Answer:
This sum is the sum of an arithmetic sequence. There is a formula for the sum of an arithmetic sequence which can be looked up or derived by a variety of means.
A nice approach for this sequence is the following. Notice that the sum of first and last number in the sequence is the same as the sum of the second and second last, and also the same as the sum of the third and third last, and so on.
There are n of these pairs. So the desired sum is n x (first number + last number). But the first number is 1 and the last on is 2n. Thus the desired sum is n(1 + 2n).
Hope this helps!!
Mark Brainleast!!!!!!!!!!!
Consider the set {1, 2, 3, 4, ..., m} where m is some natural number, i.e. a positive whole number.
Now let's say we wanted to add everything in that set.
What we can do is write out the terms
1, 2, 3, 4, ..., m
then just underneath, we write the reverse of that set
m, ..., 4, 3, 2, 1
Here's an example of what I mean. I'll use m = 7
[tex]\begin{array}{|c|c|c|c|c|c|c|} \cline{1-7}1 & 2 & 3 & 4 & 5 & 6 & 7\\\cline{1-7}7 & 6 & 5 & 4 & 3 & 2 & 1\\\cline{1-7}\end{array}[/tex]
For each column, add straight down
The third row will be nothing but 8's
[tex]\begin{array}{|c|c|c|c|c|c|c|} \cline{1-7}1 & 2 & 3 & 4 & 5 & 6 & 7\\\cline{1-7}7 & 6 & 5 & 4 & 3 & 2 & 1\\\cline{1-7}8 & 8 & 8 & 8 & 8 & 8 & 8\\\cline{1-7}\end{array}[/tex]
We can see there are seven copies of '8' being added here, so the sum of all the numbers in the set {1,2,3,4,5,6,7} is 8*7 = 56. But wait, we double-counted each item when we formed the second row. So we must divide by 2 to fix the double-counting error.
Therefore, 1+2+3+4+5+6+7 = 56/2 = 28 instead.
-----------------------------
That previous example showed that adding from 1 to 7 means we have 7 copies of (1+7). In other words, 7 copies of 8 being added.
We could write that as 7(1+7)
Then divide that by 2 to fix the double-counting error.
We have 7(1+7)/2
Now imagine that we applied all of what was mentioned to the set {1,2,3,4,5,6,7,8}. Instead of 7's, we use 8's this time to get 8(1+8)/2
Then we can extend it out to the set {1,2,3,4,..., m} and we get the formula m(1+m)/2
We have m copies of (1+m) being added; hence the m(1+m). Don't forget to divide by 2 to fix the double-counting error.
-----------------------------
The key takeaway here is that summing 1+2+3+4+...+m gets us m(1+m)/2
In this case, m = 2n because we want the first 2n natural numbers.
Therefore,
m(1+m)/2
2n(1+2n)/2
n(1+2n)
n(2n+1)
represents the sum 1+2+3+...+n+...+2n
-----------------------------
Try out a value like n = 5 to find that 2n = 2*5 = 10, and,
1+2+3+4+5+6+7+8+9+10 = 55
also
n(2n+1) = 5(2*5+1) = 5*(11) = 55
Showing that the formula works for n = 5. I'll let you try other values of n.
What is the quotient of the division below? 96 divided by 3 = 13 23 31 32
Answer:
The answer is 32
Step-by-step explanation:
9/3=3 6/3=2 32
What is the value of y in the equation 6 + y = −3? (1 point) Group of answer choices −3 −9 3 9
Answer:
y= -9
Step-by-step explanation:
y+6=-3
subtract 6 from both sides
y=-9
y=-9
Solution:First, subtract 6 from both sides.6+y=-3Ory+6=-3Why subtract? Because 6 is added to y, and we need to use the opposite operation. Remember, our goal is to find the value of y.Subtract:y=-3-6y=-9We have found the value of y; it's equivalent to -9.Hope it helps.
Do comment if you have any query.
Which temperature during the week is farther from 0? Explain how you decided this using absolute value
Answer:
The farthest temperature from zero during the week is 5 °F because it's absolute value, 5, is the highest out of all the other numbers.
Step-by-step explanation:
Mrs. smith has $1500 in a retirement account earning 5% interest. each year she makes an additional deposit of $500 to her account. after 3 years, what would her account balance be?
Answer:
$3,312.69
Step-by-step explanation:
What she started with: $1500
Year 1: 1500 + 1500(.05) + 500 = $2,075
Year 2: (2.075)1.05 + 500 = $2,678.75
Year 3: (2678.75)1.05 + 500 = $3,312.69
Find the surface area of the rectangular prism.
7 mi
4 mi
2 mi
Answer:
mi?
