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.
Khan Academy Question :)
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?
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.
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
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.
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
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
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
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%.
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
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
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
Answer:14
Step-by-step explanation:
There are 4 tablespoons in 1/4 cup. How many tablespoons are in 2 1/4 cups?
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 $4 per share.
If Krista has 17 shares of this stock,
write an integer to represent the
total change in value of her stock.
Answer:
-68$
Step-by-step explanation:
: D
hope I'm right...
Can anyone help me out
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.
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
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
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
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?
Answer:
751.8
Step-by-step explanation:
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
Answer:
C. Maximum
Step-by-step explanation:
I calculated it logically
n squared plus 3 sequence
Answer:
n² + 3
this is the expression
Step-by-step explanation:
need to know please help me !!!
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]
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
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
a circle has a radius of 11cm find the area of a sector woth central angle that measures 225 degrees
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?
Answer:
A
Step-by-step explanation:
I just did it
Someone help me please
Answer:
7/8 or the bottom right
Step-by-step explanation:
Identify any x intersepts and y intersepts