help needed!! Mark as brainliest

Help Needed!! Mark As Brainliest

Answers

Answer 1

Given:

The equation is:

[tex]2\sum_{n=3}^7n^2=\sum_{n=3}^72n^2[/tex]

To find:

Whether the equation is true or not.

Solution:

We have,

[tex]2\sum_{n=3}^7n^2=\sum_{n=3}^72n^2[/tex]

Taking LHS, we get

[tex]LHS=2\sum_{n=3}^7n^2[/tex]

[tex]LHS=2[(3)^2+(4)^2+(5)^2+(6)^2+(7)^2][/tex]

[tex]LHS=2[9+16+25+36+49][/tex]

[tex]LHS=2[135][/tex]

[tex]LHS=270[/tex]

Taking RHS, we get

[tex]RHS=\sum_{n=3}^72n^2[/tex]

[tex]RHS=2(3)^2+2(4)^2+2(5)^2+2(6)^2+2(7)^2[/tex]

[tex]RHS=2(9)+2(16)+2(25)+2(36)+2(49)[/tex]

[tex]RHS=18+32+50+72+98[/tex]

[tex]RHS=270[/tex]

Here, [tex]LHS=RHS[/tex].

Therefore, the given equation is true.


Related Questions

Khan Academy Question :)

Answers

9514 1404 393

Answer:

  40 units

Step-by-step explanation:

The slanted side is the hypotenuse of a triangle that is 8 units high and 6 units wide. Its length can be found from the Pythagorean theorem:

  d² = 6² + 8² = 100

  d = √100 = 10

The perimeter is the sum of side lengths. Those lengths can be found by counting grid squares. Clockwise from the upper left corner, the sum of side lengths is ...

  P = 8 + 10 + 14 + 8

  P = 40 . . . units

Dilbert recently hired a mechanic to do some necessary work. On the final bill, Dilbert was charged a total of $712.
$430 was listed for parts and the rest for labor. If the hourly rate for labor was $47, how many hours of labor was
needed to complete the job?

Answers

Step-by-step explanation:

Dont understand, sorry!!

PLEASE HELPP!!
An initial amount of money is placed in an account at an interest rate of 5% per year, compounded continuously. After five years, there is $3287.11 in the
account. Find the initial amount placed in the account. Round your answer to the nearest cent.

Answers

9514 1404 393

Answer:

  $2560.00

Step-by-step explanation:

The account balance is given by the formula ...

  A = Pe^(rt) . . . . principal P invested at rate r for t years

Filling in your numbers, we have ...

  $3287.11 = Pe^(0.05·5)

  P = $3287.11e^(-0.25) = $2560.00

The initial amount was $2560.00.

I need help on this
5x+x-4

Answers

Answer:

6 x − 4

Step-by-step explanation:

have a great day :D

Answer:

6 − 4

Hope this helps!!

9
Is the function shown in the
graph one-to-one?
Yes, there exists one
input for every output.
No, there exists
more than one output for at
least one input.
• No, there exists
more than
one input for at least one
output.
Yes, there exists one output for
every input.

Answers

Answer: Choice D

Yes, there exists one output for every input.

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

Explanation:

x = input

y = output

For any given x value, we have exactly one and only one y value that pairs up with it. Use the vertical line test. This is where we try to draw a single vertical line through more than one point on the curve. You'll find that no such line can be drawn. Any vertical line only crosses the curve exactly once (corresponding to exactly one output). We say that it passes the vertical line test, and therefore we have a function.

Side note: the curve does not pass the horizontal line test. That means the function is not one-to-one.

Un capital es impuesto al 12% anual y un segundo capital al 9% anual la diferencia de dichos capitales es de S/.1350. Si el interés trimestral que produce el primero es al interés semestral que produce el segundo como 5 es a 3. ¿Cuál es el mayor capital?

A) S/.2250 B) S/.3000 C) S/.4100
D) S/.4750 E) S/5200

Answers

Answer:

C

Step-by-step explanation:

1) A farmer has sheep and cattle in the ratio 8:3.
a) How many sheep has the farmer if he has 180 cattle?

b) Find the ratio of the number of sheep to the total number of animals.

c) Find the ratio of the total number of animals to the number of cattle.

2)My fortune of $ 810 000 is to be divided in the ratio 4:3:2. How much does each person receive?
Good

Answers

Answer:

Q 1)

a) No of sheep = 480

b) 8 : 11

c) 11 : 3

Q 2)

Each person will receive: $360,000, $270,000 and $180,000

Step-by-step explanation:

Ratio of sheep to cattle = 8 : 3

Let the number of sheep be 8x

And number of cattle be 3x

a)

No of cattle = 180 (Given)

Therefore,

3x = 180

x = 180/3

x = 60

Therefore, 8x = 8*60 = 480

No of sheep = 480

b)

Total animals = 180 + 480 = 660

Ratio of sheep to the total number of animals

= 480 : 660

= 8 : 11

c)

Ratio of total animals to the number of cattle

= 660 : 180

= 11 : 3

Q 2) Let each person will receive 4x, 3x and 2x dollars.

