The formula is [tex]\frac{n(n+1)(2n+1)}{6}[/tex]
What are series?
In mathematics, we can describe a series as adding infinitely many numbers or quantities to a given starting number or amount.
We will find the formula as shown as below:
Let [tex]S=1+2^2+3^2+4^2+................+n^2[/tex]
We know [tex](n+1)^3=n^3+3n^2+3n+1[/tex]
[tex](1+1)^3=1^3+3(1)^2+3(1)+1[/tex]
[tex](2+1)^3=2^3+3(2)^2+3(2)+1[/tex]
[tex](3+1)^3=3^3+3(3)^2+3(3)+1[/tex]
.
.
[tex](n+1)^3=n^3+3(n)^2+3(n)+1[/tex]
On adding
[tex]2^3+3^3+4^3......(n+1)^3=(1^3+2^3+3^3+.....+n^3)+3(1^2+2^2+.....+n^2)+3(1+2+3....n)+(1+1+1+....+1)[/tex]
[tex]2^3+3^3+4^3......(n+1)^3-(1^3+2^3+3^3+.....+n^3)=3S+\frac{3n(n+1)}{2}+(1+1+1+....+1)[/tex]
[tex](n+1)^3-1^3=3S+\frac{3n(n+1)}{2} +n[/tex]
[tex]n^3+3(n)^2+3(n)+1-1=3S+\frac{3n(n+1)}{2} +n[/tex]
[tex]2n^3+6n^2+6n=6S+3n^2+3n+2n[/tex]
[tex]6S=2n^3+3n^2+n[/tex]
[tex]6S=2n^2(n+1)+n(n+1)[/tex]
[tex]6S=(n+1)(2n^2+n)[/tex]
[tex]6S=n(n+1)(2n+1)[/tex]
[tex]S=\frac{n(n+1)(2n+1)}{6}[/tex]
Hence, the formula is [tex]\frac{n(n+1)(2n+1)}{6}[/tex]
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In triangle ABC, A is a right angle, and mB = 45°. Find BC. If your answer is not an integer, leave it in simplest radical form.
This triangle is called a 45-45-90 triangle, and the side ratio for the sides opposite to the 45-45-90 degree angles respectively are 1-1-sqrt2
Now we know one side is 6 and its opposing the 45 degrees angle and BC is opposing the 90 degrees angle the ratio between the sides are 1:sqrt2
Therefore BC=6*sqrt2=6sqrt2
Thus B is the correct answer!
Hope this helped any questions just leave them in the comments of this answer.
-8= -4+x
Solve for x
Answer:
-4 + x = - 8
x = - 8 +4
x = - 4
hope it helps :-
Answer:
-4=x or x=-4
Step-by-step explanation:
Move -4 to the other side by adding 4 on both sides:
-8+4=4-4+x
-4=x or x=-4
Hope this helps!
graph the line please help
How many liters of 30% salt solution must be added to 6 L of an 80% salt solution to obtain a 50% salt solution
Answer:
9 Liters
Step-by-step explanation:
Let us represent:
The number of liters of the 30% salt solution = x
Number of liters for the 80% solution = 6 Liters
Number of liters for the 50% solution = x + 6 Liters
Hence:
x × 30% + 6 × 80% = (x + 6)50%
0.3x + 4.8 = 0.5x + 3
Collect like terms
4.8 - 3 = 0.5x - 0.3x
1.8 = 0.2x
x = 1.8/0.2
x = 9 Liters
Therefore, the number of liters for the 30% Salt solution = 9 Liters
What is the slope between
(2,5) (4, 13)
Answer:
m=4..............
Answer:
The slope is: 4.
Step-by-step explanation:
Slope formula:
y2-y1
--------
x2-x1
Plug in the numbers
13 - 5
--------
4-2
Simplify
8
---
2
Simplify again
4
This is your slope.
can someone help me solve F(x) = -9x-5
Answer:
Step-by-step explanation:
What you've provided is only a function. What's the complete question?
workout the value of (2^3)^2
Answer:
64
Step-by-step explanation:
(2^3)^2 = (8)^2 = 64
can somebody help with this please dont put fake answers i really need to pass this test
Step-by-step explanation:
by using Pythagoras theorem,
h^2= p^2+b^2
or, b^2=h^2- p^2
Answer:
it's 24 cm
30²-18²=
b²=900-324= 576
b²=576
b=24
What is the value of Z?
