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;
[tex]\displaystyle A = \mathbf{1011 + \frac{1011}{3} + \frac{1011}{6} + \frac{1011}{10} + \frac{1011}{15} + ...+\frac{1}{2021}}[/tex]The n + 1 th term of the sequence, 1, 3, 6, 10, 15, ..., 2021 is given as follows;
[tex]\displaystyle a_{n+1} = \mathbf{\frac{n^2 + 3 \cdot n + 2}{2}}[/tex]Therefore, for the last term we have;
[tex]\displaystyle 2043231= \frac{n^2 + 3 \cdot n + 2}{2}[/tex]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
[tex]\displaystyle \frac{A}{2} = \mathbf{ 1011 \cdot \left(\frac{1}{2} +\frac{1}{6} + \frac{1}{12}+...+\frac{1}{4086460} \right)}[/tex]
[tex]\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)[/tex]
Which gives;
[tex]\displaystyle \frac{A}{2} = 1011 \cdot \left(1 - \frac{1}{2022} \right)[/tex]
[tex]\displaystyle A = 2 \times 1011 \cdot \left(1 - \frac{1}{2022} \right) = \frac{1032231}{511} \approx \mathbf{2020.022}[/tex]
A ≈ 2020.022Learn more about the sum of a series here:
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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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Mrs. Montgomery earns a 6.5% commission on her total sales. Last month, she had sales of $55,780. How much commission did Mrs. Montgomery earn last month?
Answer:
3625.7
Step-by-step explanation:
hope that will help goodbye
-16-|-2-4|+7 please solve this for me and explain. i would really appreciate it.
Answer:
-15
Step-by-step explanation:
-16 -|-6| +7
-16 - 6 + 7
= - 15
Absolute value is just taking the positive value of a number.
Step-by-step explanation:
-16-(-2-4)+7=
-16-(-6)+7=
-16+6+7=
-16+13=
-3
- The width of a rectangle is 4x – 1 feet and the length is 2x + 6 feet. Find the perimeter of the rectangle.
Answer:
12x + 10 feet
Step-by-step explanation:
Perimeter = 2( length + width)
= 2[ 2x + 6 + (4x -1)]
= 2( 2x + 6 + 4x - 1)
= 2( 6x + 5)
= 12x + 10
1/2x + 4 = 10
solve the following equation algebratically. Show the work to support the answer.
Answer:
(1/2)x + 4 - 4 = 10 - 4
2(1/2)x = 6 * 2
x = 12
Which function is shown in the graph?
Answer:
k(x)=-3/4x+5
Step-by-step explanation:
A number is between 63 and 68 It has prime factors of 2 and 11 whats the number
Answer:
66
Step-by-step explanation:
66 is the only number between 63 and 68 that is divisible by both 2 and 11.
66/2=33 66/11=6
Help help help help help math
Step-by-step explanation:
don't panic. just breathe and think logically.
why would these angles be different ? how could they be different ?
right : they cannot be different. otherwise the 2 horizontal lines would not be parallel.
so, yes, indeed, these 2 angles are identical.
3x + 2 = 2x + 6
x = 4
that's it.
what does the E stand for in PEMDAS?
Answer:
Exponents
Step-by-step explanation:
Parentheses
Exponents and roots
Multiplication
Division
Addition
Subtraction
Solve the proportion:
11/10 = 22/x
Answer:
x=20
Step-by-step explanation:
Find the equation of the function of the specified type that is the best fit for the given data
1 2/5m-3/5(2/3m+1)pls help
Answer: (10m-3)/5
Step-by-step explanation:
Convert 1 2/5 into an improper fraction
Simplify 5+25+2 to 7
Simplify 2/3m to 2m/3
Simplify 7/5m to 7m/5
Expand and remove the parenthesis
Collect the like terms
Simplify
ratio of boys to girls is 2:3 what is the ratio of boys of there are 6 girls
Answer:
4:6
Step-by-step explanation:
2 x
- = ----
3 6
6/3 = 2
2 x 2 = 4
Quantity is proportional of 40/8
1985 x 99 I already know the answer: 196515
Answer:
the answer is 196515
Step-by-step explanation:
If u already knew the why u put upped the question?
i really need help, does anyone know these
Answer: If angle A is congruent to angle E
help me plssssssssssssss
multipley by 2, to get the answer
PLZ HELPPPPP QUICKLYYYY!!!!!!!!!!!!!
Answer:
root 490
Step-by-step explanation:
f(x)=x^2-7 and h(x)=7x-5, then f(h(2))= ?
