1+3+5+7+...+25 is subtracted from 2+4+6+8+...+26. The answer is​

Answers

Answer 1

[tex]S_1 = 2+4+6+8+...+26 \\\\~~~~=2(1+2+3+4+...+13)\\\\~~~~=2 \cdot \dfrac{13(13+1)}2~~~~~~~~;\left[\text{Sum of consecutive positive integers }= \dfrac{n(n+1)}2 \right] \\\\~~~~=13 \cdot 14\\\\~~~~=182\\\\S_2 = 1+3+5+7+...+25\\\\\text{It is an arithmetic series wihere}\\\\\text{First term, a =1, ~Common difference, d = 2,~ number of terms = n} \\\\~~~~\text{Nth term} = a+(n-1)d\\\\\implies 25 = 1+(n-1)2\\\\\implies 2n-2 = 24\\\\\implies 2n = 24+2\\\\\implies 2n= 26\\\\[/tex]

[tex]\implies n = \dfrac{26}2 \\\\\implies n= 13\\\\\text{S} _2= \dfrac{\text{n(First term+ Last term)}}{2}\\\\~~~~~~=\dfrac{13(1+25)}2\\\\~~~~~~=\dfrac{13 \times 26}2\\\\~~~~~~=13 \times 13\\\\~~~~~~=169\\\\\text{Hence,}~~ S_1 - S_2 =182 - 169 =13[/tex]

Answer 2

Answer:

13

Step-by-step explanation:

2 + 4 + 6 + 8 + ...... + 26

n = 13

Sum of first 'n' even numbers = n( n +1)

                                                 = 13 * 14

                                                  = 182

1 + 3 + 5 + 7 + .....+25

n = 13

Sum of first 'n' odd numbers = n²

                                               = 13 * 13

                                               = 169

2 + 4 + 6 + 8 + ... + 26 - (1 + 3 + 5 + 7 + ......+25) = 182 - 169

                                                                            = 13


Related Questions

Which of the following is the difference of two squares? 16a^2-9b^6 4g-16h 25m^2+100n^2 2x^2-4y^2

Answers

Answer:

16a^2 - 9b^6

Step-by-step explanation:

16a^2 - 9b^6   ---> 16a² is the square of 4a; 9b^6 is the square of 3b³

This is the difference of 2 squares

4g - 16h --->  4g and 16h are not perfect squares.

 

25m^2 + 100n^2 ---> this is a sum of squares, not a difference of squares  

2x^2 - 4y^2 ---> 2x² is not a perfect square

Answer: 16a^2 - 9b^6

What is the solution to the equation 2(×+2. 4)=6. 4

Answers

Answer:

0.8

Step-by-step explanation:

2x + 4.8 = 6.4

2x = 6.4 - 4.8

2x = 1.6

x = 0.8

Answer:

x = 0.8

Step-by-step explanation:

In the question we're given with an equation that is 2 ( x + 2.4 ) = 6.4 . And we're asked to find the solution of the equation that means we have to find the value of x .

Solution : -

[tex] \longmapsto \: 2(x + 2.4) = 6.4[/tex]

Step 1 : Removing parenthesis by multiplying 2 with x and 2.4 :

[tex] \longmapsto \: 2x + 4.8 = 6.4[/tex]

Step 2 : Subtracting 4.8 on both sides :

[tex] \longmapsto \: 2x + \cancel{4.8} - \cancel{4.8 }= 6.4 - 4.8[/tex]

On further calculations :

[tex] \longmapsto \:2x = 1.6[/tex]

Step 3 : Dividing by 2 on both sides :

[tex] \longmapsto \: \frac{ \cancel{2}x}{ \cancel{2 }} = \frac{1.6}{2} [/tex]

Calculating further :

Here , we have removed decimal from 1.6 . So it'll become 16 and 10 it'll divided by 10

[tex] \longmapsto \:x = \cancel { \frac{16}{2}} \times \frac{1}{10} [/tex]

Step 4 : Cancelling 16 by 2 :

[tex] \longmapsto \:x = \frac{8}{10} [/tex]

[tex] \longmapsto \: \green{\underline{ \green {\boxed{x = 0.8}}}}[/tex]

Therefore value of x is 0.8 .

