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]
Rodney says that he can draw two rectangles that have the same areas but different perimeters.
Which of the following pairs of rectangles could Rodney draw?
Select all that apply.
LIVE
A rectangle with side lengths 4 cm and 6 cm and a rectangle with side lengths 2 cm and 12 cm
LIVE
A rectangle with side lengths 4 cm and 6 cm and a rectangle with side lengths 2 cm and 8 cm
LIVE
A rectangle with side lengths 3 cm and 6 cm and a rectangle with side lengths 2 cm and 9 cm
LIVE
A rectangle with side lengths 5 cm and 6 cm and a rectangle with side lengths 2 cm and 9 cm
LIVE
A rectangle with side lengths 5 cm and 4 cm and a rectangle with side lengths 2 cm and 7 cm
Answer:
A rectangle with sides lengths 4cm and 6cm and a rectangle with side lengths 2cm and 12 cm...
Paul invests £500 at a rate of 1.5% per year compound interest.
Find the value of the investment after 3 years.
Give your answer correct to the nearest penny.
Tthe value of Paul's investment after 3 years would be equal to 52,285 penny.
How to calculate compound interest?Mathematically, compound interest is calculated by using this formula:
[tex]A=P(1+r )^{t}[/tex]
Where:
A is the future value.P is the principal.R is the interest rate.T is the time measured in years.Given the following data:
Principal = £500.
Time = 3 years
Interest rate = 1.5% = 0.015.
Substituting the given parameters into the formula, we have;
A = 500(1 + 0.015)³
A = 500(1.015)³
A = 500 × 1.0457
A = £522.85.
Conversion:
100 penny = 1 pounds.
X penny = 522.85 pounds.
Cross-multiplying, we have:
X = 522.85 × 100
X = 52,285 penny.
Read more on interest here: brainly.com/question/24341207
Which of the following is a polynomial function in standard form with zeros at 0, 2, and 4? f(x) = x(x + 2)(x + 4) f(x) = x(x – 2)(x – 4) f(x) = x3 – 6x2 + 8x f(x) = x3 + 6x2 + 8x
Answer:
f(x) = x^3 - 6x^2+8x
Step-by-step explanation:
Remember while you are studying polynomial functions that zeros are just the solutions (and are the x-intercepts on the graph).
The question said the zeros were 0, 2 and 4, so if you were solving the equation you would get:
x=0 and x=2 and x=4
Just "undo" that last step of solving and you get:
x = 0 and
x - 4 = 0 and
x - 2 = 0
These are the factors of the function and they do look just like the second option of answers on your question. But that is in factored form and they asked you for standard form.
so f(x)=x(x-2)(x-4) is almost there, but you need to multiply all the factors back together.
(x - 2)(x - 4)
use FOIL or distributive property or area model(box) method to multiply and get
x^2 - 6x + 8
Then multiply in the x using distributive property.
f(x) = x(x^2-6x+8)
f(x) = x^3 - 6x^2 + 8x
That's the final answer (the third choice of answers on your post.) I think of this as a "working backwards" problem because you start with solutions (zeros means solutions!) and work backwards to find factors, then the function.
A babysitter charges a rate of $15 per hour. how long was the babysitter there if she makes 40
Answer:
2.7
Step-by-step explanation:
15/1 = 40/x
Cross multiply: 40/15
Divide: 2.66
Round up: 2.7
2.7 times 15= 40.5
Answer:
2hrs. 40mins.
Step-by-step explanation:
A babysitter charges a rate of $15 per hour. How long was the babysitter there if she makes $40?
x = hours she babysat
Equation:
15x = 40
Divide to isolate x:
15x = 40
/15 /15
x = 8/3 hrs.
Now, we convert into hours and minutes, since she did work for more than an hour, to earn the $15 each hour.
We know that there are 60 mins. in an hour
60 * 8/3
480/3
160 mins.