Therefore,

4x + 3x + 2x = 810,000

9x = 810000

x = 810000/9

x = 90,000

Therefore,

4x = 4*90,000 = $360,000

3x = 3*90,000 = $270,000

2x = 2*90,000 = $180,000

So, each person will receive $360,000, $270,000 and $180,000.

Plz help this is due today NO LINKS OR GROSS PICTURES OR I Will REPORT And please show work

Answers

Answer:

The volume of Kuron Pool is 600ft³.

Step-by-step explanation:

Rectangular prisms are basically cuboids.

So using the formula to calculate volume of the cuboid i.e.

V = length x breadth(width) x height

= 15 x 8 x 5

= 600ft³

A bank loaned out $28,500, part of it at the rate of 14% annual interest, and the rest at 4% annual
interest. The total interest earned for both loans was $2,640.00. How much was loaned at each rate?
$
was loaned at 14% and
was loated at 4%.

Answers

Answer:

$15,000 was invested at 14% per year, and $13,500 was invested at 4% per year.

Step-by-step explanation:

Given that a bank loaned out $ 28,500, part of it at the rate of 14% annual interest, and the rest at 4% annual interest, and the total interest earned for both loans was $ 2,640.00, to determine how much was loaned at each rate you must perform the following calculations:

28,500 x 0.14 + 0 x 0.04 = 3,990

20,000 x 0.14 + 8,500 x 0.04 = 3,140

15,000 x 0.14 + 13,500 x 0.04 = 2,640

Therefore, $ 15,000 was invested at 14% per year, and $ 13,500 was invested at 4% per year.

5 + 14 x ____ = 9 x ____ - 5
Please solve for the blanks I’m begging you with all my soul

Answers

Answer:

3, 8

Step-by-step explanation:

19x__=9x__-5

24x_=9x_

8x_=3x_

8x3=3x8

24=24

The X and Y coordinates (in feet) for station Shore are 2058.97 and 6980.06, respectively, and those for station Rock are 1408.03 and 6980.06, respectively. What are the azimuth, bearing, and length of the line connecting station Shore to station Rock

Answers

Answer:

Hence, the azimuth, bearing, and length of the line connecting station Shore to station Rock are [tex]270^{\circ},90^{\circ}[/tex] and [tex]650.94[/tex] feet.

Given :

The shore station point [tex](X_1,Y_1)[/tex] in feet,

        [tex](X_1,Y_1)=(2058.97, 6980.06)[/tex]

The Rock station point [tex](X_2,Y_2)[/tex] in feet

       [tex](X_2,Y_2)=(1408.03,6980.06)[/tex]

From the figure

     [tex]x=2058.97-1408.03=650.94[/tex] feet

    [tex]y=6980.06-6980.06=0\\[/tex] feet

Length of the line [tex]L=\sqrt{x^2+y^2}[/tex]

                           [tex]\Rightarrow L=\sqrt{(650.94)^2+0}=650.94[/tex]

                            [tex]\Rightarrow L=650.94[/tex] feet

[tex]\because[/tex] [tex]\tan \theta=\frac{y}{x}=\frac{0}{x}=0[/tex]

[tex]\Rightarrow \theta=\tan^{-1}(0)=0[/tex]

Azimuth of line[tex]=270^{\circ}+\theta[/tex]

                       [tex]=270^{\circ}+0[/tex]

                      [tex]=270^{\circ}[/tex]

[tex]\therefore[/tex] Bearing [tex]=360^{\circ}-\text{Azimuth}[/tex]

                [tex]=360^{\circ}-270^{\circ}[/tex]

                [tex]=90^{\circ}[/tex]

The bottom of a ladder is placed 4 feet from the side of a building. The top of the ladder must be 13 feet off the ground.

What is the shortest ladder that will do the job? SHOW your work.

10 foot ladder
12 foot ladder
14 foot ladder

Answers

Answer:14

Step-by-step explanation:

There are 4 tablespoons in 1/4 cup. How many tablespoons are in 2 1/4 cups?

Answers

Answer:

The answer is 36 tablespoons

Step-by-step explanation:

1/4 = 4 tablespoons

4*8 = 32

32 + 4 =36

Answer:

36 tablespoons

Step-by-step explanation:

4 tablespoons in 1/4 cup:

4*4 = 16 tablespoons in 1 cup

16*2 = 32 tablespoons in 2 cups

32+4 = 36 tablespoons for 2 1/4 cups

A certain company stock has
decreased by $4 per share.
If Krista has 17 shares of this stock,
write an integer to represent the
total change in value of her stock.