Verifying : -

We are verifying our answer by substituting value of x in given equation. So ,

2 ( x + 2.4 ) = 6.4

2 ( 0.8 + 2.4 ) = 6.4

2 ( 3.2 ) = 6.4

6.4 = 6.4

L.H.S = R.H.S

Hence, Verified .

Therefore, our value for x is correct .

#Keep Learning

The distance by rail from Leicester to Londonis 100 miles.


Assume that the train travels at an average speed of 80 mph.


Calculate the arrival time in London of a train that leaves Leicester at 11:50 a. M.


Input note: write your answer in 24 hour clock mode

Answers

The arrival time in london of a train that leaves Leicester to london at 11:50 A.M is 13:05 pm.

To calculate the arrival time in london of a train that leaves Leicester to london at 11:50 A.M, use use the formula below.

Formula:

Ta = [(d/s)+11:50]....... Equation 1

Where:

Ta = Arrival timed = distance from Leicester to Londons = Speed

From the question,

Given:

d = 100 miless = 80 mph

Substitute these values into equation 1

Ta = [(100/80)+11:50]Ta = 1.25h+11:50Ta = 1 hours 15 minutes +11:50Ta = 13:05 pm

Hence, the arrival time in london of a train that leaves Leicester to london at 11:50 A.M is 13:05 pm.

Learn more about time here: https://brainly.com/question/4931057

When f(x) = –3, what is x?

–29
–10
–3
–1

Answers

Answer:

x = - 1

Step-by-step explanation:

I hope this will help you

Math question about geometry. (will give brainliest to whoever answers correctly with an explanation)

Answers

Answer:

72 cm³

Step-by-step explanation:

The formula to find the volume of a trianglular based pyramid is [tex]V=\frac{1}{3}bh[/tex], where V is the volume, b is the area of the vase, and h is the vertical heightSubstitute in the values[tex]V=\frac{1}{3}\times (\frac{1}{2}\times 12\times 4)\times 9 = \frac{1}{3}\times 48\times 9 = \frac{1}{2}\times 48\times 3 = 72[/tex]

6.
April sold 85 tickets to a school play
and collected a total of $495. If adult tickets cost $10 each and child
tickets cost $5 each, how many adult tickets and how many child tickets did she sell?

Answers

Answer:

adult tickets =14

child tickets =71

Step-by-step explanation:

x is adult tickets

y is child tickets

x+y=85

10x+5y=495

y=85-x

2x+y=99

2x+(85-x)=99

x=99-85=14

y=85-x=85-14=71

Can any one answer this correctly?

Answers

Answer:

A

Step-by-step explanation:

The Y-intercept is -3.

The gradient is -3/4 since it goes down 3 every 4 tiles.

Answer:

[tex]y=-\frac{3}{4}x -3[/tex]

Step-by-step explanation:

Hey there!

We can form this equation in slope-intercept form

This means, we have to find the slope and the y intercept of the line

First lets find the slope

The equation for slope is [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

In order to find y and x, we need to take two points on the line

(-4, 0) and (0, -3)

x1   y1        x2  y2

Plug it in:

[tex]\frac{-3-0}{0-(-4)} \\\\\frac{-3}{4} \\\\-\frac{3}{4}[/tex]

This means, the slope is -3/4

Now we have to find the y-intercept

The y-intercept is where the line intercepts the y-axis

The line intercepts the y-axis at the point (0, -3)

So now that we have the slope and the y-intercept, we can form the equation

[tex]y=-\frac{3}{4}x-3[/tex]

50 POINTS PLEASE ANSWER ASAP
What is the diameter of a circle whose circumference is 5?

Answers

Answer:

[tex]4)\ = \frac{5}{\pi}[/tex]

Step-by-step explanation:

Formula:________________

circumference = Diameter × π

_______________________

Then

5 = Diameter × π

Then

[tex]Diameter \ = \frac{5}{\pi}[/tex]

100 Points and Brainly.

Write an Equation

Based on the information write an equation that represents the relationship between the time you spent doing the activity and the amount of the activity you completed. Make sure to define your variables.

