by mathematical induction 1.2²+2.3²+.....+n(n+1)(n+2)(3n+5)/12​

Answers

Answer 1

Step-by-step explanation:

1.2+2.3+3.4+⋯+n(n+1)=∑k=1nk(k+1)

=∑k=1n(k2+k)

=∑k=1n(k2)+∑k=1n(k)

=n(n+1)(2n+1)6+n(n+1)2

=n(n+1)6(2n+1+3)

=n(n+1)6(2n+4)

=n(n+1)6[2(n+2)]

=n(n+1)(n+2)3


Related Questions

Mrs. Conley asks her class what kind of party they want to have to celebrate their excellent behavior. Out of all the students in the class, 5 want a ice cream party, 7 want a movie, 10 want a costume party, and the rest want are undecided. If 20% want a ice cream party, how many students are in class?

Answers

Answer:

25

Step-by-step explanation:

Write equations (both, Point Slope & Slope Intercept Forms) of the line with
slope of -2 and point (9,2).

Answers

Answer:

Equation of line in Point Slope Form is [tex]\mathbf{y-2=-2(x-9)}[/tex]

Equation of line in Slope Intercept Form is: [tex]\mathbf{y=-2x+20}[/tex]

Step-by-step explanation:

We need to write equation of line having slope -2 and point (9,2)

a) Equation in Point Slope Form

The general equation of point slope form is: [tex]y-y_1=m(x-x_1)[/tex]

Where x₁ and y₁ are the points of line and m is slope.

x₁=9 and y₁=2 and m=-2

Putting values in formula and finding equation:

[tex]y-y_1=m(x-x_1)\\y-2=-2(x-9)[/tex]

So, Equation of line in Point Slope Form is [tex]\mathbf{y-2=-2(x-9)}[/tex]

b) Equation in Slope Intercept Form

The general equation of Slope Intercept Form is: [tex]y=mx+b[/tex]

where m is slope and b is y-intercept

Finding y-intercept using slope m=-2 and point(9,2)

[tex]y=mx+b\\2=-2(9)+b\\2=-18+b\\b=2+18\\b=20[/tex]

The equation in slope m=-2 and b=20 is:

[tex]y=mx+b\\y=-2x+20[/tex]

So, equation of line in Slope Intercept Form is: [tex]\mathbf{y=-2x+20}[/tex]

13. The population of a city is currently 45,000 and is declining at a rate of 2% each year. Estimate the population after a period of 5 years. Use the formula ƒ(t) = aert.

Answers

Given:

Initial population = 45,000

Decreasing rate = 2%

Time = 5 year

To find:

The population after a period of 5 years.

Solution:

Formula used:

[tex]f(t)=ae^{rt}[/tex]

where, a is initial population, r is rate and t is time.

[tex]r=\dfrac{2}{100}=0.02[/tex]

Decreasing rate represented by -0.02.

Substitute a=45000, r=-0.02 and t=5 in the above formula.

[tex]f(5)=45000e^{-0.02(5)}[/tex]

[tex]f(5)=45000e^{-0.1}[/tex]

[tex]f(5)=45000(0.904837418)[/tex]

[tex]f(5)=40717.68381 [/tex]

Approximate the value to the previous integer.

[tex]f(5)\approx 40717 [/tex]

Therefore, the population after 5 years is 40717.

Answer:

40,718

Step-by-step ex

The population of a city is currently 45,000 and is declining at a rate of 2% each year. Estimate the population after a period of 5 years. Use the formula ƒ(t) = aert. planation:

Question 5 of 8
Put these substances in order of density with the most dense first and the
least dense last.
1 iron
Trubber
cotton ball
Ti helium

Answers

Answer:

cf

cf

centru. toc htc. toc cf. activ. cfc fgfvxv. chvv

Helpppppppppppppp
asappppppppppp

Answers

Answer:

180-112=68

Step-by-step explanation:

2. Graph x < 8 and x > -1.

Answers

Answer:

I'll try my best in explaining the steps.

Considering both signs are greater than and less than sign, its an open circle.

