Find the value of n that satisfies 2(n+1)! + 6n! = 3(n+1), where $n! = n\cdot (n-1)\cdot (n-2) \cdots 2\cdot 1$.

Answers

Answer 1

Answer:

[tex]n = 5[/tex]

Step-by-step explanation:

Given

[tex]2(n+1)! + 6n! = 3(n+1)![/tex]

Required

Find n

Simplify (n + 1)!

[tex]2(n+1)*n! + 6n! = 3(n+1)*n![/tex]

Factorize

[tex]n![2(n+1) + 6] = 3(n+1)*n![/tex]

Divide both sides by n!

[tex]2(n+1) + 6 = 3(n+1)[/tex]

Open brackets

[tex]2n + 2 + 6 = 3n + 3[/tex]

[tex]2n + 8 = 3n + 3[/tex]

Collect like terms

[tex]2n - 3n = 3 -8[/tex]

[tex]-n =-5[/tex]

Multiply both sides by -1

[tex]n = 5[/tex]


Related Questions

Consider a person from birth to age 18 and the height of that person each of the years between birth and age 18. Which best describes the variables of age and height?


no correlation

positive correlation

negative correlation

Answers

Answer:

Seems to be no correlation at all.

Answer:

anges between -1 and +1 and quantifies the direction and strength of the linear association between the two variables. The correlation between two variables can be positive (i.e., higher levels of one variable are associated with higher levels of the other) or negative (i.e., higher levels of one variable are associated with lower levels of the other).

The sign of the correlation coefficient indicates the direction of the association. The magnitude of the correlation coefficient indicates the strength of the association.

For example, a correlation of r = 0.9 suggests a strong, positive association between two variables, whereas a correlation of r = -0.2 suggest a weak, negative association. A correlation close to zero suggests no linear association between two continuous variables.

It is important to note that there may be a non-linear association between two continuous variables, but computation of a correlation coefficient does not detect this. Therefore, it is always important to evaluate the data carefully before computing a correlation coefficient. Graphical displays are particularly useful to explore associations between variables.

The figure below shows four hypothetical scenarios in which one continuous variable is plotted along the X-axis and the other along the Y-axis.

Step-by-step explanation:

the exact volume is ___ pi cm^3

Answers

Answer: 54π

Step-by-step explanation: volume = π · r^2 · h

Find the area of this parallelogram. Be sure to include the correct unit in your answer. 14 m 6 m 8 m​

Answers

Answer:

question what number is on the top or bottom of the parallelagram

Step-by-step explanation:

and what is on the left or right of the parallorgram I need to know to help you

The area of the parallelogram will be 98 square feet.

What is a parallelogram?

It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal.

Let h be the perpendicular distance between the parallel side and b be the length of the base of the rectangle.

Then the area of the parallelogram will be given as,

Area of parallelogram = b x h

The length of the base of the parallelogram is 14 feet, and the value of h is 7 feet.

Then the area of the parallelogram will be

Area pf parallelogram = 14 x 7

Area pf parallelogram = 98 square feet

Then the area of the parallelogram will be 98 square feet.

The complete question is given below.

More about the parallelogram link is given below.

https://brainly.com/question/1563728

#SPJ2

Which expression gives the solutions of -5 + 2x^2 = -6x?

Answers

Answer:

the correct answer is: D

80 pts !!

Which of the following expressions can you multiply using the FOIL Method? Check all that apply.

A. (x - 1) (x^2 + 2x + 5)
B. (6x - 5) (x + 4)
C. 3x (2x^2 + 5x - 4)
D. (x + g) (x - h)

Answers

Answer:

I think B,D is the best answer.

Answer:

B and D.

Step-by-step explanation:

B and D,

(6x - 5)((x + 4) =

6x * x +  6x*4 -  5* x - 5 * 4

   F           O         I          L

What is the axis of symmetry for y=8x2+2x−6?

Answers

Answer:

y=2( x - [tex]2^{2}[/tex])-2

Step-by-step explanation:

Use the vertex form,  y=a(x - [tex]h^{2}[/tex])+k to determine the values of A,H,K

a=2

h=2

k=   -2

Since the value of a is positive the parabola opens up.

Find the vertex (h,k)

(2, -2)

Find p the distance from the vertex to the focus.

[tex]\frac{1}{8}[/tex]

Find the focus

(2,  -[tex]\frac{15}{8}[/tex])

Find the axis of symmetry by finding the line that passes through the vertex and the focus.

x=2

 

PLS HELP IF U DONT KNO DONT ANSWER PLS

Answers

Answer: A, I think

Step-by-step explanation:

Answer:

Step-by-step explanation:

→ Thanks ← God bless keep ur head up king/queen and have a good rest of ur day

I need this answer please

Answers

Answer:

D

Step-by-step explanation:

The pattern is clear

4x+10 in which x is how ever many games are rented at once. So, 4(1)+10 = 14

Same for 3x+15

Marcy mailed a package weighing1.337 kilograms. How does the value represented by the 3 in the tenths place compare with the value represented by the 3 in the hundredths place?

