A = 1011 + 337 + 337/2 +1011/10 + 337/5 + ... + 1/2021
Answers
The sum of the given series can be found by simplification of the number
of terms in the series.
A is approximately 2020.022Reasons:
The given sequence is presented as follows;
A = 1011 + 337 + 337/2 + 1011/10 + 337/5 + ... + 1/2021
Therefore;
\(\displaystyle A = \mathbf{1011 + \frac{1011}{3} + \frac{1011}{6} + \frac{1011}{10} + \frac{1011}{15} + ...+\frac{1}{2021}}\)The n + 1 th term of the sequence, 1, 3, 6, 10, 15, ..., 2021 is given as follows;
\(\displaystyle a_{n+1} = \mathbf{\frac{n^2 + 3 \cdot n + 2}{2}}\)Therefore, for the last term we have;
\(\displaystyle 2043231= \frac{n^2 + 3 \cdot n + 2}{2}\)2 × 2043231 = n² + 3·n + 2
Which gives;
n² + 3·n + 2 - 2 × 2043231 = n² + 3·n - 4086460 = 0
Which gives, the number of terms, n = 2020
\(\displaystyle \frac{A}{2} = \mathbf{ 1011 \cdot \left(\frac{1}{2} +\frac{1}{6} + \frac{1}{12}+...+\frac{1}{4086460} \right)}\)
\(\displaystyle \frac{A}{2} = 1011 \cdot \left(1 - \frac{1}{2} +\frac{1}{2} - \frac{1}{3} + \frac{1}{3}- \frac{1}{4} +...+\frac{1}{2021}-\frac{1}{2022} \right)\)
Which gives;
\(\displaystyle \frac{A}{2} = 1011 \cdot \left(1 - \frac{1}{2022} \right)\)
\(\displaystyle A = 2 \times 1011 \cdot \left(1 - \frac{1}{2022} \right) = \frac{1032231}{511} \approx \mathbf{2020.022}\)
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A is equal to 1,685.00049.
Given that A = 1011 + 337 + 337/2 +1011/10 + 337/5 + ... + 1/2021, the following calculation must be performed to determine the result of this operation:
337/2 = 168.5 1011/10 = 101.1 337/5 = 67.4 1/2021 = 0.00049 1011 + 337 + 168.5 + 101.1 + 67.4 + 0.00049 = A 1685.00049 = A
Therefore, A is equal to 1,685.00049.
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Related Questions
if a small cup is 10 oz and cost 2.69 what is the cost per ounces
Answers
Answer:
The cost per ounce of the small cup is $0.269
Step-by-step explanation:
To find the cost per ounce, we can divide the cost of the cup by the number of ounces it holds.
Cost per ounce = Cost of the cup ÷ Number of ounces in the cup
Cost of the cup = $2.69
Number of ounces in the cup = 10 oz
So,
Cost per ounce = $2.69 ÷ 10 oz
Cost per ounce = $0.269 per oz (rounded to the nearest thousandth)
Therefore, the cost per ounce of the small cup is $0.269.
solve ((-3) x (10 + (-7))) to the power of 2 divided by 3 - (-9) to the power of 2)
Answers
The solution of the given expression will be 9/16.
What is an expression?Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given an expression, [-3*(10+(-7))]²÷[(3-(-9)]²
= [-3*(10+(-7))]²÷[(3-(-9)]² = (-9)²/12²
= 9/16
Hence, The solution of the given expression will be 9/16.
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Michael's mom loves Bright Scents candles. A 4-inch candle will burn for 8 hours. Michael bought his mom a 10-inch candle for Mother's Day.
If Bright Scents candles all burn at the same rate, how many hours will the 10-inch candle burn?
Answers
Answer:
Step-by-step explanation:
is abc ~ Def explain
Answers
The two triangles are congruent since they have equal angles and equal sides.
What is congruent triangles?Congruent triangles are two triangles that have exactly the same size and shape.
In other words we can say that they have the same angles and the same side lengths.
So when two triangles are congruent, all of their corresponding parts including the angles and sides are equal.
For the given triangles
The missing value of angle C = 180 - (18 + 110) = 52⁰
The missing value of angle F = 180 - (18 + 52) = 110⁰
So it is obvious that the two triangles are congruent since they have equal angles and equal sides.
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Given that the expression f(x)=2x³+px² 8x+q is exactly divisible by 2x²-7x+6, evaluate p and q and factorise completely
Answers
The values of p and q are given as follows:
p = 3.5, q = 6.
Hence the factored expression is given as follows:
2(x - 1.5)(x - 2)(x + 2).