Suteri Anar
Answer:
Right rectangular prism
Solve for surface area
A=100
l Length
7
w Width
4
h Height
2
Solution
A=2(wl+hl+hw)=2·(4·7+2·7+2·4)=100
Choose all numbers that are greater than 12%
CHECK
1/8
1/12
23/200
7/50
15%
0.025
Answer:
1/8, 7/50, 15%,
Step-by-step explanation:
I asked siri
can someone please help me with this question
Answer:
B. 15 inches
Step-by-step explanation:
you multiply 6 x 5 since those are the dimensions of the triangles which equals 30 then you divide by 2 to get an answer of 15
Answer:
i would say A. 10in
Step-by-step explanation:
what is the angle of BTC, Angle TBC,Angle TCB
By geometric and algebraic properties the angles BTC, TBC and TBC from the triangle BTC are 128°, 26° and 26°, respectively.
How to determine the angles of a triangle inscribed in a circle
According to the figure, the triangle BTC is inscribed in the circle by two points (B, C). In this question we must make use of concepts of diameter and triangles to determine all missing angles.
Since AT and BT represent the radii of the circle, then the triangle ABT is an isosceles triangle. By geometry we know that the sum of internal angles of a triangle equals 180°. Hence, the measure of the angles A and B is 64°.
The angles ATB and BTC are supplmentary and therefore the measure of the latter is 128°. The triangle BTC is also an isosceles triangle and the measure of angles TBC and TCB is 26°.
By geometric and algebraic properties the angles BTC, TBC and TBC from the triangle BTC are 128°, 26° and 26°, respectively.
To learn more on triangles, we kindly invite to check this verified question: https://brainly.com/question/2773823
In a school, 5/8 of the students are boys. If there are 240 girls, find the number of boys in the school.
Answer:
400 boys
Step-by-step explanation:
First use the fraction along with the given information (240 girls)
If 5/8 of the school are boys, then that means 3/8 of the school's students are girls. 3/8 happen to be equal to 240, which means we can conclude that 1/8 is equivilant to 240/3 = 80
80 multiplied by 5 = 400
There are 400 boys in the school. (640 total students in school)
Tip: Easy way to check answer is by putting the boys over the total students to find the ratio, and if it matches, your answer is correct. 400/640 = 0.625, which equals 5/8
Hope this helps :)
how do you solve -4 + y = 6 and y= 7x - -6 by substitution?
Answer:
by doing the math
Step-by-step explanation:
do (7x)-(-6) then the other problem and find out witch one is more
Answer:
x=4/7 and y=10
Step-by-step explanation:
To solve for x, we must isolate y in one of the equations to then insert it into the other equation. We can take the first equation, -4 + y = 6, and add 4 to both sides. This gives us y = 4+6, or y = 10. Since y is a variable, we can subsititute 10 into the second equation, y = 7x - (-6), giving us 10 = 7x - (-6). The minus negative six is equal to plus six. This gives us 10 = 7x +6. Now we can solve for x. Subtract 6 from both sides; 4 = 7x. Now to find x, we have to divide both sides by 7. This gives us x = 4/7.
What is the area of the the figure?
Answer:
830 yd
Step-by-step explanation:
Theres a few ways you can do this but I'll show you one of the easeist way for solving this problem.
You can slipt this figure into 2 rectangles by just cutting the small rectangle out (the one thats kind of sticking out)
Then, all you have to do is find the area of both rectangles and add them together.
For the big rectangle : 20x40 = 800
For the little rectangle : 30x10 = 30
Add all togther:
800 + 30 = 830 yd
Hope this helps :)
Isaiah earned a score of 61 on Exam A that had a mean of 78 and a standard deviation
of 10. He is about to take Exam B that has a mean of 200 and a standard deviation of
50. How well must Isaiah score on Exam B in order to do equivalently well as he did
on Exam A? Assume that scores on each exam are normally distributed.
Answer:
isaiah must get a score of 115
Find the coordinates of A.
Answer:
(-4, 1)
Step-by-step explanation:
Coordinates on the plane are written (x, y), meaning you write where the point is located on the x-axis (across) and then you write where the point is located on the y-axis (up and down).
You can see that A's location on the x-axis is -4, so now we have (-4, y). We can also see that A's location on the y-axis is 1, so we have (-4, 1) as our coordinates of A.
I hope this helps! Have a lovely day!! :)
find four rational number between -1/7 and 2/7...
Rational numbers are numbers which can be expressed as a fraction or in decimals. Integers, Whole numbers, Natural numbers are rational.
======================================================
Rational numbers between -1/7 and 2/7 : -
-0.1-0.0500.050.10.150.20.25Make a number line and find the numbers between the two given numbers.
Round 67.34 to the nearest tens place
A. 68
B. 67
C. 70
D. 60
Answer:
67 because it is closer to 67 than other options
Answer:
67 B
Step-by-step explanation:
16. Twelve inches is what percent of a yard?
Answer:
There are 3 feet in one yard, so each foot is 1/3 of a yard/
To find the percentage of each foot, divide 1 by 3
One foot is 33 1/3 percent of a yard.
