defined to be zero, so there really are only α many terms when α is a whole number.)
Differentiating both sides with respect to x gives
[tex]\alpha (1+x)^{\alpha-1} = \displaystyle \sum_{r=0}^\infty r \binom\alpha r x^{r-1}[/tex]
Multiply both sides by some arbitrary x in |x| < 1 :
[tex]\alpha x (1+x)^{\alpha-1} = \displaystyle \sum_{r=0}^\infty r \binom\alpha r x^r[/tex]
Repeat:
[tex]\alpha (1+x)^{\alpha-1} + \alpha(\alpha-1) x(1+x)^{\alpha-2} = \displaystyle \sum_{r=0}^\infty r^2 \binom\alpha r x^{r-1}[/tex]
[tex]\alpha x (1+x)^{\alpha-1} + \alpha(\alpha-1) x^2 (1+x)^{\alpha-2} = \displaystyle \sum_{r=0}^\infty r^2 \binom\alpha r x^r[/tex]
Let α = 20, and let x approach 1 from below. The right side converges to the sum we want, while the left side converges to
[tex]20 \times 2^{19} + 20\times19\times 2^{18} = (20 + 10\times19)\times2^{19} = \boxed{210\times2^{19}}[/tex]
11. Reduce 48/72 to its lowest terms.
A. 6/9
B.2/3
c. 24/36
D. 30/54
Answer:
its A my friend because: 48/2=24. 72/2=36
24/2=12. 36/2=18
12/2=6. 18/2=9
If someone can help me step by step exactly
The value of z using the information and the formula provided in the question is -5.292.
What is the value of z?
Subsituting for the missing values in the formula, the formula becomes: [tex]\frac{130 - 135}{\frac{5}{\sqrt{28} } }[/tex]
Solving for the numerator, the number becomes -5. Solving for the denominator, the number becomes 0.94491
z = -5/0.94491
z = -5.292
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PLEASE HURRY 30 POINTS
A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 2 and the coln
toss is heads?
Write your answer as a fraction in simplest form.
hope it helps...!!!!
The probability that the number rolled is greater than 2 and the coin toss is heads is,
⇒ 1/ 3
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one
Now, In probability theory, "AND" means multiplication and "OR" means "addition".
Hence, We can find the 2 probabilities separately and multiply them (as there is "AND")
So, Probability for number rolled greater than 2 = number of numbers that are greater than 2/total number of numbers
Since, There are 4 numbers greater than 2 in a die (3, 4, 5, 6) and total 6 numbers, so
P(number greater than 2) = 4/6 = 2/3
Now, Probability that heads come up in coin toss = 1/2 (there are 1 tail and 1 head in a coin)
Hence,
P(number greater than 2 and heads in coin) = 2/3 × 1/2 = 1/3
Thus, the probability that the number rolled is greater than 2 and the coin toss is heads is,
⇒ 1/ 3
Learn more about the probability visit:
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absolute value of 19/24
Answer:
-19/-24 ?
Step-by-step explanation:
The absolute value is the distance between a number and zero. The distance between −19 and 0 is 19 .