Convert into hour and mins:
1 hr. = 60 mins
160/60 = 2 40/60 ==> 2 2/3
Convert 2/3 into mins to add to the hours:
60 * 2/3
120/3 = 40
2hrs. + 40 mins.
2hrs. and 40mins
Therefore, the babysitter was there for 2hrs. 40mins.
Hope this helps!
solve the system of equations:
-3x + 7y = -15
3x + 5y = 15
what do X and Y equal?
Answer:
x=5
y=0
Step-by-step explanation:
Let's solve the system of equations through elimination
Solving by elimination is when you add or subtract one equation by the other to eliminate one variable
In this case, adding 3x and -3x would cancel each other out so we should add the equations
[tex]-3x + 7y = -15\\+(3x + 5y = 15)\\0+12y=0\\12y=0[/tex]
Now solve for y
Divide both sides by 12 to isolate y
[tex]12y=0\\\\\frac{12y}{12} =\frac{0}{12} \\\\y=0[/tex]
Now sub in the value of y into one of the original equations and solve for x
[tex]3x+5y=15\\3x+5(0)=15\\3x=15\\[/tex]
Divide both sides by 3 to isolate x
[tex]\frac{3x}{3} =\frac{15}{3} \\x=5[/tex]
Evaluate [tex]\frac{1}{2^{-2}x^{-3}y^{5} }[/tex] for x=2 and y=-4.
A)-16
b)-4
c)[tex]-\frac{1}{32}[/tex]
d)16
Answer:
[tex]\bf C)\: -\cfrac{1}{32}[/tex]
Step-by-step explanation:
[tex]\tt \cfrac{1}{2^{-2}x^{-3}y^5}[/tex]
[tex]\tt x=2\\y=-4[/tex]
~
Substitute ''x'' with '2' & 'y' with "-4":-
[tex]\tt \cfrac{1}{2^{-2}\times \:2^{-3}\left(-4\right)^5}[/tex]
First let's solve [tex]\tt 2^{-2}\times \:\:2^{-3}\left(-4\right)^5[/tex]
[tex]\tt 2^{-2}\times \:2^{-3}=\boxed{\cfrac{1}{32} }[/tex]
[tex]\tt \cfrac{1}{32}\left(-4\right)^5[/tex]
Calculate exponents:- -4^5= -1024
[tex]\tt \cfrac{1}{32}\left(-1024\right)[/tex]
Remove parentheses, apply rule:- [tex]\tt a\left(-b\right)=-ab[/tex]
[tex]\tt-\frac{1}{32}\times \:1024[/tex]
[tex]\tt \cfrac{1}{32}\times \cfrac{1024}{1}[/tex]
Apply fraction rule:-
[tex]\tt -\cfrac{1\times \:1024}{32\times \:1}[/tex]
[tex]\tt \cfrac{1024}{32}[/tex]
Divide numbers:-
[tex]\tt -32[/tex]
Now that we're done factoring the denominator let's bring down the numerator which is ' 1 ':-
[tex]\tt -\cfrac{1}{32}\;\; \bf Answer[/tex]
☆-------☆-------☆-------☆
[tex]\dfrac 1{2^{-2}\cdot x^{-3}\cdot y^5}\\\\=\dfrac 1{2^{-2} \cdot2^{-3} \cdot (-4)^5}\\\\=-\dfrac 1{2^{-2} \cdot 2^{-3} \cdot (2^2)^5}\\\\=-\dfrac{1}{2^{-2} \cdot 2^{-3} \cdot 2^{10}}\\\\=-\dfrac{1}{2^{-2-3+10}}\\\\=-\dfrac 1{2^{5}}\\\\=-\dfrac 1{32}[/tex]
Monica buys a postage stamp the area of the stamp is more likely to be 1 square inch or 1 square meter? Explain
Answer:
HEyy
Step-by-step explanation:
its one square inch because if you think about it a little postage samp is very tiny
Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 34 liters per minute. There are 400
liters in the pond to start.
