What is the sum of the series *picture attached*

What Is The Sum Of The Series *picture Attached*

Answers

Answer 1

Answer:

[tex]\sum_{n=4}^{18}(n+1)^2=2440[/tex]

Step-by-step explanation:

Series: [tex]\sum_{n=4}^{18} (n+1)^2[/tex]

Formula :[tex]\sum_{k=m}^n=\sum_{k=1}^n-\sum_{k=1}^{m-1}[/tex]

[tex]\Rightarrow \sum_{n=4}^{18}(n+1)^2=\sum_{n=1}^{18}(n+1)^2-\sum_{n=1}^{3}(n+1)^2[/tex]

[tex]\sum_{n=1}^{18}(n+1)^2=2469[/tex]

[tex]\sum_{n=1}^{3}(n+1)^2=29[/tex]

[tex]\Rightarrow \sum_{n=4}^{18}(n+1)^2=2469-29[/tex]

[tex]\Rightarrow \sum_{n=4}^{18}(n+1)^2=2440[/tex]

So, Option C is true


Related Questions

The owner of a minor league baseball team has found that when he charges an average of $13.00 per seat, the average attendance is 810 fans per game. He noticed that for every $2.00 increase in average ticket price, the attendance decreased by an average of 27 fans per game. Which equation shows the revenue, R, as a function of d, the number of $2.00 increases over $13.00? A. R(d) = -54d2 + 1,269d + 10,530 B. R(d) = -54d2 - 1,269d - 10,530 C. R(d) = 54d2 + 1,269d D. R(d) = 27d2 + 459d + 10,530

Answers

Answer:

The correct answer is A. R(d) = -54d2 + 1,269d + 10,530

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Price per seat when the average attendance is 810 fans = $ 13

For every $2.00 increase in average ticket price, the attendance decreased by an average of 27 fans per game.

2.  Which equation shows the revenue, R, as a function of d, the number of $2.00 increases over $13.00?

R(d) = (13 + 2d) (810 - 27d)

R(d) = 10,530 + 1,620d - 54d² - 351d

R(d) = -54d² + 1,269d + 10,530

The correct answer is A. R(d) = -54d2 + 1,269d + 10,530

Ordered pair for this point? (I circled the point in Pink)

Answers

Answer:

(-4,-3)

Step-by-step explanation:

The first coordinate of the ordered pair is the x value or go across

to the right is positive  and the left is negative   so x = -4

The second coordinate of the ordered pair is the y value or go up and down

up is positive and down is negative  so y = -3

(-4,-3)

Answer:

(-4, -3)

Step-by-step explanation:

You can move 4 left from the x axis to get -4, and then move 3 down from the y axis to get -3, leading to the coordinates (-4, -3).

A software designer is mapping the streets for a new racing game. All of the streets are depicted as either perpendicular or parallel lines. The equation of the lane passing through A and B is -7x + 3y = -21.5. What is the equation of the central street PQ? A. -3x + 4y = 3 B. -1.5x − 3.5y = -31.5 C. 2x + y = 20 D. -2.25x + y = -9.75

Answers

Answer:

  B.  -1.5x − 3.5y = -31.5

Step-by-step explanation:

You want an equation of the line perpendicular to -7x +3y = -21.5 that goes through the point (7, 6).

When the equation of the reference line is given in this form, the equation of a perpendicular line can be found by swapping the x- and y-coefficients, and negating one of them. Swapping coefficients, we have ...

  3x -7y = constant

Negating the x-coefficient gives ...

  -3x -7y = constant

Filling in the given point values, we can find the constant:

  -3(7) -7(6) = constant = -21 -42 = -63

None of the answer choices matches this, but one does match when we divide the numbers by 2:

  -3x -7y = -63

  -1.5x -3.5y = -31.5 . . . . . . matches choice B

Answer:

y = (-3/7)x + 9

Step-by-step explanation:

IF AB has the equation -7x + 3y = -21.5, then 3y = 7x - 21.5 is equivalent.  Dividing both sides by 3 yields y = (7/3)x - 21.5/3.  This reveals that the slope of AB is 7/3 and that the slope of any line perpendicular to AB, as central street PQ is, is the negative reciprocal of the slope of AB, or -3/7.