-24 has an absolute value of 24
Answer:
0.791666667 I hope this helped
Step-by-step explanation:
simplify the expression m^-6n^-3/m^-13n^-1
A)m^7n^2
B)n^-9/n^-14
C)m^3n^12
D)m^7/n^2
[tex]\dfrac{m^{-6} \cdot n^{-3}}{m^{-13} \cdot n^{-1}}\\\\=m^{-6-(-13)} \cdot n^{-3-(-1)}\\\\=m^{-6+13} \cdot n^{-3+1}\\\\=m^7 \cdot n^{-2}\\\\=\dfrac{m^7}{n^2}[/tex]
Kala and david each opened a savings account today, kala opened her account with a starting amount of $180, and she is going to put in $70 per month. David opened his account with no starting amount, and he is going to put in $100 per month
let x be the number of months after today
(a) for each account, write an expression for the amount of money in the account after x months
(b) write an equation to show when the two accounts have the same amount of money
[tex]Elsa:y_1=70x+180[/tex]
[tex]brian,y_2=100x[/tex]
Step-by-step explanation:[tex]Rnown\ by\ the\ topic,[/tex]
[tex]Assuming\ that\ the\ Elsa\ amount\ of\ money\ is\ y_1,[/tex]
[tex]Brian's\ amount\ of\ money\ is\ y_2[/tex]
[tex]so,y_1=70x+180[/tex]
[tex]\{put\ in\ \$70\ per\ month,\ storting\ amount\ of[/tex]
[tex]y_2=100x[/tex]
[tex]\{\ put\ in\ \&\ 100\ per\ month,\ no\ starting\ emount[/tex]
[tex]\{\$70,\ \$100\ are\ monthly\ voriation,[/tex]
[tex]\$180\ is\ fixed\ value?[/tex]
I hope this helps you
:)
Jia is thinking of a number she gives
three clues about the number. the number is
even, the number is less than 12 and the absolute
value of the number is between 9 and is what
is Jia's number? Explain how
you know.
The flower shop makes bouquets with ten flowers in each bouquet.
The florist said she can't make any bouquets because she has 207 flowers and there is a 0 in the tens place of 207!
Do you agree or disagree with the florist? Explain why in a full sentence below.
Question 1.
Let P = {3, 5, 7, 9, 11} Q = {9, 11, 13} R = {3, 5, 9} S = {13, 11}
Write the elements for the following: [4 marks]
(a) R ⊂ P
(b) Q ⊂ P
(c) R ⊂ S
(d) S ⊂ Q
(e) S ⊂ P
(f) P ⊄ Q
(g) Q ⊄ R
(h) S ⊄ Q
Question 2.
i) Write down all the possible proper subsets for each of the following:
[3marks]
(a) {a, b, c, d}
(b) {1, 2, 3}
(c) {p, q, r}
(d) {5, 10}
(e) {x}
(f) ∅
ii) Which of the following sets is a universal set for the other four sets?
(Select your answer) [1mark]
(a) The set of even natural numbers
(b) The set of odd natural numbers
(c) The set of natural numbers
Answer:
Question 1
a) { 3, 5, 9 }
b) { 9, 11 }
c) { }
d) { 11, 13 }
e) {11}
f) {3, 5, 7}
g) {11, 13}
h) {9}
Question 2 ( i )
a) { a,b,c,d }
{a}
{b}
{c}
{d}
{a,b,c}
{a,b}
{a,c}
{a,d}
{b,c}
{b,d}
{c,d}
{a,b,d}
{b,c,d}
{a,c,d}
{ }
b) {1,2,3}
{1,2}
{1,3}
{1}
{2}
{3}
{2,3}
{ }
c) {p, q ,r}
{ p,q}
{ p,r}
{ q,r}
{p}
{q}
{r}
{ }
d) { 5,10}
{ 5}
{10}
{ }
e) {x}
{ }
f) { ○ }
{ }
Question 2 ( ii )
(c) The set of natural numbers
Find the chance of having a face card if a card is drawn randomly from a deck of cards.
Answer:
3/13
Step-by-step explanation:
P(Choosing a Face card) =
12/52= 3/13
pls mark as brainliest
I can't manage. Can you help? Ty :)
first question is true and second question is 6cm
PLEASE HELP ASAP!!! WITH EXPLANATION IF POSSIBLE!!!!!!!!!
Two chords PQ and ST of length 6cm and 10cm respectively of a circle are parallel to each other and are on opposite side of its center. If the distance between PQ and ST is 5cm. Find the radius of the circle
Answer:
Draw two parallel chords AB and CD of lengths 5 cm and 11 cm. Let the center of the circle be O. Join one end of each chord to the center.
Draw two perpendiculars OM and ON to AB and CD, respectively, which bisects the chords.
Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its center. If the distance between AB and CD is 6 cm, find the radius of the circle.
Thus, MB = 2.5 cm and ND = 5.5 cm [The perpendicular drawn from the center of the circle to the chords bisects it.]