Let W represent the total amount of water in the pond (in liters), and let T represent the total number of minutes that water has been
added. Write an equation relating W to T. Then use this equation to find the total amount of water after 16 minutes.
Equation:
D=0
X
Total amount of water after 16 minutes: liters
5
?
Multiply liters per minute by number of minutes and add that to the starting amount.
W = 34t + 400
now replace t with 16 and solve:
W = 34(16) = 400
W = 544 + 400
W = 944
After 16 minutes there are 944 liters in the pond
What is 35 - 2 ????? I am very confused and need help. I’m in college pls.
Answer:
33
Step-by-step explanation:
35 take away 1 is 34 take away one more its 33
The formula for a ciprofloxacin otic drop
quantity of each ingredient required to is given in the literature as follows10:
make 1500 g of the powder. Ciprofloxacin 1 g
Calcium Carbonate Propylene Glycol 5 parts 50 mL
Magnesium Oxide Glycerin qs ad 1 part 100 mL
Sodium Bicarbonate 4 parts How many grams of ciprofloxacin Bismuth Subcarbonate 3 parts would be required to prepare 200 15-mL
Answer:
I dont know bro, I am here for the free answers.
Dan made $5000 in taxable income last year.
Suppose the income tax rate is 10% for the first $7500 plus 15% for the amount over $7500
How much must Dan pay in income tax for last year?
well, we know is 10% for the first 7500, but Dan only made 5000 of taxable income, so he's in that range of 0 - 7500, so he only gets to pay 10% of 5000.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10\% of 5000}}{\left( \cfrac{10}{100} \right)5000}\implies 500[/tex]
On Friday, Hayley has purchased more flour and eggs, but only has 22 cups of sugar and 4 sticks of butter. Which combination of loaves of zucchini bread and banana bread can Hayley make?
Answer:
It is C
Step-by-step explanation:
Expand binomial (x+1)1
Answer:
x + 1Step-by-step explanation:
Given binomial
(x + 1)¹Use the property
a¹ = aThe binomial remains same without brackets
(x + 1)¹ = x + 1Can you do number 1 for me
Answer:
c. 3/5
Step-by-step explanation:
Find the area of right angled triangle at J, if ZJ = 14 and JW = 1.
Answer:
7 sq units
Step-by-step explanation:
Area of right angled triangle
= 1/2 * ZJ * JW
= 1/2 * 14 * 1
= 7 sq units
NEED AN ANSWER NOW! WILL GIVE YOU BRAINLIEST!!
I can't figure out what's the answer, I'm clueless.
Answer:
10
Step-by-step explanation:
On the chart, it says "Number of hostel rooms: 10". The rest of the data is useless and is just there to confuse you.
What is the value for y when x = 8
Answer:
x+y=0
8+y=0
y=8
Step-by-step explanation:
correct me if I'm wrong
Answer:
D. 44
Step-by-step explanation:
y = (8 x 5) +4
y= 40 + 4
y= 44
On January 1, 2022 Hideki Matsuyama provides services in exchange for a $10,000 zero-interest bearing note due in 4 years. The effective interest rate for a note of this type is 15 percent. How much revenue does Hideki recognize on January 1, 2022?
Answer:
Revenue=$6000
Step-by-step explanation:
A = PRT
100
A= (10,000×4×15)/100
= (10,000×60)/100
= 600,000/100
=$6000
Hideki recognizes a $17,490.06 revenue.
What is Revenue?Revenue is the total amount of income generated by the sale of goods and services related to the primary operations of the business.
Given that on January 1, 2022, Hideki Matsuyama provides services in exchange for a $10,000 zero-interest bearing note due in 4 years, and the effective interest rate for a note of this type is 15 percent,
To determine how much revenue does Hideki recognize on January 1, 2022, the following calculation must be made:
x = 10000 x 1.15^4
x = 10000 x 1.749
x = 17490.06
Therefore, Hideki recognizes a $17,490.06 revenue.