For the first equation, you would have an open circle, basically one that isn't colored in, on 8 on the number line. The arrow would be pointing to the left because the equation is telling us numbers that are less than 8.

For the second equation, you would have an open circle, basically one that isn't colored in, on -1 on the number line. The arrow would be pointing to the right because the equation is telling us numbers that are greater than -1.

Step-by-step explanation:

What is 8.15 rounded to the nearest whole number

Answers

Answer:

the answer is 8.

Step-by-step explanation:

Brainliest? uwu

Answer:

8 :)

You round down. If it was 8.5 then you'd round up, anything below would be rounded down, for example, 8.4, 8.3, 8.2, 8.1.

help me please somone

Answers

Answer:

Iscoccecles

Sorry if i spelled it wrong.

Step-by-step explanation:

i think that would be an isosceles triangle

The diagram compares the ratio of girls in the chorus to boys in the chorus. What is the ratio of girls to boys? If there are 30 students in the chorus, how many are girls and how many are boys.

girls 3 parts
boys 2 parts

Answers

Answer:

it should be girls 12 to 18

Step-by-step explanation:

i just messed around with a calculator and found it.

The length of a rectangle is twice the width if the perimeter of the rectangle 60 units find the area of the rectangle

Answers

Answer:

200

Step-by-step explanation:

Length = 2w

2w + 2l = 60

substitute l out with 2w

2w + 2(2w) = 60

2w + 4w = 60

w = 10

l = 20

Area = w • l

        = 10 • 20

        = 200

A grocery store recently changed their apple supplying vendor. The vendor told the store manager that the mean weight for each apple is bell-shaped with # mean of 7.5 ounces and a standard deviation of 1.33 ounce (a) One customer comes to this grocery store and randomly picks 25 apples. What is the mean and standard deviation of the distribution of the mean weight for 25 apples? (b) What is the probability that the mean weight of 25 apples exceeds 8.2 ounces? (c) Another customer randomly picks 10 apples. Will the probability of the mean weight that the 10 apples exceeds 8.2 ounces of this customer be higher than the last customer in part b? Explain it.

Answers

Answer:

b) 0.0042495

c) 0.048021

Hence, the probability of the mean weight that the 10 apples exceeds 8.2 ounces of this customer wil be higher than the last customer in part b because the number of random samples in part b is greater that that in part c

Step-by-step explanation:

mean of 7.5 ounces and a standard deviation of 1.33 ounce

When random number of samples are given, we solve using z score with the formula

= z = (x-μ)/σ/√n, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

n is the random number of samples

(a) One customer comes to this grocery store and randomly picks 25 apples. What is the mean and standard deviation of the distribution of the mean weight for 25 apples?

(b) What is the probability that the mean weight of 25 apples exceeds 8.2 ounces?

x > 8.2 ounces

= z = (x - μ)/σ/√n

z = (8.2 - 7.5)/1.33/√25

z = (8.2 - 7.5)/1.33/5

z = 2.63158

Probability value from Z-Table:

P(x<8.2) = 0.99575

P(x>8.2) = 1 - P(x<8.2) = 0.0042495

(c) Another customer randomly picks 10 apples. Will the probability of the mean weight that the 10 apples exceeds 8.2 ounces of this customer be higher than the last customer in part b?

For n= 10

x > 8.2 ounces

= z = (x - μ)/σ/√n

z = (8.2 - 7.5)/1.33/√10

z = 1.66436

Probability value from Z-Table:

P(x<8.2) = 0.95198

P(x>8.2) = 1 - P(x<8.2) = 0.048021

Hence, the probability of the mean weight that the 10 apples exceeds 8.2 ounces of this customer wil be higher than the last customer in part b because the number of random samples in part b is greater that that in part c

can somone help me pls ?

Answers

[tex]\huge\mathtt{Hello!}[/tex]

[tex](6x - 23) = (4x + 9)[/tex]

[tex]6x -4x = 9 + 23[/tex]

[tex]2x = 32[/tex]

[tex]x = 16[/tex]

It is because the sides are equal, so the angles opposite to them also are equal.

Have a nice day!