Let OM = x and ON = 6 - x
Consider ΔOMB
By Pythagoras theorem,
OM2 + MB2 = OB2
x2 + 2.52 = OB2
x2 + 6.25 = OB2..................(1)
Consider ΔOND
By Pythagoras theorem,
ON2 + ND2 = OD2
(6 - x)² + 5.52 = OD2
36 + x2 - 12x + 30.25 = OD2
x2 - 12x + 66.25 = OD2............... (2)
OB and OD are the radii of the circle. Therefore OB = OD.
Thus, OB2 = OD2
Equating (1) and (2) we get,
x2 + 6.25 = x2 - 12x + 66.25
12x = 60
x = 5
Substituting the value of x in (1),
OB2 = x2 + 6.25
OB2 = 52 + 6.25
OB2 = 31.25
OB = 5.59 (approx.)
Thus, we get the radius of the circle = 5.59 cm.
Express (x+9)^2 as a trinomial in standard form.
Answer:
x^2 + 18x + 81
Step-by-step explanation:
(x+9) (x+9)
then distributive property
[tex](x+9)^2\\\\=x^2 + 2\cdot 9 \cdot x + 9^2\\\\=x^2 +18x+81[/tex]
If z = 3cis30°, z3 in rectangular form is:
[tex]\qquad \textit{power of two complex numbers} \\\\\ [\quad r[cos(\theta)+isin(\theta)]\quad ]^n\implies r^n[cos(n\cdot \theta)+isin(n\cdot \theta)] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ z=3[\cos(30^o)+i\sin(30^o)] \\\\\\ z^3=3^3[\cos(3[30^o])+i\sin(3[30^o])]\implies z^3=27[\cos(90^o)+i\sin(90^o)] \\\\\\ z^3=27(0~~ + ~~i1)\implies z^3=0+27i[/tex]
so that gives us the point (0 , 27) on the imaginary plane, and we also know the line goes through the origin, since it'd be a line in component form, and to get the equation of a line we only need two points off of it, let's use those two.
[tex]\stackrel{origin}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})}\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{27}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{27}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{0}}}\implies \cfrac{27}{0}\implies und efined[/tex]
a line with an undefined slope is a vertical line, namely in this case x = 27.
B
ca
(3y +9)°
1149
4yº
D C
А
1.
o
Which selection shows the correct order of points from least to greatest on the number line?
SUOSI
27 4 7 4
3 8 5 10 3
H
-2
+
0
2.
-1
A.
nim
4
5'
-
-
bu
4 7
3' 10
in
NICO
3
av
4
7
B.
4 2
5' 3'
7
3' 8' 10 de file upon two locou
2
4.
-
C.
4 7 7
5' 10' 8
3
3
4
2
7
7
D.
---
3
5'
3
10
8
Answer:
D.
Step-by-step explanation:
As is often the case with multiple choice questions, you only need to find part of a correct answer to be able to make the right choice.
The number line picture shows the left-most point has a value less than -1. That means the numerator of its negative fraction will be greater than the denominator. The only fraction like that on the list is -4/3, and the only answer choice with that listed first is choice D.
D. -4/3, -4/5, -2/3, 7/10, 7/8
D. -4/3, -4/5, -2/3, 7/10, 7/8
Step-by-step explanation:
# Brainliest Bunch
Let f(x) =5x-1, h(x)= -x+5.
Find (h of)(3).
(hof)(3)
(h ◦ f)(x) is the composition of h(x) with f(x),
(h ◦ f)(x) = h(f(x))
which we can compute by simplying replacing in h(x) every instance of x with f(x) itself:
(h ◦ f)(x) = h(f(x))
(h ◦ f)(x) = h(5x - 1)
(h ◦ f)(x) = -(5x - 1) + 5
(h ◦ f)(x) = -5x + 1 + 5
(h ◦ f)(x) = -5x + 6
Then
(h ◦ f)(3) = -5 • 3 + 6
(h ◦ f)(3) = -15 + 6
(h ◦ f)(3) = -9
Order the numbers from least to greatest.