Answers

Answer:

-68$

Step-by-step explanation:

: D

hope I'm right...

Can anyone help me out

Answers

Answer:

14.49 people per square mile

Step-by-step explanation:

Divide to find the answer:

836,109/57,714 = 14.49

Write 3 3/4 feet as a single fraction greater than one.

Answers

answer:
9/4

step-by-step explanation:
3/4 + 3/4 + 3/4
9/4

The solution is  3 3/4 feet as a single fraction greater than one is: 15/ 4

What is fraction?

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

here, we have,

given that,

3 3/4 feet

now, we have to Write 3 3/4 feet as a single fraction greater than one.

so, we have,

3 3/4

i.e. 3*4 + 3 / 4

= 15/ 4

or, we have,

3 3/4

i.e.

3/4 + 3/4 + 3/4

=9/4

now, single fraction greater than one 15/ 4 > 1.

Hence, The solution is  3 3/4 feet as a single fraction greater than one is: 15/ 4.

To learn more on fraction click:

brainly.com/question/10354322

#SPJ2


Combine like terms in 3x + 2y + 2x + 4y + 1

Answers

Answer:

The final answer is 5x + 6y + 1

Step-by-step explanation:

3x+2x = 5x

2y+4y = 6y

5x+6y+1

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!

Answer:

Hello! Mizuki here to answer! The correct answer should be 5x + 6y + 1

Step-by-step explanation:

Just separate it into categories first, then add

soo...

3x, 2x is the only x

2y, 4y is the only y

1 is the only number

3x + 2x = 5x

2y + 4y = 6y

1 = 1

add up

5x + 6y + 1

What is it < > or =
1000kg 100000 g

Answers

9514 1404 393

Answer:

  >

Step-by-step explanation:

1 kg = 1000 g

Multiplying by 1000, you have ...

  1000 kg = 1,000,000 g

  1,000,000 g > 100,000 g

The appropriate relation symbol is >.

PLS GIVE ME AN EXPLANATION.. BUT NO LINKS...If the diameter of a cylinder is 14 feet and its height is 4 feet, the volume of the cylinder is 2,461.76 square feet. True False

Answers

Answer:

False

Step-by-step explanation:

Answer: False

Step-by-step explanation: Look up cylinder and enter the height and diameter into the calculator and you will see it does not equal 2,461.76 sqaure feet.

What is 10% of 7,518?

Answers

Answer:

751.8

Step-by-step explanation:

10% of 7,518 is 751.8

The Sine Function

In a basic sine curve, where can the zeros NOT be found?

a. middle
b. beginning
c. maximum point
d. end

Please select the best answer from choices provided

Answers

Answer:

C. Maximum

Step-by-step explanation:

I calculated it logically

n squared plus 3 sequence

Answers

Answer:

n² + 3

this is the expression

Step-by-step explanation:

N2+3 that sis the answer

need to know please help me !!!

Answers

Answer:

9.5  feet/ 1 second is your unit rate

Step-by-step explanation:

In order to make a unit rate you have to make the denominator 1 so it can be a whole number which means you divide by the denominator on both sides both numerator and denominator.

[tex]24x^{2}+bx^{2} =25x^{2}[/tex]

Answers

Answer:

x = 0

Step-by-step explanation:

Subtract 25x^2 from both sides

24x^2 + bx^2 - 25x^2 - 25x^2

Simplify

bx^2 - x^2 = 0

Factor bx^2 - x^2: x^2(b - 1)

bx^2 - x^2

Factor out common term x^2

= x^2 (b - 1)

x^2(b - 1) = 0

Using the Zero Factor Principle: If ab = 0 then a = 0 or b = 0

x^2 = 0

Apply rule x^n = 0   x = 0

x = 0

x-y=6, if x=2, then y= -4

Answers

Answer:

That is correct.

Step-by-step explanation:

x - y = 6

2 - (- 4) = 6

2 + 4 = 6

Find the volume of this triangular prism:

Answers:
350in3
175in3
22in3
200in3

Answers

The answer is 175in3.

a circle has a radius of 11cm find the area of a sector woth central angle that measures 225 degrees

Answers

Answer:

237.46 cm squared

Step-by-step explanation:

look at the image for explanation

The grades of a science test are normally distributed. Thanh finds that his grade on the test has a z-score of -25
Which statement must be true?

Answers

Answer:

A

Step-by-step explanation:

I just did it

Someone help me please

Answers

Answer:

7/8 or the bottom right

Step-by-step explanation:

Identify any x intersepts and y intersepts

Answers

The x-intercept of the line is (-5,0) and the y-intercept is (0,5)
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