This is my data
-------------------------------------------------------------------------
3. I did the activity 105 Times in a minute and a half

4. The Dependent Variable is 105

5. The Independent Variable is 1 minute.

-------------------------------------------------------------------------

Answers

Answer:

See below

Step-by-step explanation:

Feel free to be creative or even to come up with an activity you think your teacher has not seen before.

Liked that. So let's be creative.

Part 1: Record Information

Spend a short amount of time (one to five minutes) doing your activity. Answer the following questions:

1. What was the activity?

I am from Japan and practice Kendo (feel free to search about it). Suppose you are doing suburi. You did 100 joge suburi.

2. How long did you spend doing your activity?

Suppose it took you 5 minutes.

3. How much of the activity did you complete in the time period? (Example: I did 24 sit-ups in one minute.)

You did 100 joge suburi in 5 minutes. It means [tex]\frac{100}{5} =20[/tex] [tex]per[/tex] [tex]minute[/tex]

4. Which of these variables is your dependent variable?

If you want to calculate how much suburi you did in an amount of time , given the time in minutes, we can write the function

[tex]y=f(x)=20x[/tex]

Therefore, the dependent variable is the number of suburis. More precisely it is given by [tex]y[/tex]. On the other hand, the independent variable is [tex]x[/tex], the time.

Considering the example: I did 24 sit-ups in one minute.

sit-ups is the dependent variable and the number of minutes represents the independent variable.

Note: The number of sit-ups will depend on the time. 24 is the coefficient. In this case, the function would be

[tex]g(x)=24x[/tex]

5. Which one is the independent variable?

The time in minutes.

6. Write a sentence that describes the relationship between the dependent variable and the independent variable. (Hint: Ratio language can help.)

You can write: The ratio of suburi done is 100:5 or 20:1 because for every 1 minute passed you did 20 suburis.  

Part 2: Prepare a Table

Assuming that you could complete the activity at the same rate over different time periods, how much of the activity could you complete in two minutes, three minutes, four minutes, and five minutes? (Note: If you spent two minutes doing your activity, then you should edit the table below and use multiples of 2 up to 10).

You may use the table below for your variables.

Time (minutes)          Quantity of suburi

0                                         0

1                                          20

2                                         40

3                                         60

4                                          80

5                                         100

Part 3: Prepare a Graph

Create a graph to show your relationship. Make sure you include all the parts for a graph and show the data clearly. Include a title for the graph and label the x- and y-axes.

This part I will let it to your. But is is just a linear graph.

Part 4: Write an Equation

Based on your recorded values, write an equation that represents the relationship between the time you spent doing the activity and the amount of the activity you completed. Make sure to define your variables.

[tex]y=f(x)=20x,[/tex] ∀[tex]x[/tex] ∈ [tex]Z[/tex][tex]\geq_0[/tex]

[tex]y:[/tex] [tex]number[/tex] [tex]of[/tex] [tex]suburis[/tex]

[tex]x:[/tex] [tex]time[/tex]

7. If you were able to maintain this rate of your activity for 12 minutes, how much of the activity would you be able to complete?

For [tex]x=12[/tex]: [tex]y=f(12)=20*12=240[/tex]

240 suburis

8. How long would it take you to reach 100 for the number of times you did your activity?

5 minutes.

9. Which representation do you believe is the best way to share this information with someone else? This is your opinion. No answer is right or wrong.

The function is the best because it describes all the variables easily.

What is the exact circumference of a circle with a diameter of 18
inches?

Answers

Answer:

18 pi inches

Step-by-step explanation:

Circ of circle = pi * d

                      = 18 pi      exactly

                     

please help youll get brainliest

Answers

Answer:

B) f(x) = 2/5㏒(x) + 2

Step-by-step explanation:

Given graph

f(x) = ㏒₂ x

Changes

Transformed up by 2 unitsvertically compressed by factor of 0.4

Solving

Shifted up by 2 units

f(x) = ㏒₂ (x) + 2

Vertically compressed by factor of 0.4

f(x) = 2/5㏒(x) + 2

Please help! Please break down what equation or process I need to do to get the answer as well :/

Answers

Check the picture below.

A 2-gallon container of window cleaner costs $13.20. What is the price per quart?