13/50
22%
0.28
1/5
0.41
1/5, 13/50, 0.28, 0.41, 22%
Step-by-step explanation:
hopes this helps
What is the lateral surface area of the triangular prism?
Round to the hundredths place.
Answer:
A triangular prism is a three-dimensional shape having two triangular bases and three rectangular sides.
Mark bought two candy bars and a soda for $3.96. If each candy bar cost $1.10 how much did the soda cost?
Answer:
$1.76
Step-by-step explanation:
$1.10+$1.10 = $2.2
$3.96 - $2.2 = $1.76
Solve one half ÷ 8 = ___.
one seventh
one sixteenth
one twenthieth
one thirtieth
Answer:
one sixteenth
Step-by-step explanation:
I hope this helps! Have a lovely day!! :)
what is the volume of this now I don't really get it
Answer:
12
Step-by-step explanation:
Answer:
24 cubic units
Step-by-step explanation:
Count the front layer by fours because there are 3 rows of 4 and 3 rows of 4 on the other side.So count by 4's on the front layer then the back layer.
help please!!!!!!!! please be correct
Answer:
Step-by-step explanation:
the answer is 66. To find the third angle subtract 80 and 34 by 180.
PLEASE HURRY What is the surface area of this right rectangular prism?
Enter your answer as a mixed number in simplest form
first off, let's change all the mixed fractions to improper fractions.
Check the picture below.
[tex]\stackrel{\textit{\Large Areas}}{\stackrel{\textit{left and right}}{2\left( \frac{4}{3}\cdot \frac{5}{2} \right)}~~ + ~~\stackrel{\textit{front and back}}{2\left( 3\cdot \frac{4}{3} \right)}~~ + ~~\stackrel{\textit{top and bottom}}{2\left( 3\cdot \frac{5}{2} \right)}} \\\\\\ \cfrac{20}{3}+8+15\implies \cfrac{89}{3}\implies 29\frac{2}{3}[/tex]
Question 11
1 pts
A baby was 6 lb 8 oz at birth. At one month old, she weighed 9 lb 2 oz. How much weight did the
baby gain in the first month?
Answer:
2 lb and 4oz
Step-by-step explanation:
because if you do 9lb 2oz minus 6lb 8oz you get 2 lb 4oz
Donna received a $90 gift card for a coffee store. She used it in buying some coffee that cost $7.59 per pound. After buying the coffee, she had $59.64 left on her card. How many pounds of coffee did she buy?
Answer: 4 pounds
Step-by-step explanation:
First, we will see how much the coffee cost by subtracting what was left by the total gift card.
$90 - $59.64 = $30.36
Now, we will divide how much the coffee cost by how much one pound costs. This will give us how many pounds she bought, and the answer to your problem
$30.36 / $7.59 = 4
She bought four pounds of coffee.
Solve the absolute value inequality 3x-1<8
Answer:
3
Step-by-step explanation:
3x - 1 < 8
Solve this inequality like a two-step equation.
Add 1 to both sides to cancel the -1.
3x - 1 < 8
3x < 9 Divide both sides by 3 to cancel the 3 in 3x.
x < 3
Find the absolute value (distance the number is from 0).
Absolute value = 3
I hope this helps and please mark me as brainliest!
PLEASE HELP: PICTURE ATTACHED
Multiply 80 by number of copies sold and add to her salary:
P = 80N + 1700
Now replace N with 26:
P = 80(26) + 1700
P = 3,780
Answer:
P=1,700+80n
Total Pay if Yoko sells 26 Copies; 3,780
Hope This Helps! :) Please Mark Brainliest!
If the total profit per month is Rs 200,000 and the revenue per month can be obtained as twice
the cost per month minus 50,000, find the revenue and cost per month.
Answer:
200000×2
=R400 000 and minus 50000
=300000
Lines a, b, c, and d Intersect as shown.
124
95
42°
53
39°
95°
What is x ?
Answer:
95 is the answer I took the test