How to obtain the values of p and q and factor the function?The function f(x) is divisible by 2x² - 7x + 6, which has the roots given as follows:
x = 1.5 and x = 2.
(using a quadratic equation calculator with coefficients a = 2, b = -7 and c = 6).
Hence the following relation holds true, considering the linear factors of the function:
2x³ + px² + 8x + q = 2(x - 1.5)(x - 2)(x - a).
In which a is the third root.
Hence:
2x³ + px² - 8x + q = 2(x² - 3.5x + 3)(x - a)
2x³ + px² - 8x + q = 2(x³ - x²(3.5 + a) + x(3.5a + 3) - 3a)
2x³ + px² - 8x + q = 2x³ - x²(7.5 + 2a) + x(7a + 6) - 3a.
Hence the system of equations is given as follows:
p = 7.5 + 2a.7a + 6 = -8.q = -3a.From the second equation, the value of a is given as follows:
7a = -14
a = -2
Then the value of q is given as follows:
q = -3a = 6.
The value of p is given as follows:
p = 7.5 - 4
p = 3.5
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ANSWERS FOR THESE!!!
Answers
Answer:
Question 23) 12 x 6√3 = 72√3
Question 24) 672 cm³
Given cot ø = 4/3. Find the other two reciprocal trigonometic ratios. 1) scs 2) sec
Answers
Answer:
csc ø = 5/3 ; sec ø = 5/4
Step-by-step explanation:
cot ø = adj/opp
adj = 4
opp = 3
after that, we must find the hypotenuse by using phytagoras theorem
hpy² = adj² + opp²
hpy² = 4² + 3²
hpy² = 25
hpy = 5
now let's find the other
csc ø (not scs) = hyp/opp = 5/3
sec ø = hyp/adj = 5/4
Converting Mixed Numbers to Improper Fractions.
1) 2 5/9. 2) 3 1/2.
3) 7 2/5. 4)3 1/5.
5) 5 3/4. 6) 6 3/5
Answers
23/9
7/2
37/5
16/5
23/4
33/5
The answers are in order you put it in like 1-6
Can I have brainiest please
25
A man earns N 5,000.00 for 10
days work. How should he earn in
14 days, if working at the same
rate
Answers
Answer:
N 7,000.00
Step-by-step explanation:
He earns N 5,000.00 for 10 days of work so divide the 5,000.00 by 10
5,000.00/10= 500.00 ; this is the amount of money he makes in 1 day
Then multiply this amount make in 1 day by 14 to find how much the man makes in 14 days.
500.00*14=7,000.00
Therefore, the man makes N 7,000.00 in 14 days.
In each figure for what values of x and y is the figure a parallelogram
Answers
The values of x and y that makes the figure a parallelogram are x = 17 and y = 26
How determine what values of x and y makes the figure a parallelogram?
A parallelogram is a four-sided geometric shape that has opposite sides that are parallel to each other.
The opposite sides of a parallelogram have the same length, and the opposite angles are also equal. The opposite sides of a parallelogram are also known as the bases, and the other two sides are known as the legs.
Since the opposite sides of a parallelogram are equal in length, we can say:
3x + 6 = 4 - x
3x + x = 4 - 6
4x = -2
x = -2/4
x = -1/2 = -0.5
y + 2 = 2y - 3
2 + 3 = 2y - y
5 = y
y = 5
Likewise, the opposite angles of a parallelogram are equal, so we can say:
(4x - 12)° = (3x + 5)°
4x - 12 = 3x + 5
4x - 3x = 5 + 12
x = 17
(3y + 46)° = (5y - 6)°
3y + 46 = 5y - 6
46 + 6 = 5y - 3y
52 = 2y
2y = 52
y = 52/2
y = 26
Thus, x = 17 and y = 26 makes the figure a parallelogram
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PLEASE HELP WILL MARK BRAINLIEST THANK YOU
Answers
Answer: 5 square units
Step-by-step explanation:
Answer: 18 TOTAL I THINK, IF IM WRONG THEN U CAN REPORT ME IF U WANT
Step-by-step explanation:
What does the net decimal equivalent (NDE) represent?
Answers
Answer:
the product of the decimal equivalents of all discount in the series
Is 0,4,8,12 an arithmetic sequence?
Answers
\( \frac{1}{3} (x - \frac{2}{3} ) = - \frac{17}{9} \)
solve for x
Answers
15) Cost of a computer game: $4.99
Markup: 40%
Discount: 55%%
Tax: 1%
Answers
Answer:
$3.18
Step-by-step explanation:
(4.99×0.4)+4.99=6.986
6.986-(6.986×0.55)=3.1437
(3.147×0.01)+3.147=3.175137
after five years of owning a roth individual retirement account (ira), a person wants to buy his first home, the person can withdraw money from the roth ira
Answers
A person who has owned a Roth IRA for five years may withdraw money from the account to buy their first home. The individual has to meet certain requirements and can't withdraw more than $10,000 per person.