Answers

Answer: 1.65

4 quarts are in one gallon
2gallons = 8 quarts

13.20/8= 1.65 :)
Hope this helps <4

Answer:

$ 1.65 per gallon

Step-by-step explanation:

4 quarts in 1 gallon so 8 quarts in 2 gallons.

Cost for 2 gallons $13.20 so $13.20 ÷ 8 =  $1.65

Which triangle would be most helpful in finding the distance between the points (-4,3) and (1, -2) on the coordinate
plane?

Answers

Answer:

Right Triangle, the distance between these two coordinates is 5.83 in whatever unit you're measuring.

Step-by-step explanation:

Generally when you're using triangles to find the distance between two graphed points, you're using a right triangle.

[tex]9 + 25 = 34\\\sqrt{34}=5.83[/tex]The reason behind that being you can draw lines on the x and y axis of these points and find where they connect. After doing so, you can directly connect the two points and create a right triangle.

To find the distance between the two points using a right triangle, we can use the formula for the hypotenuse: [tex]a^2 + b^2=c^2[/tex]

A and B is the distance between the point and where the lines you've drawn intersect. C is the resulting distance between the two points.

Plugging in A and B, which is 3 and 5, we can find C. 3 squared is 9 and 5 squared is 25.

[tex]3^2 + 5^2 = 9 + 25[/tex]

Now we add the two and find the square root.

[tex]9+25=34\\\sqrt{34} =5.83[/tex]

Your answer is 5.83

Can somebody help me please!

Answers

Answer:

Less than

Step-by-step explanation:

1/3 * 7/15 is less than 1/3 because 1/3 * 7/15 is being multiplied by a number that is less than 1.

Cylinder A has a radius of 7 inches and a height of 5 inches. cylinder B has a volume of 490 pi. What is the percentage change in volume from cylinder A to cylinder B

Answers

Units of volume : in^3

Volume of Cylinder A
pi(r^2)(h) = (pi) (49) (5) = 245pi

Volume of Cylinder B
490pi

490pi = 2(245pi)
So the percentage change in volume is 200%

Which inequality is represented by this graph? A. B. C. D.

Answers

The correct answer is C. This is because the shaded part, the y, is less than the line, so it would be <, but the line is not dotted, so then it would be less than or equal to.

Which of the following statements is true about the three quadrilaterals?

A and B are similar but not congruent.
A and C are similar but not congruent.
A and B are similar and also congruent.
B and C are similar and also congruent.

Answers

hii the answer is
A and B are similar but not congruent
I think it should be right

Find the value of x (show all work on paper):
Adj: 48
Hyp: 50

A:42
B:10
C:14
D:70

Answers

Answer:

16.260 (3 d.p.)

Step-by-step explanation:

Use SOHCAHTOASince you have the adj and hyp, use CAHcos(x) = adj / hyp = 48 / 50x = cos-1(48/50) [What i mean by cos-1 is the inverse of cosine. You can find this by pressing shift + cos on most calculators)This gives you 16.260 (to 3 d.p.)

write 701.3% as a whole number or mixed number in simplest form

Answers

7013/10

Step-by-step explanation:

first, count the decimal to the right

as you can tell, we can only do it once so therefore we get 10

we then multiply 701.3/1 both sides with 10

then we get out answer 7013/10

Can someone teach me how do this! Please and thanks!

Answers

Check the picture below.

4x+3y=9 and 3x +4y = 36

Answers

The solution of the system of equations:

( -16.7, 19.28)

How to solve the system of equations?

Here we have the system:

4x+3y=9

3x +4y = 36

First, we need to isolate one of the variables in one of the equations, let's isolate x on the second one:

x = 36/3 - (4/3)y = 9 - (4/3)y

Now we can replace this in the other equation:

4*(9 - (4/3)y) + 3y = 9

36 - (16/3)y + (9/3)y = 9

- (7/3)y = -36 - 9 = -45

y = (3/7)*45 = 19.28

To get the value of x, we get:

x = 9 - (4/3)*19.28 = -16.7

Then the solution of the system is ( -16.7, 19.28)

If you want to learn about systems of equations:

https://brainly.com/question/13729904

#SPJ1

Tyson's baby brother weighed 7 pounds, 3 ounces when he was born. The baby lost 9 ounces after a few days and then gained 1 pound, 6 ounces by the end of the week. How much did the baby weight at the end of the week?