Answers

If a number has a decimal point , then the first digit to the right of the decimal point indicates the number of tenths. The second digit to the right of the decimal point indicates the number of hundredths.  

In this case the .3 indicates 3/10ths of a kilogram.  or 300 grams!

In the other case 0.03 indicates 3/100ths of a kilogram or 30 grams!

So, to compare the two:

the tenths decimal is 10 times bigger than the decimal in the next spot (hundredths)

Hope this helps!

Chris examines a salt crystal under his microscope. He finds that it is a cube with each side length 6
millimeters.

Answers

Answer:

if each side is 6 millimeters and its a cube what is 6x4

Step-by-step explanation:

Find the surface area of the figure below. Round your answer to the nearest hundredth if necessary.
6 in
8 in
7 in
7 in
8 in
292 in

347 in
236 in?
Od
391 in

Answers

Answer:

The surface area of the shape is 292 in^2

Step-by-step explanation:

Here, we want to find the surface area of the cuboidal shape

Mathematically, the area of a cuboid can be calculated using the formula;

A = 2(lb + lh + bh)

where l is the length which is 7 inches

b is the breadth which is 6 cm

h is the height which is 8 cm

Substituting these values, we have

A = 2((8 * 6) + (7 * 6) + (8 * 7))

A = 2(56 + 42 + 48)

A = 2 * 146

A = 292 in^2

Find the value of x and y that will make each quadrilateral a parallelogram.​

Answers

Step-by-step explanation:

2x+5=3x-12

or, 2x-3x=5-12

or, -x= -7

i.e X=7

again

y+4=3x+2

or, y+4=3*7+2

or, y+4=21+2

or, y+4=23

or, y =23-4

i.e y = 19

hence, the value of X is 7 and y is 19

Please third time asking I’ll mark brainliest

Answers

Answer: A≈440.44

Step-by-step explanation:

Answer:

1,536

Step-by-step explanation:

i calculated it

a gping out if bisinuess sale has the entire store marked 80./. off

Answers

Answer:

huh- So lemme get this straight if a dollar tree (where I live) goes out of business I can buy it for like 20 cents??? AWESOME. I'll do that.

Step-by-step explanation:

Find the slope of the line
5x - 5y = 7​

Answers

slope of this line is 1....

The ages of customers at a store are normally distributed with a mean of 45 years and a standard deviation of 13.8 years.
(a) What is the z-score for a customer that just turned 25 years old? Round to the nearest hundredth.
(b) Give an example of a customer age with a corresponding z-score greater than 2. Justify your answer.
Best answer gets brainliest!

Answers

The Standard Normal distribution follows a normal distribution and has mean 0 and ... z = s. Example. Find the z-score corresponding to a raw score of 132 from a ... be less than a given value, greater than a given value, or in between two values. ... P(z < 2.37). Solution. We use the table.

ANSWER BRAINLIEST:

Kim asked 6 friends how many siblings they had. The responses were: 0, 3, 2, 1, 1, 2, 3.

Find the MEAN ABSOLUTE DEVIATION (MAD) of the responses.

Answers

Answer:

number 1 will be the Mean absolute deviation

Help please will give brainiest!
Write the equation of the line in Slope-Intercept form.

Answers

Answer:

Y=-2/3+4

Step-by-step explanation:

The slope of the equation can be solved with

2-4/3-0 y2-y1 divide by x2-x1 which gives 3/2 and the y intercept the point at which the slope hits the y intercept which is 4. Also the slope is negative as it’s pointed downwards.

Getting the slope:

m=[tex](y_1 - y_2 )/(x_1 - x_2)[/tex]

Using this formula, the slope is calculated to be -2/3

To find intercept, plug in a point value into equation and solve.

Intercept = 4

Total equation: y=-2/3x + 4

​  

 

​  

 

 

An event planner can set up 6 tables in 30 minutes. How many tables can the event planner set up in 4.5 hours?

Answers

First convert 4.5 hours to minutes

4.5 hours = 270 minutes

6:30 = ?:270

Divide 270 and 30

270/30 = 9

Then multiply 6 and 9

9*6 = 54

The event planner can set up 54 tables in 4.5 hours(270 minutes)

54 tables

Pls help
Pls help
Pls help

Answers

Answer:

Step-by-step explanation:

this will be the outter circle minus the inner circle for the area of the sidewalk

area of circle = [tex]\pi[/tex][tex]r^{2}[/tex]

[tex]\pi[/tex][tex]11^{2}[/tex] = 380.1327

[tex]\pi[/tex][tex]9^{2}[/tex] = 254.469

380.1327 - 254.469 =125.6637062[tex]m^{2}[/tex]

PLS HELP ME THIS IS Probability (Single event) PLS HELP ME

Answers

Answer:

Hi! The answer to your question is D. 7/6

Step-by-step explanation:

☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆

☁Brainliest is greatly appreciated!☁

Hope this helps!!