Thus PQ, being perpendicular to AB, has the slope -3/7.  Starting with y = mx + b, and using the coordinates of P(7, 6), we get:

6 = (-3/7)(7) + b, or 9 = b, so that y = (-3/7)x + 9.

Krista was assigned a homework problem that stated there were 45 stamps purchased for $18.75. Some stamps were 40 cents, and some stamps were 55 cents. To solve this problem, she wrote the system of equations that is shown below. 0.40 x + y = 45. x + 0.55 y = 18.75. Which explains the error that Krista made? Krista put 0.40 in the first equation meant for the number of stamps. Krista put 0.55 in the second equation meant for the value of stamps. Krista did not use the correct decimal to represent the total cost of the stamps. Krista mistakenly put 45 in the first equation when it should have been in the second equation.

Answers

Answer:

Option A.

Step-by-step explanation:

there were 45 stamps purchased for $18.75. Some stamps were 40 cents, and some stamps were 55 cents.

Let x and y be the number of stamps of 40 cents and 55 cents respectively.

Total number of stamps is 45. So

[tex]x+y=45[/tex]

Total cost of stamps is $18.75. So

[tex]0.40x+0.55y=18.75[/tex]

But Krista wrote the system of equations as

[tex]0.40x+y=45[/tex]

[tex]x+0.55y=18.75[/tex]

Krista put 0.40 in the first equation meant for the number of stamps.

Krista did not write 0.40 in the second equation meant for the value of stamps.

Therefore, the correct option is A.

Answer:

The answer is A

Step-by-step explanation:

TOOK THE TEST!

Solve:
3x - 9 = 5(x-3)

Answers

Hi,

[tex]3x - 9 = 5(x-3)\\3x - 9 - 5(x-3)= 0\\3x -9 -5x +15 =0\\6-2x=0\\6=2x\\x=3[/tex]

Have a good day.

Please solve for x, and use statement reason. First correct answerer will be brainliest, + two thanks.

Answers

Answer:

x=26

Step-by-step explanation:

m<MNQ=m<P + m<Q by the EXTERIOR ANGLE THEOREM

132=3x+54 SUBSTITUTION

132-54=3x

78=3x

x=26 ALGEBRA

Convert 18 ft to yards

Answers

Answer:

6 yds

Step-by-step explanation:

We know there are 3 ft in 1 yd

Divide  by 3 ft

18 ft / 3 ft = 6 yds

Answer:

6 yards

Step-by-step explanation

1 yard= 3 feet

Which expression is equal to ....

Answers

Answer:

the last one is equal to the question....

Step-by-step explanation:

Answer:

(5√11)/11 (option 1)

Step-by-step explanation:

If you multiply both the top and bottom by √11, you will get 5√11/11.

Next, make sure that the other answers are wrong.

5=√25, so

√11*5=√11*√25

So option 2 and 3 are incorrect.

#4 is obviously wrong, as you cannot simply switch the square root symbol between the denominator and numerator.

What solid is represented by this net? A. cylinder B. triangular pyramid C. rectangular prism D. triangular prism E. cone F. rectangular pyramid

Answers

Answer:

Triangular Prism

Step-by-step explanation:

Answer:

Triangular Prism

Step-by-step explanation:

Because I'm smart

*DIFFICULT QUESTION, PLEASE ANSWER ASAP * *MAKE SURE YOU PROVIDE DETAILS* Without knowing their diameters, which sporting ball has the smaller surface area--a golf ball or a tennis ball? Explain how you know.

Answers

Answer:

Golf ball

Step-by-step explanation:

The formula for the surface area of a sphere is 4[tex]\pi[/tex]r².  The variable is the radius.  Therefore, the sphere with the smallest radius would have the smallest surface area.

Hi there!! (✿◕‿◕)

⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐

Golf ball. The formula for surface area of a sphere is 4πr². The sporting ball that has the smaller surface area is golf ball because it has a smaller radius.