Learn more about revenue in brainly.com/question/14695611
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A babysitter charges a rate of $15 per hour. how long was the babysitter there if she makes $5
Answer:
20 mins.
Step-by-step explanation:
A babysitter charges a rate of $15 per hour. How long was the babysitter there if she makes $5?
x = hours she babysat
Equation:
15x = 5
Divide to isolate x:
15x = 5
/15 /15
x = 1/3 hrs.
Now, we convert into minutes, since she didn't work for a whole hour, to earn the $15
We know that there are 60 mins. in an hour
60 * 1/3
60/3
20 mins.
Therefore, the babysitter was there for 20 mins.
Hope this helps!
Is 10 times as much as 0.007
Answer:
10 x 0.007 = 0.07
Step-by-step explanation:
im not sure if thats what you meant
The number of peanuts in bags is normally distributed with a mean of 172.5 peanuts and a standard deviation of 1.9 peanuts.
What is the z-score of a bag containing 168 peanuts?
−2.37
−2.06
−1.32
−1.05
Solve for x in the equation x2-12x+36 = 90
X
=
O X=6+3/10
O x=6+217
X
X= 12+3^22
X= 12+3/10
Answer:
Step-by-step explanation:
hello : (x-6)² = 90 .....continu
In a writing competition, the first place winner receives 1/2 of the prize money. The second runner up receives 1/4 of what the winner won. What was the total amount of prize money distributed if the winner receives $8000
Answer:
10,000 is the total amount of.money that was distributed
which is greater 1.59 or 1.6
Answer:
1.6 is greater than 1.59
Step-by-step explanation:
It goes. 1.5 -> 1.51 -> 1.52.... -> 1.58 -> 1.59 -> 1.6 -> 1.61...
Please help me with these 2 questions, I don’t really need explanations I just need straight forward answers ! The questions are linked below. 50 points
Answer:
1. The value of 5 is fifty thousand
2. The value of 6 is six thousand
Step-by-step explanation:
1. 8.156 million - 8,156,000
2. 6,521
^ 6000
Mrs. Becker drives past the Route 50 drawbridge light every morning on the way to
work. Eight out of 10 times, the traffic light is red. There are only 25 days of school le
how many of those days should she expect to get stopped at that light?
Answer:
20 days
Step-by-step explanation:
1) [tex]\frac{8}{10}[/tex] must be written as a fraction where the denominator is 25 since there are 25 days of school.
[tex]\frac{8}{10} = \frac{x}{25}[/tex]
2) Cross multiply them.
[tex]10(x) = 25(8)[/tex]
[tex]10x = 200[/tex]
3) Solve for [tex]x[/tex].
[tex]x = \frac{200}{10}[/tex]
[tex]x = 20[/tex]
which of the following are solutions
Answer:
-5 and 9
Step-by-step explanation:
To find the solutions we will factor the equation.
First we take out a 2:
[tex]2(x^2-4x-45)[/tex]
Then we can factor again:
[tex]2(x+5)(x-9)[/tex]
This provides us with the answer of:
[tex]x+5=0[/tex]
and
[tex]x-9=0[/tex]
Hence the solutions of -5 and 9.
The transformation of triangle ABC is an example of what?
Answer:
The relation between preimage and image
Step-by-step explanation:
A culture started with 6000 becteria. after 3 hours it grew to 7200 becteria. Predict how many bacteria will be present after 19 hours. Round your answer to the nearest whole number. p=ae^kt
Answer: 13,600.
Step-by-step explanation: every hour is 400 bacteria produced. 400x19= 7600. 7600+6000=13600
A certain number added to its square is equal to 90. What is/are the number(s) that work?
Answer:
9,-10
Step-by-step explanation:
Let u be a number.
[tex]u + {u}^{2} = 90[/tex]
[tex]u {}^{2} + u - 90 = 0[/tex]
[tex](u + 10)(u - 9) = 0[/tex]
[tex]u = - 10[/tex]
or
[tex]u = 9[/tex]
9, -10