A Roth IRA is a type of individual retirement account that allows for tax-free withdrawals of contributions at any time, without penalty or taxes. After five years of ownership, a person who has a Roth IRA may withdraw money from the account to buy their first home. This withdrawal is known as a "first-time homebuyer distribution."
However, there are certain rules and limitations to be aware of when withdrawing money from a Roth IRA for a first home purchase. The individual must be a first-time homebuyer, defined as someone who has not owned a home in the past two years. Additionally, the maximum amount that can be withdrawn for a first home purchase is $10,000 per person.
It's important to note that while contributions to a Roth IRA can be withdrawn tax-free and without penalty, earnings on those contributions may be subject to taxes and penalties if withdrawn before age 59 and a half.
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Lesson 17: Use the Four Operations to Solve Problems Cool Down: Andre's Balloons Andre has 125 balloons. He and 4 friends hung up some balloons for a party at school and now there are 80 balloons left. If each person hung up the same number of balloons, how many balloons did each person hang up? 1. Write an equation with a letter for the unknown quantity to represent the situation. 2. Solve the problem. Explain or show your reasoning.
Answers
a) Using the four basic mathematical operations, the number of balloons that each person hang up is 9.
b) An equation representing the situation is x = (125 - 80)/5.
What are the mathematical operations?The four basic mathematical operations include addition, subtraction, division, and multiplication.
The mathematical operations provide solutions to mathematical problems using operands.
What is an equation?An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.
The total number of balloons that Andre has = 125
The number of balloons remaining after hanging some for the school party = 80
The difference (number of balloons used) = 45 (125 - 80)
The number of friends who hang the balloons = 5
The number of balloons hung by each friend of Andre = 9 (45/5)
Thus, we can conclude that each of the 4 friend and Andre hung 9 balloons, with 80 remaining.
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Describe the relationship between the values of the two 7s in the number 3,772 what equation could you use to help describe the relationship
Answers
Answer:
y = 10x, which is the relationship between two 7 in the number 3772
Step-by-step explanation:
In the given number 3772
3 is at thousandth position its value is 3000 numerically
7 is at the hundredth position its value is 700 numerically
next 7 is at tens position its value is 70 numerically
and 2 is at unit position its value is 2 numerically
thus, 3772 can also be written as sum of number based on its position
3000
+700
+ 70
+ 2
___-
= 3772
Thus,
since Third 7 from left has value of 70
and Second 7 from left has value of 700
we know 70*10 = 700
Thus, 70 is 10 times to that 700
Thus, we can say that
value of Second 7 from left = 10*value of Third 7 from left
Thus,
let value of Second 7 from left be y
value of Third 7 from left be x
then
y = 10x, which is the relationship between two 7 in the number 3772
which of the fallowing is a mononial
Answers
Answer:
A monomial is a polynomial, which has only one term. A monomial is an algebraic expression with a single term but can have multiple variables and a higher degree too. For example, 9x3yz is a single term, where 9 is the coefficient, x, y, z are the variables and 3 is the degree of monomial.
Bound
Figure 2.
Jenny would like to buy a new air conditioner for his home. As seen in Figure 2 above he has
3 types of brands that he can consider. The cash price for Daewoo is RM1,899, Daikin at a
price of RM1,699 and last choice is Mitsubishi at a price of RM1.999. He plans to make 18
monthly instalments, if he pays RM300 as a down payment for the air conditioner that he would
like to buy, find the interest charge for each brand if the interest rate is 4% based on originall
balance if he chooses to buy from Daikin, find the monthly instalment price and instalment
price that he needs to pay.
Answers
if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).
How to determine the monthly instalment price and instalment price that Daikin needs to pay.Calculating the loan amount for each brand by subtracting the down payment from the cash price:
Loan amount for Daewoo = RM1,899 - RM300 = RM1,599
Loan amount for Daikin = RM1,699 - RM300 = RM1,399
Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699
Calculating the interest charge for each brand:
Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96
Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96
Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96
To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:
Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22
Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89
Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72
Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).