Hope this helped!!  ٩(◕‿◕。)۶

Help me ASAP for this question

Answers

Answer:

The third option is your answer

Step-by-step explanation:

Because the fee is equal 6% or 0.06 of the balance  in order to find the fee you would have to times 0.06 and the balance .Therfore your equation is [tex]f=0.06b[/tex]

hope this helps, if it does please mark brainliest!!

What is the area of the circle below? Use π = 3.14 to solve. Round your answer to the nearest hundredth. 160.36 feet² 184.96 feet² 190.56 feet² 200.96 feet²

Answers

Answer:

A =200.96 ft^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

The radius is 8

A = pi 8^2

A = 64 pi

Letting pi = 3.14

A = 64 ( 3.14)

A =200.96 ft^2

Answer:

[tex]\boxed{\mathrm{200.96 \: feet^2}}[/tex]

Step-by-step explanation:

Apply formula for the area of a circle.

[tex]area=\pi r^2[/tex]

The radius is 8 ft.

[tex]A=\pi (8)^2[/tex]

[tex]A=64\pi[/tex]

Take [tex]\pi[/tex] as 3.14

[tex]A=64(3.14)[/tex]

[tex]A=200.96[/tex]

What does 3 3/5 * 2 5/7 equal

Answers

Hey there! I'm happy to help!

First, let's turn these into improper fractions. We keep the denominators and to find the new numerator you multiply the denominator by the whole number and add then numerator.

[tex]\frac{18}{5} *\frac{19}{7} =\frac{342}{35} =9\frac{27}{35}[/tex]

Therefore, the answer is 9 27/35. Now you can multiply mixed numbers!

Have a wonderful day!

Answer:

As a mixed number the answer to your question will be 9 27/35 or 6 3/7

The steps will be below.

Step-by-step explanation:

You first have to convert theses mixed numbers to fractions.

3 3/5 ,multiply the 5x3=15 and add the 3 which will be 18/5.

Since we converted 3 3/5 to a fraction now it’s 2 5/7 turn!

2 5/7 will be 19/7 because 7x2=14 and 14+5 will give us 19/7.

Finally since we have our two fractions (18/5) and (19/7), it’s time to find the answer!

Now if we multiply both of the factions we get the answer.

18/5 X 19/7

= 9 27/35 or 6 3/7

(For 6 3/7 we have to multiply the whole numbers and the fractions to get that answer)

Hope this helps!

A standard die (a six-sided cube with the numbers 1‚ 2‚ 3‚ 4‚ 5‚ and 6 on the sides) is rolled 150 times. Which of the following is the most likely number of times that a 1 or a 4 would appear? A 2 B 25 C 50 D 100

Answers

Answer:

50

Step-by-step explanation:

1÷6×150=25

1÷6×150=25

ans:25+25

=50

Two bicycles are driving on the circle in the same direction with speeds of 9 mph and 5 mph respectively. How many points are there on the circle where the two bicycles meet?

Answers

Answer:

4 points

Step-by-step explanation:

.

Let  L  be the circumference of the circle.

Then the faster cyclist will catch the slower cyclist first time  when the faster cyclist will cover

the distance which exactly 1 circumference longer than the distance covered by the slower cyclist

9t-5t=l

It gives the time to get first meeting point

t=l/9-5=l/4 hours

and the distance which the faster cyclist covered during this time is

d1=9t=9l/4 miles

The distance which the slower cyclist covered during this time is

d2=5t=5l/4

The meeting point is geometrically the same point on the circle for both cyclists, and its angle measure on the circle is

 (1/l)(5l/(4)-l)=1/4

of the full angle of 2pi radians, or 90 degrees.

So, they started simultaneously, and their first meeting point is at the 90 degrees angle.

Next, they started from this point  SIMULTANEOUSLY  and . . . and everything was repeated.

Hence, their next meeting point is the point on the circle with the angle of 180 degrees.

So, there are 4 remarkable points on the circle: first point is the starting point, and 3 other points

(the points where whey meet/catch each other) are the images of the starting point, rotated 90°, 180°, and 270° along the circle.

There are 4 remarkable points on the circle which is the first point is the starting point and 3 other points.

What is the circumference of the circle?

The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

The circumference of the circle = 2πr

Let  L represent the circumference of the circle.