6x -23= 4x +9
-4x = -4x
______________
2x -23= 9
2x +23= + 23

2x = 32
/ 2x. /2

X = 16

First, you cancel out the x by moving the one in the right to the left. You subtract the 6 from the left to the one in the right, giving you 2x. Then you cancel out the number on the left to the right (same thing as the x, remember by cancelling a number out you make it the opposite of what it is so if it’s negative it turns to positive to cancel out). Final step is to cancel out the x so you can divide it by the number that’s left to get the x by itself !

3.
1
y=x+3
1
slope: +: y-intercept: 3
4
B slope: 4; y-intercept: -3
1
slope: ; y-intercept: -3
D slope: 4; y-intercept: 3

PLEASE HELP ME

Answers

Answer:

A

Step-by-step explanation:

remember y=Mx+b where M is slope mad B is y intercept

PLSSSS HELPPP I WILLL GIVEEE BRAINLIESTTTT!!!!!!!!!!!!!!!!!
PLSSSS HELPPP I WILLL GIVEEE BRAINLIESTTTT!!!!!!!!!!!!!!!!!
PLSSSS HELPPP I WILLL GIVEEE BRAINLIESTTTT!!!!!!!!!!!!!!!!!
PLSSSS HELPPP I WILLL GIVEEE BRAINLIESTTTT!!!!!!!!!!!!!!!!!

If f(x) = -3x + 4, find f(-4)

Answers

Answer:

Step-by-step explanation:

-3x+4

-3(-4)+4

12+4

16

Answer:

3x+4

3(-4)+4

12+4

16

Step-by-step explanation:

the is factoring quadratics with a leading coefficient: 5x to the 2 power - 14x + 8

Answers

Answer:

The factorization of [tex]5x^2-14x+8[/tex] is (5x-4)(x-2)

Step-by-step explanation:

Given quadratic polynomial is:

[tex]5x^2-14x+8[/tex]

To factor a quadratic polynomial with leading co-efficient has to be factorized, the leading co-efficient and the constant are multiplied and pairs(a,b) of the product are made so that their sum or subtraction is equal to the co-efficient of x

We get 40 by multiplying 8 and 5

And the pair we get are: 10 and 4

[tex]=5x^2-10x-4x+8\\=5x(x-2)-4(x-2)\\=(5x-4)(x-2)[/tex]

Hence,

The factorization of [tex]5x^2-14x+8[/tex] is (5x-4)(x-2)

State the number of complex roots and the possible number of real and imaginary roots for each equation. The find all roots? If possible.

Answers

Answer:

x =2

x = -2

Step-by-step explanation:

(x - 2)(x + 2)(x^2 + 4) = 0

(x - 2) = 0

x = 0 + 2

x =  2

(x + 2) = 0

x = - 2

x = - 2

(x^2 + 4) = 0

x^2 = 4

x = [tex]\sqrt{4}[/tex]

x = 2

Q14.
Solve the simultaneous equations
2x - 3y = 24
6x + 2y = -5
landimorament

Answers

-3y=24-2x
2y=-5-6x

-y=8-2/3x y=-8+2/3x
y=-5/2-3x

-8+2/3x=-5/2-3x
-8+5/2=-3x-2/3x
-11/2= -11/3x
x=3/2
hope it helps!!!

The trapezoids are similar shapes. Find the lengths

Answers

X = 25
Y = 10.8
All I did is divide 30 by 50 which is .6 then I multiple by 18 which is 10.8 for y. Then 15 divided by .6 equals to 25

A tree is 72 feet (ft) tall. How many inches (in) is this? First fill in the blank on the left side of the equation using one of the ratios. Then write your answer on the right side of the equation.

Answers

1 foot = 12 inches:

1/72 = 12/x

Cross multiply:

1x = 72 * 12

x = 864 inches

Evaluate the circulation of G =xyi +zj +4yk around a square of side 9, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis.