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a parrelogram has sides of 13 and 17 and an angle that measure 64 degrees. Wht is x, the length of the diagonal
Answers
The length of the diagonal x of the parallelogram is x = 16.25 units
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the length of the diagonal of the parallelogram be x
Let the length of the first side be b = 13
Let the length of the second side be c = 17
The measure of the angle A = 64°
Now , for a parallelogram
The diagonal of a parallelogram separates it into two congruent triangles
So , from the law of cosines ,
x² = b² + c² - 2bc ( cos A )
Substituting the values in the equation , we get
x² = ( 13 )² + ( 17 )² - 2 ( 13 ) ( 17 ) cos 64°
x² = 169 + 289 - 442 ( cos 64° )
x² = 458 - 193.76
On simplifying the equation , we get
x² = 264.24
Taking square roots on both sides of the equation , we get
x = √264.24
x = 16.25 units
Hence , the length of the diagonal of the parallelogram is 16.25 units
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Simplify the expression (64)2.
Answers
Answer:
See below.
Step-by-step explanation:
(64)2
64*2
128
-hope it helps
Answer:
128
Step-by-step explanation:
it's multiplication(64)2
64*2
128
Help NEed help help .
Answers
Answer:
Oh lord, what is this-
Step-by-step explanation:
El primer término de una progresión geométrica es 3 y el séptimo 12 288. Hallar la suma de los siete términos.
Answers
Answer:
16383
Step-by-step explanation:
El primer término de la progresión geométrica es 3 y lo llamaremos \(a\).
Se tiene que una progresión geométrica es de la forma:
\(a, ar, ar^2, ar^3, ar^4, \cdot \cdot \cdot\)
Donde \(r \neq 0\) y es la proporción es común. Por lo tanto si el séptimo número de la sucesión es 12.288 este se puede re-escribir como:
\(ar^6 = 12.288\)
Si se resuelve la ecuación para hallar \(r\) se tiene
\(r = \sqrt[6]{\frac{12.288}{a} } = \sqrt[6]{\frac{12.288}{3} } = \sqrt[6]{ 4096} = 4\)
Ahora se halla cada número de la progresión geométrica entre 1 y 7 para finalmente sumarlos
\(ar^0+ar^1+ar^2+ar^3+ar^4+ar^5+ar^6\)
\(3+12+48+192+768+3072+12288\) = 16383
Por lo tanto la sumatoria de los primeros \(7\) términos de la sucesión son 16383
The table below shows the number of students who attend various after-school activities. After-School Activities Activity Number of Students Spanish Club 19 Basketball 24 Drama 15 Homework Help 17 Soccer 20 Which ratio compares the number of students in the Spanish club to the total number of students? a.19:95 b.20:95 c.95:24 c.95:19
Answers
Answer:
C. 95:19
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
because the total number of students is 95 and those who play Spanish club is 19
what is the median of numbers 20,35,28,15,22,36,26
Answers
The median of the given data set is 26.
What is the median?In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.
Given the data set, we need to find the median.
So, let's arrange the numbers from smallest to largest in order to find the median.
\(\sf 15,20,22,26,28,35,36.\)
\(\text{Median}=\sf 26\)
Therefore, the median of the data set is 26.
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Hey, my name is Ishaan and I want to start a tech company (basically selling websites and apps). I don't know what to name it though, does anyone have any suggestions? I wanted "ishaanx" but it's taken.
Answers
Answer:
ishaantech maybe, that's all I can think of.
NO LINKS!! URGENT HELP PLEASE!!!
1. Find an exponential function of the form f(x) = ba^-1 + c that has the given horizontal asymptote and y-intercept and passes through P
y = 33; y-intercept 408; P(2, 93)
Answers
Answer:
\(\bold{f(x) = 375(2.5)^{-x}+ 33}\)
Step-by-step explanation:
An exponential function of form f(x) = ba^(-x) + c has a horizontal asymptote of y = c as x approaches infinity, and a y-intercept of (0, b + c). We can use the given information to set up a system of equations and solve for the unknowns.
The horizontal asymptote is given as y = 33, so we have:
c = 33
The y-intercept is given as (0, 408), so we have:
b + c = 408
Substituting c = 33, we get:
b + 33 = 408
b = 375
So the function we're looking for is of the form:
\(\bold{f(x) = 375a^{-x}+ 33}\)
To find a, we use the fact that the function passes through P(2, 93):
93 = 375a^(-2) + 33
60 = 375a^(-2)
a^2 = 375/60
a^2 = 6.25
a = \(\sqrt{6.25 } =2.5\)
Therefore, the exponential function that satisfies the given conditions is:
\(\bold{f(x) = 375(2.5)^{-x}+ 33}\)
I need a answer to 77.5% of 13.270
Answers
Answer:
10.28425
Step-by-step explanation:
Pls help can’t figure it out
Answers
Y = 20
Let me know if you want me to show my work (: