for any positive integer n, the sum of the first n positive integers equals n(n 1)/2. what is the sum of all the even integers between 99 and 301 ?

Answers

Answer 1

The sum of all the even integers between 99 and 301 is 20200

To find the sum of even integers between 99 and 301, we will use the arithmetic progressions(AP). The even numbers can be considered as an AP with common difference 2.

In this case, the first even integer will be 100 and the last even integer will be 300.

nth term of the AP = first term + (n-1) x common difference

               ⇒    300 = 100 + (n-1) x 2

Therefore, n = (200 + 2 )/2 = 101

That is, there are 101 even integers between 99 and 301.

Sum of the 'n' terms in an AP = n/2 ( first term + last term)

                                                = 101/2 (300+100)

                                                = 20200

Thus sum of all the even integers between 99 and 301 = 20200

Learn more about arithmetic progressions at https://brainly.com/question/24592110

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Related Questions

Which expression is equal to
[tex]\frac{7}{8}[/tex]?
A.7 divided by 8
B.8x7
C.8 divided by 7
D. 7x8

Answers

Answer: A

Step by step explanation:

Which expression is equivalent to x^2-17 x-60?​

Answers

Answer: (x+3) (x-20)

Step-by-step explanation:

Anybody have unwanted pets in adopt me? my only pet isn't for trade​

Answers

Tip: Try taking care of, that pet and make more money to buy eggs to trade or hatch and thats an easy way to get rich if you don't have robux

Step-by-step explanation:

No, sorry. But I have a tip/hack for everyone! (I don't know if it still works)! Get 3 cracked eggs, and 1 royal egg... take care of them all until their last need. Hatch your cracked eggs first, THEN the royal egg last ... there should be a legendary in the royale egg! I tried this two times and I got a legendary each time! <3

Which fraction can be a terminating decimal? 2/9, 1/3, 1/7, 7/8

Answers

Answer:

Hi! I think the answer is 7/8.

Step-by-step explanation:

divide 7 by 8 longhand. I can't duplicate this but the answer is 875. It does not repeat it terminates. Hope this makes sense! Happy Holidays! (and hope this is correct.)

What is the frequency of (x) = 4 sin(6 π x) +1

Answers

Answer:

Frequency is 3

Step-by-step explanation:

A sine function repeats in periods and it's frequency can be gotten using:

y(x) = sin(2πfx) where f is the frequency

We are given x = 4sin(6πx) + 1

This can be rewritten as: x = 4sin(3*2πx) + 1

Therefore, our f = 3.

Hence frequency of the sine function is 3.

Can someone explain?

Answers

87
Because the ratio is 3:7
So we plug in 203 for 7
3:7=?:203
7 goes into 203 29 times
29*3 is
87
it is 87! you put 7 into 203 29 times :))

Luke rides his bike to his aunt's house. He travels 10 mi/h. Because it starts to rain, Luke's aunt drives him home in a car traveling at 25 mi/h. It takes Luke 1.5 h longer to get to his aunt's house than to return home. How many hours did it take Luke to ride to his aunt's house?

Answers

Answer:

2.5 hours

Step-by-step explanation:

Let t = time in hours for reach friend's house

(t-1.5) = time for friend to drive her home

:

Both trips are the same distance, Write a distance equation from this fact:

Distance = speed * time

Drive distance = Bike distance

Equation-

step1)   25 (t-1.5) = 10t          (here u multiply 25 by t and 25 by 1.5)

step2)  25t - 37.5 = 10t        (move 37.5)          

step3)  25t - 10t = +37.5      (subtract 25t from 10t)

step4)  15t = 37.5                 (divide 37.5 by 15)

step5)  t = 2.5                     (time it took Luke to reach his aunt's house)

How long will it take for a debt to double at 42% p.a. compound interest?

Answers

According to the given statement ,

a debt to double at 42% p.a. compound interest will take approx 2 years.

What is compound interest ?