==================================================
Work Shown:
h(x) = 7x-5
h(2) = 7(2)-5
h(2) = 14-5
h(2) = 9
f(h(2)) = f(9)
f(x) = x^2-7
f(9) = 9^2-7
f(9) = 81-7
f(9) = 74
f(h(2)) = 74
-----------
Here's a slightly alternative approach:
f(x) = x^2 - 7
f(h(x)) = ( h(x) )^2 - 7
f(h(x)) = ( 7x-5 )^2 - 7
f(h(2)) = ( 7*2-5 )^2 - 7
f(h(2)) = ( 14-5 )^2 - 7
f(h(2)) = ( 9 )^2 - 7
f(h(2)) = 81 - 7
f(h(2)) = 74
Suppose you receive a shipment of 29 engines, two of which are defective. What is the probability of picking a sample of 4 engines with two bad engines in it? (Round approximations to the nearest thousandth.)
Answer:
0.4%
Step-by-step explanation:
2 are defective and 27 are good out of 29. Chance of picking 1 defective is 2/29 or .069. Chance of picking good is 27/29 or .931.
2 good and 2 bad is
.931 * .931 * .069 * .069 = .004
There is a 0.4 % chance of 2 bad.
help , I have like no clue on what I'm doing
Answer:
Step-by-step explanation:
Linear equations can have the form y = mx + b
where m is the slope of the line and equals Δy/Δx
and b is the y intercept.
Just for fun, let's choose the first and last sets of data points.
Δy = (275 - 135) = 140
Δx = (5 - 1) = 4
so slope m = 140/4 = 35 and the units on the slope would be $/month
Answer:
The slope of the line is 35
Step-by-step explanation:
We'll select [tex](1,135)[/tex] and [tex](2,170)[/tex] for this problem.
The slope is defined as the rate of change. Its formula is [tex]Slope=m=\frac{Rise}{Run}=\frac{y_2-y_1}{x_2-x_1}[/tex] where our two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
Therefore, we have [tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{170-135}{2-1}=\frac{35}{1}=35[/tex] as our slope.
Simplify the linear expression. −4x+5(−5x−1) Enter your answer in the box.
Answer:
-29x - 5
Step-by-step explanation:
-4x - 25x - 5 = -29x - 5
Answer:
- 29x - 5
Step-by-step explanation:
- 4x + 5(- 5x - 1) ← distribute the parenthesis by 5
= - 4x - 25x - 5 ← collect like terms
= - 29x - 5
50pt Which of the following are maximum and minimum points of the function y=sin(x+ π)?
Answer:
none of the above
Maximum (3π/2, 1); Minimum (π/2, -1)
Step-by-step explanation:
The sine function is shifted left 1/2 cycle by the addition of π to x in the argument. That basically inverts the function, so it is equivalent to ...
y = -sin(x)
This has a minimum of -1 at π/2, and a maximum of +1 at 3π/2. This does not match any of the offered answer choices.
__
You might want to discuss this question with your teacher.
Answer:
The correct answer is C!
Step-by-step explanation:
The dude that said there’s no answer doesn’t know what he’s talking about.
4781/32 without a decimal
Answer:
149(13/32)
Step-by-step explanation:
4781/32 and then take the remainder to make it an improper fraction
Find the future value of 1000 at 7 % interest compounded annually for 10 years.
Answer:
1967.15
Step-by-step explanation:
1000 x 1.07^10 = 1967.15
The future value of 1000 with annual compounding for 10 years is $1967.15.
The formula for calculating with annual compounding is:
FV = P (1 + r)^n
FV = Future value P = the amount deposited R = interest rate N = number of years1000 x (1.07)^10 = $1967.15
To learn more about future value, please check: https://brainly.com/question/18760477
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Which answer best describes the complex zeros of the polynomial function?
f(x) = 13 - 22 + 6x - 6
The function has two real zeros and one nonreal zero. The graph of the function intersects the x-axis at exactly one
location.
The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly two
locations.
The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly one
location.
The function has three real zeros. The graph of the function intersects the x-axis at exactly three locations.
Answer:
The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly one
location.
No clue if someone can explain
Answer:
your trying to find out how much each cookie cost
from looking at this we can see that 2 cookies is 1 dollar so each cookie is 50 cents
Hope This Helps!!!
What is the slope of the line containing (-3, 1) and (1, -2)?
Answer:
C is the answer
Step-by-step explanation:
Answer: The answer is C, -3/4.
Explanation: First graph the points, then add the straight line through them and to find the slope you do rise/run, formula being y2-y1/x2-x1. This means putting the second y value minus the first y value and dividing that by the second x value minus the first x value. Then simplify.
How many times do 5 go into 32
Answer:
6 times or 6.4
Multiply and write the result in Scientific notation
(3 x 10^5) (2 x 10^2)
?