Then the faster cyclist will catch the slower cyclist the first time when the faster cyclist will cover the distance which is exactly 1 circumference longer than the distance covered by the slower cyclist

9t - 5t = L

It gives them time to get the first meeting point

t = L/9 - 5

t = L/4 hours

The distance which the faster cyclist covered during this time;

d1 = 9t = 9L/4 miles

The distance that the slower cyclist covered during this time is

d2 = 5t = 5L/4

The meeting point is geometrically the same point on the circle for both cyclists, and its angle measured on the circle;

(1/l)(5l/(4)-l)=1/4

Therefore, their next meeting point is the point on the circle with an angle of 180 degrees.

So, there are 4 remarkable points on the circle which is the first point is the starting point and 3 other points.

Learn more about circumference here;

brainly.com/question/12512221

#SPJ2

Create the smallest cone possible with the tool and record the values of the radius height and volume in terms of pi then scale the original cone by the given factors and record the resuling volumes

Answers

Answer:

PLATO sample answer

Step-by-step explanation:

.

Answer:

Step-by-step explanation:

Which equation can be used to find AB?

Answers

Answer:

cos 42 = 10 / AB

Step-by-step explanation:

Since this is a right angle, we can use trig functions

cos theta = adjacent / hypotenuse

cos 42 = 10 / AB

Dhidhdjdkdjdndjskdkndndkdjdndn

Find the area of a rectangle whose length is 12cm and width 6cm A. 720cm² B. 702cm² C. 722cm² D. 72cm² I will mark you us brainliest

Answers

Area = length x width

Area = 12 x 6 = 72 cm^2

Answer is D

Answer:

The answer is option D.

72cm²

Step-by-step explanation:

Area of a rectangle = length × width

From the question

length = 12 cm

width = 6 cm

Area = 12cm × 6cm

We have the final answer as

72cm²

Hope this helps you

Which is the equation of a parabola with focus (0, 5) and directrix y= -1?

Answers

Answer:

Can you include more detail like the equations to choose from so I can help

Step-by-step explanation:

Help me ASAP for this question? Which group of numbers is in order from smallest to largest?

69% 3/4 0.08
0.08, 35% 2/5
7/10 0.85, 79%
0.17 3/20 37%

Answers

Answer:

the second one

Step-by-step explanation:

when turning a percentage into a fraction put it over 100. I then turned that into a decimal which was 0.35. 2/5 is 0.4 which is also equal to 0.40

What is the difference between a Rate and a Ratio? Explain

Answers

Answer:

The difference is that a rate is a comparison of two numbers with different units, whereas a ratio compares two numbers with the same unit. For example, in a room full of students, there are 10 boys and 5 girls.

This is question 18 for the recent post please help!!

Answers

Answer: D) 6

Step-by-step explanation:

Because this triangle's legs are x and x*root(3), it is a 30-60-90 triangle.  Thus, the hypotenuse equals 2x, or 6.

Hope it helps <3

Write the equations after translating the graph of y = | 1/2x−2|+3, one unit to the right

Answers

[tex]y=|\dfrac{1}{2}x-2|+3[/tex]

Since we are translating this graph one unit to the right, replace x with (x-1)

Note: If you are translating a graph to the left by k units, replace x with (x+k), and if by the right, replace x with (x-k)

[tex]y=|\dfrac{1}{2}(x-1)-2|+3[/tex]

After simplifying, we now have the following equation:

[tex]=|\dfrac{1}{2}x-\dfrac{5}{2}|+3[/tex]

This is the new equation. Let me know if you need any clarifications, thanks!

Answer:

we are given

y=|2x|-1

we are given to translate this equation

Whenever we translate any function to right side by 'c' units

we can replace x as x-c

Here , we have to translate one unit right

so, we can replace x as x-1

and we get

y=| 2( x-1 ) | 1

Hope this helps <3

1. The perimeter of a rectangle is 230 cm. If the length of the rectangle is 70 cm, find its breadth and area.

Answers

Answer:

Step-by-step explanation:

Feel pleasure to help u...

Answer:

Breadth: 45 cm.

Area: 3,150 cm^2.