Answers

Answer:

I didn't know the answer and sorry I am here taking freepoint because I needed them in a hurry so that I can ask my questions from someone else that's why I really sorry and thank you for free points

Please help I’ll mark brainliest if u give a small explanation

Answers

the answer is 4 because the bottom and line DE form a right angle

#12: Kara is deciding between The Lyme Point Inn and Ever After Farms for 1 point

her wedding reception. The Lyme Point Inn charges $3,000 for the venue

and $100 for each meal. Ever After Farm charges $5,400 for the venue and

$70 for each meal. Write and solve an equation to find the number of

meals at which the total cost charged by the two venues would be the

same. *

Your answer

ooo

Answers

Answer:

80 meals

Step-by-step explanation:

Set up an equation where x is the number of meals:

100x + 3000 = 70x + 5400

Solve for x:

100x + 3000 = 70x + 5400

30x + 3000 = 5400

30x = 2400

x = 80

So, at 80 meals, the cost of the 2 venues will be the same

Answer:

80 metals

Step-by-step explanation:

100x + 3000 = 70x + 5400

How to Solve for x:

100x + 3000 = 70x + 5400

30x + 3000 = 5400

30x = 2400

x = 80

So, at 80 meals, the cost of the 2 venues will be the exact same

Give the values of the coefficients [a], [b], and [c], regarding the product in the form of ax^2-bx + xy - cy. Use "0" if the term isn't present.

Answers

Answer:

[tex]x^{2} -6x+xy-6y[/tex]

Step-by-step explanation:

Answer:

The values of coefficients a, b and c are

a=1

b=6

c=6

Step-by-step explanation:

We need to give the values of coefficients [a],[b] and [c]  regarding the product in the form of [tex]ax^2-bx + xy - cy[/tex]

The term given is: [tex](x+y)(x-6)[/tex]

First we will multiply the terms

[tex](x+y)(x-6)\\=x(x-6)+y(x-6)\\=x^2-6x+yx-6y[/tex]

Now comparing the product [tex]x^2-6x+yx-6y[/tex]  with the given form [tex]ax^2-bx + xy - cy[/tex]

The values of coefficients a, b and c are

a=1

b=6

c=6

5 yds=? Ft (PLEASE HELPP!!!)

Answers

Answer:

5 yards = 15 feet

Step-by-step explanation:

Following the formula that for every 1 yard we have 3 feet.

x = amount of yards

y = amount of feet per yard

z = amount of feet total

[tex]x * y = z[/tex]

Substitute:

[tex]5 * 3 = z[/tex]

[tex]15 =z[/tex]

Final answer:

5 yards = 15 feet

best answer get brainly


Farrell football team has a total 30 uniform shirts.20% of the uniforms are medium-sized how many uniforms are medium?

Answers

Answer:

I would believe that it would be close 7 whatever is closest to seven bro

Answer:

12

Step-by-step explanation:

20%=2/5

2/5 is equivalent to 12/30

therefore 12 uniforms are medium

Write the slope-intercept form of the equation of the line described. through (2, -5) perpendicular to y = 1/3x -1

Answers

Answer:

y = -3x + 1

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes, so the slope will be -3.

Plug in the slope and given point into y = mx + b

y = mx + b

-5 = -3(2) + b

-5 = -6 + b

1 = b

Then, plug in the slope and y intercept into y = mx + b again:

y = -3x + 1 will be the equation of the line

16. [-12 Points]

DETAILS

CURRENMEDMATH11 3.S.001.

Solve the equation. A calculator may be used.

Express your answer to the nearest tenth.

0.8 1.4.

X

0.45 1

Express your answer to the nearest hundredth.

1.4

0.8

Х

0.45

=

1

Answers

Answer:

Answer: A. 5:4 Step-by-step explanation: Since the question mentions twelfths of a pie, it is easier to say each pie has 12 pieces or 36 total pieces ordered from the 3 pies. Ty ate 5 and Rob ate 15 which is 3 times more than Ty. A total of 20 pieces have been eaten from the 36 you started with. Eaten = 16. So the ratio is 20:16 which is simplified to = 20 and Remaining 5:4.

(I'LL BE GIVING BRAINLIEST AND EXTRA POINTS TO WHO EVER HELPS ME!! :D)



Petra eats five and three fifths pies in a pie-eating contest. Paulie eats three and fourteen sixteenths pies in the contest. How many more pies did Petra eat?