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

Compound interest is calculated on the initial principal of a deposit or loan, which also takes into account all of the accumulated interest from prior periods.

The yearly interest rate is raised to the number of compound periods minus one, and the starting principal amount is multiplied by both of these factors.

According to the given data,

Let principal = P

Time = t

Rate == 42%

Amount = A

Given Condition is A = 2P

=> P[1+ r/100]ⁿ =  2P

=> P [1 + 42/100 ]ⁿ = 2P

=> (1.42)ⁿ=2

n= log₁.₄₂ 2 =0.301/0.152

n=1.980≅2

Hence , the time it take for a debt to double at 42% p.a. compound interest is approx 2 years.

To know more about compound interest, visit

https://brainly.com/question/14295570

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The graph above shows the costs of two phone plans. How many minutes does a person need to call each month so that Plan B is the less expensive plan to use?

A. Less than 10 minutes

B. More than 10 minutes but less than 20 minutes

C. More than 30 minutes but less than 40

D. More than 40 minutes

Answers

Answer:

uhm, i need this answer also

Step-by-step explanation:

did you ever get the answer ? if so could you be kind enough to give it to me pleasee

PLZ ANSWER AS SOON AS POSSIBLE!!

A lampshade needs to be rotated 75 degrees to fit snugly on its base. It has been rotated 40 degrees as shown.

How many more degrees does the lampshade need to be rotated?

Answers

your answer would be 35 degrees

4x + 3z for x=7 and z=2​

Answers

The answer is 36!!! Hope it helps

Answer:

34

Step-by-step explanation:

plug 7 into 4x

plug 2 into 3z

do the math so...

4 X 7 =28

2 X 3 = 6

add 28 + 6 = 34

I need the answer to 26. And 27. Please

Answers

Answer:

Below in bold.

Step-by-step explanation:

26.

First convert each mixed number to an improper fraction:

-12 2/3 = -38/3

- 1 1/9 = -10/9

-38/3 = -10/9 * y

y = -38/3 / -10/9

y = -38/3 * -9/10

  = -38 * -3 / 10

  = 114/10

  = 57/5

  = 11 2/5.

27,

1 5/7 = 1 13/14 a

12/7 = 27/14 a

a = 12/7 / 27/14

  =  12/7 * 14/27

  = 24/27

  = 8/9.

 

800,000,000,000 + 20,000,000,000 + 3,000,000,000 + 50,000,000 + 4,000,000 + 600,000 + 50,000 + 8,000 + 700 + 80 + 6

Write the standard form of the number shown above.

Answers

Answer:

823,546,580,786

Step-by-step explanation:

If you look at the place values, that will help you determine the standard form. Hope this helps!

If you anwser CORRECTLY you will be brainlest thanked and 5 starred if it is wrong you will be giving a warning and reported with a 1 star. Get it correct!

Answers

Answer:

um what is the question?

whats the question??

What is the value of y?
88

need help

Answers

Answer:

The answer to your question is 44 degrees.  

Step-by-step explanation:

find equation of the line PLEASE HELP!

Answers

Answer:

y=1/2x-3

Step-by-step explanation:

Hope this helps :) Have a great day!!!

The answer is 0.5x-3=y

PLEASE I NEED DESPERATE HELP

Answers

OK ILL HELP U I PROMISE

Graph a line that contains the point (6,-4)and has a slope of -2/3

Answers

Answer:

Graph (6,-5) then graph (3,-3)

Step-by-step explanation:

Picture is help

slope of (-2,-5) (-1,-6)​

Answers

Answer:

your slope will be -1

Step-by-step explanation:

if you do y-y and x-x you then divide those answers  and you will end up with m=-1

the dimensions of a rectangular plot of land are 28.3m by 53.7m. Find
1) the perimeter of the land, correct to the nearest 10
2) the area of grass needed to fill up the entire plot of land, correct to the nearest 100m^2


also show the steps​

Answers

Answer:

1. Answer is 160 m

2. Answer is 1500 m²

Step-by-step explanation:

perimeter = 2(l+b)

which implies 2( 28.3 + 53.7) m = 160 m

Area is length× breadth

which implies 28.3× 53.7 = 1500 m²

Please mark me brainliest

What is the value of the function for x = 2?