Step-by-step explanation:

The perimeter is 230. Since the length of the rectangle is 70 cm, and 70 * 2 = 140, the sum of the two breadths will be 230 - 140 = 90. That means that the breadth is 90 / 2 = 45 cm.

If the breadth is 45, and the length is 70, then the area is 45 * 70 = 3,150 cm^2.

Hope this helps!

According to the diagram below, LMK = XYZ by HL. If the Pythagorean
theorem is used to show LK=XZ. congruence can also be shown by which of
the following theorems?

A. AAS
B. НА
C. LA
D. SSS

Answers

Answer: D. SSS

SSS = side side side, basically it says that if we have three pairs of congruent corresponding sides, then we have enough information to prove the triangles congruent. The first two pairs of sides are visually shown by the tickmarks. The third pair of sides is LK = XZ as found by the pythagorean theorem. The pythagorean theorem only works for right triangles.

Triangle A B C is shown. Angle A B C is a right angle. An altitude is drawn from point B to point D on side A C to form a right angle. The length of A D is 5 and the length of B D is 12. What is the length of Line segment B C, rounded to the nearest tenth?

Answers

The measure of the length of line segment BC will be 31.2 units.

What is the triangle?

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

If the two triangles are similar, the ratio of the corresponding sides will be constant.

The triangle ΔABC and ΔBDA are the similar triangle. Then the ratio of their corresponding sides will be constant.

Let x be the length of BC.

x / 12 = 13 / 5

      x = 31.2

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ5

Answer:

31.2 units

Step-by-step explanation:

What is the surface area of the rectangular pyramid below? 13,13,13

Answers

Answer:

1,014

Step-by-step explanation:

Assuming those 13’s represent the Length and Width of the sides of the prism, the equation would be

13x13x6 (6 sides)

=1014

Answer:

507

Step-by-step explanation:

apeex

A 5cm x 11cm rectangle sits inside a circle with radius of 12 cm. What is the area of the shaded region? Round your final answer to the nearest hundredth.

Answers

Answer:

Step-by-step explanation:

area of shaded region = 3168/7 - 55 = 397.5cm^2 (app)= 0.397cm^2 ( since we have to round to nearest hundredth

Answer:

The answer is

397.40 cm²

Step-by-step explanation:

To find the area of the shaded area first find the area of both the rectangle and the circle and subtract the smaller one from the larger one.

that's

For the rectangle

Area of rectangle = length × width

From the question

length = 5cm

width = 11 cm

So we have

Area of rectangle = 5cm × 11cm = 55cm²

For the circle

Area of a circle = πr²

where r is the radius

From the question

r = 12 cm

Area of circle = π (12)²

= 144π

= 452.40 cm²

Area of shaded figure

Since the area of the rectangle is smaller than that of the circle we subtract the area of the rectangle from the circle

That's

452.40 cm² - 55cm²

= 397.40 cm² to the nearest hundredth

Hope this helps you

If a△ b=a2+ab−b2, then find (3 △ 2) △ 13. WILL MARK BRAINLIEST PLS HELP!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

The answer is

18

Step-by-step explanation:

a ∆ b = a² + ab + b²

(3 ∆ 2)

a = 3 b = 2

(3 ∆ 2) = 3² +3(2) + 2²

= 9 + 5 + 4

= 9 + 9

= 18

Hope this helps you

Answer:  95

=====================================================

Work Shown:

First we compute 3 △ 2

a △ b = a^2 + ab - b^2

3 △ 2 = 3^2 + 3*2 - 2^2 ... replace 'a' with 3, replace b with 2

3 △ 2 = 9 + 6 - 4

3 △ 2 = 15 - 4

3 △ 2 = 11

Replace the ( 3 △ 2 ) in the original expression with 11.

We now want to find 11 △ 13

a △ b = a^2 + ab - b^2

11 △ 13 = 11^2 + 11*13 - 13^2

11 △ 13 = 121 + 143 - 169

11 △ 13 = 264 - 169

11 △ 13 = 95

A Roman statue is three times as old as a Florentine statue. One hundred years from now the Roman statue will be twice as old as the Florentine statue. How old is the Roman statue?

Answers

Answer:

300 years

I hope this helps!

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