A) one and fifty eight eightieths pies

B) one and seventeen twenty firsts pies

C) two and fifty eight eightieths pies

D) two and seventeen twenty firsts pies


(Here is an image if needed) :

Answers

Answer:

2 7/20

Step-by-step explanation:

Find the values of a and b such that x² - 2x + 2 = ( x - a )² + b

Answers

Answer:

a = b = 1

Step-by-step explanation:

x² - 2x + 2 = ( x - a )² + b

x² - 2x + 2 = ( x² - 2x + 1) - 1 + 2 = (x - 1)² + 1

a = b = 1  

indicate in standard form the equation of the line passing through the given points, in the equation box below. X(0, 6), Y(5, 6)

Answers

Answer:

0x + y = 6

Step-by-step explanation:

Equation of the Line

The equation of a line passing through points (x1,y1) and (x2,y2) can be written as follows:

[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

It can be later converted to any other form of the line. For example, the standard form is:

[tex]Ax + By = C[/tex]

Let's find the equation by using the given points (0,6) (5,6):

[tex]\displaystyle y-6=\frac{6-6}{5-0}(x-0)[/tex]

Operating:

[tex]\displaystyle y-6=\frac{0}{5-0}(x-0)[/tex]

y - 6 = 0

Or, equivalently:

0x + y = 6

This corresponds to a horizontal line

Other Questions
Which equation matches the story: Elena spends $17 and buys a $3 book and a bookmark for each of her 5 cousins. How much does each bookmark cost?3(x+5)=173x+5=175(x+3)=175x+3=17 Scientists use i ____to represent magnetic fields which of the following functions is graphed below 64kg and 4 meters per second squared. how much force was used? 16. Who did not benefit greatly from the Industrial Revolution?A. CraftspeopleB. The aristocracyC. The middle classD. Factory owners I need the answer pls. To find the inverse of f(x) = 2x 1, Patel begins by replacing f(x) with y. He then switches x and y. What is the next step?A.Solve the equation for x.B.Subtract 1 from both sides of the equation.C.Solve the equation for y.D.Replace y with f1(x).it a the mass of the whole object is equal to the sum of all its parts A. Law of Conservation of Energy B. Law of Conservation of Mass C. Law of Conservation of WeightHELP PLEASE ILL GIVE YOU BRAINLIEST OR WHATEVER AND LIKE 30 POINTS JUST PLEASE ANSWER ME Find the values of x and y by writing two equations and solving the system of equations. what are the three subsections of movement PLEASE HELP 5. Some consider the winter at Valley Forge in 1777 both a low point and a turning point in the American Revolution.Which BEST describes why the winter at Valley Forge might be considered a turning point?O A Baron Friedrich von Steuben successfully trained the Continental Army how to fight a European style war.OB The Continental Army was well fed and well rested.O c The hardships the soldiers faced helped them to develop the character necessary to win.OD George Washington was able to lobby Congress for more money and weapons which gave the Continental Army an advantage. Find the distance between (6,4) and (-6,-5) by using the distance formula Help me ASAP please!! explain the interrelationships between population, environment and development? 3. Which property of multiplication is shown by the equation14.y.1 = 14y?A. AssociativeC. CommutativeB. DistributiveD. Identity Which of the following is equivalent to 7a^4+3a^4 How do I solve 8x+5y=-20 ? The carpenter singing his, as he measures his plank or beam,The mason singing his, as he makes ready for work, or leaves off work;The boatman singing what belongs to him in his boat the deckhand singing on the steamboat deck;The shoemaker singing as he sits on his bench the hatter singing as he stands.I Hear America Singing,Walt WhitmanIn what three ways does Whitman use repetition in this passage from his poem?1.by repeating rhymed words2.by repeating singing 3.by including the workers first names 4.by starting each line with a type of worker5.by ending each line with what each person does while singing Will GIVE BRAINILEST TO WHO ANSWERSSubtract 9x^2+7x-29x 2 +7x2 from 8x-108x10. Choose the slope and y-intercept thatcorrespond with the graph.