Answer:
21
Step-by-step explanation:
Answer:
The first option is the answer
PLEASE HELP ASAP!!!!
Answer:
Step-by-step explanation:
What will be the cost of the paving if cement costs $26.50 per square metre?
Answer:
hey
Step-by-step explanation:
The lengths of text messages are normally distributed with a population standard deviation of 6 characters and an unknown population mean. If a random sample of 27 text messages is taken and results in a sample mean of 25 characters, find a 95% confidence interval for the population mean. Round your answers to two decimal places. z0.10 z0.05 z0.04 z0.025 z0.01 z0.005 1.282 1.645 1.751 1.960 2.326 2.576 You may use a calculator or the common z-values above.
Answer:
(22.74 ; 27.26)
Step-by-step explanation:
The confidence interval relation is stated as :
Mean ± Zcritical * σ/sqrt(n)
Mean = 25
σ = 6
The Zcritical at 95% = 1.96
Hence,
25 ± 1.96 * (6/sqrt(27))
25 ± 1.96 * 1.1547005
Lower boundary :
25 - (1.96 * 1.1547005) = 22.73678702
Upper boundary :
25 + (1.96 * 1.1547005) = 27.26321298
(22.74 ; 27.26)
The heights of tomato plants are Normally distributed with Calculate the Z-score for a tomato plant that has a a mean of 3.56 feet and a standard deviation of 0.25 feet height of 4.07 feet. Use the z-lable to answer the question. The Z-score, rounded to 2 decimal places, for a tomato plant that has a height of 4.07 feet is About what percent of tomato plants have a height less than 4.07 feet? Round the percent to 2 decimal places, if necessary About % of tomato plants have a height less thah 4.07 feet
the answers are for the first 2.04% and the second tis 97.93% trust bb :>
Answer:
97.03
Step-by-step explanation:
it is the answer
if it is not then I am sorry
In Normal distribution(z) tomato plants have height less than 4.07 feet is 97.93 %.
What is normal distribution?Normal distribution is a "continuous probability distribution that its symmetrical around its mean with most values near the central peak".
According to the question,
The heights of tomato plants are Normally distributed.
Mean(μ) = 3.56
Standard deviation (σ) = 0.25
For a tomato plants that has a height of 4.07 feet
In order to find Percentage of tomato plants have a height less than 4.07 feet
Standard Normal Distribution Formula,
z = (x-μ)/σ where X~(μ,σ).
= [tex]\frac{4.07-3.56}{0.25}[/tex]
= [tex]\frac{0.51}{0.25}[/tex] = 2.04.
P ( x < 4.05) = P( z < 2.04 )
= 0.9793 ( Using standard Normal distribution table)
To find the percentage of tomato plants have height less than 4.07 feet is
multiply 0.9793 by 100
= 97.93%
Hence, Using Standard Normal distribution we find tomato plants have height less than 4.07 feet is 97.93 %
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Type the correct answer in the box.
V12 V5
The value of V10 V6 is closest to the whole number
Answer:
the nearest whole number is one i took the test
Step-by-step explanation:
3 x (5 + 7)
What two words can describe (5 + 7) in the expression above?
O A. quotient and factor
OB.
difference and factor
OC. sum and factor
OD. sum and quotient
The expression contain sum and factor.
The correct option is (C).
What is Expression?Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
Given:
3 x(5+7)
In the Above Expression we have two operation Multiplication and Addition.
Also, the Multiplication is also termed as factor.
Hence, the expression contain sum and factor.
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For George’s party, his dad bought an ice cream cake. After the party, 1/3 of the cake was left. The next day, George ate half of what was left. Choose the model that shows what fraction of cake George ate
Answer :
1/3 ÷ 2 = 1/6 left
The equation below shows the total volume (V), in cubic units, of 9 identical boxes with each side equal to s units:
V = 9s3
If s = 1.6 units, what is the value of V?
23.040 cubic units
36.864 cubic units
58.980 cubic units
129.60 cubic units
36.864 cubic units is what the answer is
Mr.Evans filled up his 14 gallon gas tank for $28.00. What was the price per gallon?