1 pound = 16 ounces


Solution:______ pounds or ounces

Answers

8 pounds because i say so

What is the probability of rolling a dice and rolling a 5, then rolling it again and rolling an 6?

Answers

Answer:

1/6

Step-by-step explanation: Im going to guess the dice has 6 sides, rolling any number on that 1 dice would be a 1/6 chance. I hope this helps!

In one-half hour, a car traveled 20 km. Find the average velocity in km/min. (Round to the nearest
hundredth)

Answers

Step-by-step explanation:

[tex]s = 20km \\ t = 30min[/tex]

[tex]v = \frac{s}{t} \\ v = \frac{2}{3} [/tex]

[tex]v = 0.67[/tex]

[tex]v = 0[/tex]

A microwave raises the temperature of water by about 90 F in 5 minutes . Which graph has the slope that represents this rate of increase

Answers

Answer:

B.

Step-by-step explanation:

Look at all graphs and find 90 deg on the left side. Follow it to the right until you intersect the graph. then go straight down. You must intersect the x-axis is 5 minutes. The only graph that does this is B.

Answer: B.

I think the answer is B because here's the explenation.

144=(n+1)^2 this equation should have 2 answers

Answers

Answer:

(12)^2=(n+1)^2

12=n+1

12-1=n

n=11

Step-by-step explanation:

another one

(12)^2-(n+1)^2=0

(12-n-1)(12+n+1)=0

either:-

n=11 or n=-13

[tex]~~~(n+1)^2 =144\\\\\implies n+1= \pm\sqrt{144}\\\\\implies n+1 = \pm12\\\\\implies n = \pm12 -1\\\\\text{Hence,}~ n = 11 ~\text{and}~ n = -13[/tex]

need help on this question

Answers

Answer: 4

Step-by-step explanation:

Select the correct answer from each drop-down menu. betty picks 4 random marbles from a bowl containing 3 white, 4 yellow, and 5 blue marbles. the probability that exactly 1 of the 4 marbles drawn is blue is . the probability that at least 1 of the 4 marbles drawn is white is .

Answers

The probability of exactly 1 of the 4 marbles drawn being blue and at least 1 of the 4 marbles drawn being white will be 0.3535 and 0.7454 respectively.

What is probability?

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Betty picks 4 random marbles from a bowl containing 3 white, 4 yellow, and 5 blue marbles.

The total number of the marbles will be

Total marble = 3 + 4 + 5

Total marble = 12

Then the probability of exactly 1 of the 4 marbles drawn being blue will be

[tex]\rm P(B) = \dfrac{^5C_1 \times ^7C_3}{^{12}C_4}\\\\P(B) = \dfrac{35}{99} = 0.353535[/tex]

Then the probability of at least 1 of the 4 marbles drawn being white will be

[tex]\rm P(W) = \dfrac{^{3}C_1\times \ ^{9}C_3}{^{12}C_4} + \dfrac{^{3}C_2\times \ ^{9}C_2}{^{12}C_4} + \dfrac{^{3}C_3\times \ ^{9}C_1}{^{12}C_4} \\\\\\P(W) = \dfrac{252}{495} + \dfrac{108}{495} + \dfrac{9}{495}\\\\\\P(W) = \dfrac{369}{495}\\\\\\P(W) = 0.745454[/tex]

More about the probability link is given below.

https://brainly.com/question/795909

Answer:

A. 0.3535.

B. 0.7455.

Step-by-step explanation:

The probability that exactly 1 of the 4 marbles drawn is blue is 0.3535. The probability that at least 1 of the 4 marbles drawn is white is 0.7455.

Solve |d + 4| > 10
a.d<-14
b. d> 6
c. -14 < d<6
d. d<-14 or d > 6

Answers

Answer:

b. d > 6

Step-by-step explanation:

Answer:

D. d<-14 or d>6

Step-by-step explanation:

To solve for d, isolate it on one side of the equation.

|d+4|>10

d+4<-10 or d+4>10

1. d+4<-10

First, you have to subtract by 4 from both sides.