Twelve inches is 33.33 percent of a yard.
What is Percentage?Percentage is defined as a number that can be expressed as a fraction of 100.
The statement is
Twelve inches is what percent of a yard
12 inches in terms of % yard
1 inch = 0.0277778 yard
12 inches = 0.333336 yard
In percentage = 33.33 % yard
To know more about Percentage
https://brainly.com/question/13450942
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Layla makes necklaces to sell online. she spends $46 on supplies at the first store and then $30 at the second store. she press to make a necklaces and sell each necklace at a markup of 75%. how much will she charge for each necklace?
Triangle JKL has vertices J(-4, 4), K(-1, 3), and
L(-2, 1). Graph the figure and its rotated image after a
clockwise rotation of 90° about the origin. Then give the
coordinates of the vertices for triangle J'K'L'.
K
o
NO LINKS
Answer:
J(0,6)
K(-1,3)
L(-3,4)
Step-by-step explanation:
Use the number line below to determine which of the following answer choices has statements that are all true.
Answer:
1st option, and 4th option
Step-by-step explanation:
Is it select one, or select all that are correct?
please help fast it is due
Answer:
25
Step-by-step explanation:
use the formulae SOHCAHTOA. cos45=adjacent/hypotenuse. cos45=x/25square root 2=25A pattern of dots is shown below. At each step, more dots are added to the pattern. The pattern continues indefinitely. How many dots would be found in the 30th step? Explain a rule that you could use to find the number of dots in any given step.
Using an arithmetic sequence, it is found that 89 dots would be found in the 30th step.
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
Researching the problem on the internet, it is found that the first step has 2 dots, the second has 5 dots, the third has 8 and so on, hence the first term is [tex]a_1 = 2[/tex] and the common difference is d = 3.
Then, the number of dots in the nth step is given by:
[tex]a_n = 2 + 3(n - 1)[/tex]
In the 30th step, the number will be given by:
[tex]a_{30} = 2 + 3(30 - 1) = 89[/tex]
More can be learned about arithmetic sequences at https://brainly.com/question/6561461
help me bro fr i need dis done
Answer: 6^5 = 6^3 * 6^2
When your multiplying exponents, you just add the exponents. So, 3 should be the exponent in the box.
anyone single i am lonely and sad... contact me if you are im a male 15 years old live in alabama hope your ready to go on a date :) but any way i am gonna add a math question to this
what is 1284×342÷9×62×4÷98×2÷106?
Answer:
2329.69 is the answer......
give me a brainliest
(show ur work) You spend $40 on 5 pounds of concrete. What is the unit rate in dollars per pound?
answer choices
$8 per pound
$35 per pound
$5 per pound
$0.125 per pound
Answer:
8 dollars per pound
Step-by-step explanation:
40 divided by 5 will give you the $/lb
40/5=8 so its $8/lb
Give correct answer with good explanation. Please and thank you very much
Answer:
Step-by-step explanation:
V = B×H ⇒ H = V ÷ B
H = 729 ÷ 108 = 6.75 inches
Answer:
h = 6.75 inches
Step-by-step explanation:
The volume (V) of a prism is calculated as
V = Ah ( A is the area of the base and h the height )
here V = 729 and A = 108 , then
108h = 729 ( divide both sides by 108 )
h = 6.75 inches
UREGENT!!!! HELP NEEDED !!! QUICKLY!!! FAST!!!!
You spend a $20 per turn on a fair game to win $40 for each win. You win the first two rounds and lose the third one.
What was the net payoff?
$20
$120
-$60
$140
Answer:
I think 20 is the answer tho I might be wrong
A circle has a diameter with endpoints at -2 + i and -6 -11i. What is the center of the circle?
O-8-10i
O -4 – 5i
O -2- 6i
O 2 +i
Answer:
- 4 - 5i
Step-by-step explanation:
The centre of the circle is the average of the endpoints
centre = (- 2 + i - 6 - 11i ) ÷ 2
= (- 8 - 10i ) ÷ 2
= - 4 - 5i
Find the volume - PLSS HELPP AND HURRY PLS
Answer:
264
Step-by-step explanation:
(11 x 6)/2 x 8 = 264
B x h = V
Aashna thinks that the largest place value that 82.3 and 11.45 have in common is the tens place. Jake thinks that the largest place value they have in common is the tenths place.
Answer the following questions with complete sentences:
Who is correct, Aashna or Jake?
Write how you would explain your answer to the person who answered incorrectly.
Answer:
Aashna is correct
Step-by-step explanation:
I would explain it that the tens places are 8 and 1, which are about 7 apart
The tens places however are 3 and 4 which is closer.
Determine the equation of the line shown in the graph:
10
-8 -6 -4 -2.
-
I
y = -1
y = 0
Ox=-1
X=0
Answer:
X=-1
Step-by-step explanation:
As you can see the line is not intercepting at y also