Answer:
$2 per gallon
Step-by-step explanation:
28/14=2
Work out the values of a and b in the identity
4(9x + 11)+5(3x+b)
A=
B=
Answer:
=36x+44+15x+5bƩƩƩƩ
=51x+44+5b ƩƩƩƩƩ
Find the value of x
A. 5 square root 2/2
B 5
C 10
D 10 square root 2
Answer:
The answer is C
Step-by-step explanation:
That side with the 5 is equal to 7.071067812.... (irrational number)
To get x you need to use the equation a^2 + b^2 = c^2
A^2 and B^2 will both be the same thing. The red line indicates they are the exact same length.
7.071037812.... ^2 is 50
Now your equation would be 50+50= c^2 (which is the same as x^2)
100= c^2 is simplified by finding the square root of 100.
Your answer is 10 for side X because the square root of 100 is 10.
This problem was solved using the Pythagorean Theorem.
The hypotenuse x of the right triangle is (c) 10
Finding the hypotenuse, x of the right triangleFrom the question, we have the following parameters that can be used in our computation:
The right triangle
Where, we have
Leg a = 5√2
Leg b = 5√2
The hypotenuse of the right triangle can be calculated using the following Pythagoras theorem
h² = a² + b²
Using the above as a guide, we have the following:
x² = (5√2)² + (5√2)²
Evaluate
x² = 100
Take the square roots
x = 10
Hence, the hypotenuse of the right triangle is (c) 10
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This is for one person (you know who you are) lol
Answer:
Nope...
Step-by-step explanation:
Check out my profile for [tex]incredible \lim_{n \to \infty} a_n[/tex] answers!
Answer:
Step-by-step explanation:
Just for curiosity, which ‘high school/secondary school’ education is harder, the UK or USA?
Answer:
UK
Step-by-step explanation:
x y
0 -6
1 -4
2 -2
3 0
The table above represents what type of function?
A.
neither linear nor nonlinear
B.
nonlinear
C.
linear and nonlinear
D.
linear
Answer: let me check
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
0 -6 is a linear and a nonlinear and it keeps on going
Is 1 + 4(3x – 10) – 12x equivalent to -9?
Answer:
No.
Step-by-step explanation:
Remove parenthesis:
1+12x-40-12x
Combine like terms:
-39+0x = -39. -39 is NOT equal to -9.
Triangle PQR has coordinates P (2, 4), Q (-2, 4), R (0,-6).
Write the coordinates of the vertices of the image of a
triangle after a dilation of 2.5.
Select 3 coordinates only.
A) P' (5, 10)
B) P' (0.8, 1.6)
C) Q' (-5, 10)
D) Q' (-0.8, 1.6)
E) R' (-6,0)
F) R' (0, -15)
Answer: P’ (5,10) , Q’ (-5,10) , R’ ( 0,-15)
Step-by-step explanation:
Just multiply 2.5 by the x,y
Answer:dec I think
Step-by-step explanation:
Plss help (IF ITS BOTH OR NEITHER PLS TELL ME) Zoom in to see full pic!!
to find the missing length for the equation you would use b.
Can someone plz help me with these. Will chose Brainlist.
Answer:
19= 11
20= 33
21= 22
22= 38
23= 74.8
Step-by-step explanation: if it's correct can i get brainliest.... hopes this helps.
What is the volume of the cylinder below?
Answer:
11253.76
Step-by-step explanation:
We know that the formula for the volume of a cylinder is pi(r^2)(h) and we have both the radius (8 yards) and the height (56 yards) given to us. Given this, we can plug those numbers into the equation and do pi x (8)^2 x 56 which is simplified to 3.14 x 64 x 56, and when we solve this out we can get a final answer of 11253.76
Hiii, I have a little maths problem. So I have this at the photo. I checked and the answer should be -0,0081 . But I don't get why is it with a minus cuz a rule says: if ,,a" is a negative number and the degree is an even number then we should make the final number positive but here it's negative. I don't get why. I'll give brainliest if you can help me!
Answer:
you are correct with -0.0081
Step-by-step explanation:
but if you are multiplying a negative times a positive it is a negative always. So you do a negative times a negative you get a positive. Then you multiply the positive with a negative to get a negative then you do the negative times a negative to get a negative.
Answer:
this is my other account
Step-by-step explanation:
here you can get free question answer things, so
1+0 = ?
u can get free “helped people”by this
Answer:
the answer is 1
........
1+0=1
Because anything plus zero equals itself (Example) :
3+0=3, 4+0=4, etc
Therefore
1+0=1
Have a good day!