[tex]\sf{d+4-4 < -10-4}[/tex]

Solve.

Add or subtract the numbers from left to right.

-10-4=-14

[tex]\Longrightarrow: \boxed{\sf{{d < -14}}}[/tex]

2. d+4>10

Subtract by 4 from both sides.

[tex]\sf{d+4-4 > 10-4}[/tex]

Solve.

Subtract the numbers from left to right.

10-4=6

[tex]\Longrightarrow: \boxed{\sf{d > 6}}[/tex]

Therefore, the correct answer is "D. d<-14 or d>6".

I hope this helps. Let me know if you have any questions.

Other Questions
Henry is researching the elephant exhibit at his town's zoo.Which of the following is a statistical question Henry could ask?A.When was the zoo opened?B.What was the name of the first elephant in the exhibit?C.What is the average weight of the adult elephants in the exhibit?D.How many elephants are in the exhibit? The controller of Mercury Shoes Inc. instructs you to prepare a monthly cash budget for the next three months. You are presented with the following budget information: June July AugustSales $160,000 $185,000 $200,000 Manufacturing costs 66,000 82,000 105,000 Selling and administrative expenses 40,000 46,000 51,000 Capital expenditures _ _ 120,000 The company expects to sell about 10% of its merchandise for cash. Of sales on account, 60% are expected to be collected in the month following the sale and the remainder the following month (second month after sale). Depreciation, insurance, and property tax expense represent $12,000 of the estimated monthly manufacturing costs. The annual insurance premium is paid in February, and the annual property taxes are paid in November. Of the remainder of the manufacturing costs, 80% are expected to be paid in the month in which they are incurred and the balance in the following month.Current assets as of June 1 include cash of $42,000, marketable securities of $25,000, and accounts receivable of $198,000 ($150,000 from May sales and $48,000 from April sales). Sales on account in April and May were $120,000 and $150,000, respectively. Current liabilities as of June 1 include $13,000 of accounts payable incurred in May for manufacturing costs. All selling and administrative expenses are paid in cash in the period they are incurred. An estimated income tax payment of $24,000 will be made in July. Mercury Shoes' regular quarterly dividend of $15,000 is expected to be declared in July and paid in August. Management desires to maintain a minimum cash balance of $40,000.Required:Question Content Area1. Prepare a monthly cash budget and supporting schedules for June, July, and August. The best determination of a communitys quality of life is _______. a. the per capita income b. the climate and weather c. the energy used per capita d. its geographic location PLS HELPSelect all of the pairs of expressions that are equivalent.A c + d + c + d and 2(c + d) B 4y + 3y - x and -x + 7y C 2(3n + 4m) and 6n + 4m D 8p - 5r and 5r - 8p E 4j + 6k and 2(2j + 3k) 3 examples of unalienable rights what does foil mean please help me this is do tomorrow Annabelle and Navene are multiplying (4275)(4372). Annabelle's Work Navene's Work(4275)(4372) = 42 + 375 + 2 = 4577 (4275)(4372) = 423752 = 46710Is either of them correct? Explain your reasoning Government regulations that prevent a firm from dumping toxic waste into a river address which type of market failure?. What is the sum? 3 5/x-9x+3 Species that have a narrow range of conditions they can live within are consideredO speciesO invasiveO specialistsO generalists can someone make a song i need it until friday it can be english or tagalog hi, um whats 33 divided by 548 whith an remainder ? but no decimal A taxi ride costs $3 plus $2.50 per mile. Write and graph an equation in two variables that represents the total cost of a taxi ride. Let m represent number of miles and represent the total cost (in dollars) of the taxi ride.Equation: c= An area of 3.5m is the same as 350000mm. True or false. Justify your answer The network security team of a company wants to reduce the system attack surface to limit the ways an attacker can connect to the network. How can the team achieve this to harden the network Why was the potato easier to balance on the ruler when the forks were added Jane paid for her dinner with a $50 bill. Her bill was $38.63. How much change should she receive? simplify Squrareroot -50 The question is in the photo A loan has an APR of 8%. The maximum that Steve can pay back monthly on a loan is $129.60. He wants the loan for 1 year.