Answers

Answer:

To make this easier, first draw or imagine a vertical line at x=2Find where the vertical line and the graph intersects.Draw or imagine that point

Find the equation of the line.
y=__x+__​

Answers

y = 4x - 9 is the equation of the line.

Answer:

y=4x-9

Step-by-step explanation:

The equation of a line is typically written in slope-intercept form, which is y=mx+b. Here's what the variables mean:

y=the y-coordinate

m=the slope

x=the x-coordinate

b=the y-intercept (the point on the line that intercepts the y-axis)

The only values that we have to calculate to find the equation are the slope of the line and the y-intercept. Let's start off by finding the slope.

To find the slope of a line, we would need to find 2 points that fall on the line, [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] and plug them into the expression [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. Let's use the points (1, -5) and (3, 3).

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\frac{3-(-5)}{3-1}[/tex]

[tex]=\frac{3+5}{3-1}\\= \frac{8}{2}\\= 4[/tex]

Therefore, the slope of the line is 4.

To find the y-intercept, all we need to do is look at which point the line crosses the y-axis, and that point is -9.

Finally, we plug the slope and the y-axis into the equation y=mx+b as m and b.

y=mx+b

y=4x-9

I hope this helps!

a student earned a grade of 80% on a math test that had 20 problems how many problems on this test did the student answer correctly

Answers

Answer:

16

Step-by-step explanation:

To find 80% of 20, multiply .80 x 20

.80×20 = 16

This is how you multiply percentages--put the decimal point 2 places to the left, then multiply.  In this case, you're looking at 80%, so move the decimal point two places to the left

80.0 becomes .80

Then multiply that by the number you're trying to find the percentage of

What is the range of the graphed function?
{x |1< x < 5)
{y |1 < y <5}
{x | x is a real number}
{y|y is a real number}

Answers

Answer:

Please check the explanation.

Step-by-step explanation:

Given the expression

[tex]V=\sqrt[3]{x-1}+3[/tex]

Determining the domain:

We know that the domain of a function is the set of input values for which the function is defined.

From the given graph, it is clear that the function has no undefined points nor domain constraints.

Therefore, the domain is:

{x | x is a real number}

In other words:

[tex]\mathrm{Domain\:of\:}\:\sqrt[3]{x-1}+3\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]

Determining the range:

We know that the range of a function is the set of values of the dependent variable for which a function is defined.

It is clear from the graph that the range can be any real number.

i.e. the range is:

{y|y is a real number}

In other words,

[tex]\mathrm{Range\:of\:}\sqrt[3]{x-1}+3:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<f\left(x\right)<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]



8x + 3y = 13

3.x + 2y = 11

Answers

Answer:

what it means ,if there is already ans

Tropical Storm Zeta will bring 0.36 in. of rain to New Orleans. Which fraction is equivalent to this amount of rain in inches?

Answers

Answer:

36/100

Step-by-step explanation:

Solve this equation 2/3 x - = x - 1

Answers

Answer:

X=1/7

Step-by-step explanation:

help pls Ix would really appreciate

Answers

Answer:

B

Step-by-step explanation:

g(2)=-7 because -(2)-5=-7

f(-7)=-18 because 2(-7)-4=-18

Simplify the following expression: (12x – 7) + (7x + 9)
A) 19x – 2
B) 5x+ 16
C) 5x – 16
D) 19x + 2

Answers

Answer:

D.

Step-by-step explanation:

12x + 7x = 19x

-7 + +9 = 2

Answer:

d

Step-by-step explanation:

please help I need to get school work done before 3​

Answers

1-distributed property
2.Multiplication
3.addition
4.Divison
5.Sum
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