- Brooklynn Deka

The cost of electricity is obtained as follows: A fixed charge of $(a), rent of a meter $(b) and a charge of (c) cents for unit of electricity supplied Determine the total cost of using n units of electricity.

Answers

Answer:

$(a + b) + cn cent

Step-by-step explanation:

Given :

Fixed charge = $a

Rent of a meter = $b

Charge per unit of electricity = c cents

The total cost of using n units of electricity :

For n units of electricity ;

Fixed charge is paid once

Meter rent is paid once

The cost of electricity = (number of units * cost per unit) = (n * c) = nc cents

Total cost of n units of electricity :

$(a + b) + cn cent

Select all the expressions equivalent to: (4^5)⋅4^3 Group of answer choice 2^14 4^12 2^16 16^8 4^8 16^4

Answers

Answer:

Choices given as [tex]2^{16}, 4^8[/tex] and [tex]16^4[/tex] are correct.

Step-by-step explanation:

Given expression is,

[tex](4^5)(4^3)[/tex]

By applying law of exponents in the given expression,

[tex](4^5)(4^3)=4^{5+3}[/tex]

            [tex]=4^8[/tex]

[tex](4^5)(4^3)=(2^2)^5(2^2)^3[/tex]

            [tex]=(2^{2\times 5})(2^{2\times 3})[/tex]

            [tex]=2^{10}\times 2^6[/tex]  

            [tex]=2^{16}[/tex]

            [tex]=(2^4)^4[/tex]

            [tex]=(16)^4[/tex]

Therefore, choices given as [tex]2^{16}, 4^8[/tex] and [tex]16^4[/tex] are correct.

A right triangle has legs that are 18 centimeters and 27 centimeters long
What is the length of the hypotenuse?

__cm

Answers

Answer:

32

Step-by-step explanation:

use the formula [tex]a^{2} +b^{2} =c^{2}[/tex] instead of a put 18 and instead of b put 27 it should look something like this [tex]\sqrt{18^{2}+27^{2} }[/tex] which is 32


Please help worth 30 points it’s geometry.

I have a grade check tmr and I have an F in geometry please help!!!

Answers

That would be a 45 degree angle

Answer:

everything is in the photo

Simplify the expression.
Please I need help
Thank you

Answers

You cant simplify further than that. Look at the file attached to this.

EDIT:

If that was wrong, try,

= -8x

enter the value for x that makes the equation 4x-2+3x-7 true

Answers

Answer:

I think the answer is

[tex]x = \frac{9}{7} [/tex]

Step-by-step explanation:

Reason :

[tex]4x - 2 + 3x - 7 = 0 \\ collect \: like \: terms \\ 4x + 3x - 7 - 2 = 0 \\ 7x - 9 = 0 \\ 7x = 9 \\ x = \frac{9}{7} [/tex]

Therefore

[tex]x = \frac{9}{7} [/tex]

If f(x) =2x+4 and g(x)=1-x, then which of the following represents y=f(x)+g(x)?

Answers

Answer:

y = x +5

Step-by-step explanation:

2x +4 + 1-x = x +5

hope this helps

What two numbers multiply to +34 and add to -19

Answers

Answer:

17 * 2 = 34

-10 + (-9) = -19 or -29 + 10 = -19

Step-by-step explanation:

For the first question, divide 34 * 2 and you get 17, DOUBLE CHECK YOUR ANSWER!

17*2 = 34 ✔

For the second, mess around with a few numbers add +10 and -29,  COUNT DOWN from 10 and -29.

since + + + = + then - + - = -

if 10+9=19 then do the same with -

-10 + (-9) =-19

~R3V0

Answer:

-17, -2 work for both of them

Step-by-step explanation:

I need help please!!

Answers

It looks like it’s b. Triangle 2
Other Questions
GIVING BRAINLIEST!!!!Sam really wanted to try out for the community play, but he was nervous. He wasn't sure he would be good at it. His mother told him to try it before giving up. "Nothing ventured, nothing gained," she told him.What is the meaning of the phrase nothing ventured, nothing gained as it is used in this sentence?A) Adventure is only for successful people.B) It's okay to be nervous about performing in a play.C) If you want something, ask for help from a friend.D) You don't gain anything if you don't try. Based on this cladogram, which statement best describes relationships among millipede onders? F. Stemmlullda is more dosely related to Verochesa tran Peniciuata is to Merocheta. G.Sprostreptida is more closely related to Glonenda than Sphaerctheriida is to Glomerida. H. Polyzoniida is more closely related to Glomeridesmida than Spheeratheriida is to GlamandesmidaJ. Merocheta is more closely related to Glomeridesmida than Glomerda is to Glamandesmida. A sample of sulfur dioxide occupies a volume of 6052 mL at 352 K and 892 mm Hg. What volume will the sulfur dioxide occupy at STP? Major authors of the Beat Generation included ____. Select all that apply. HELP PLEASE!Life Science:Why does Nitrogen have to be continually converted into other compounds in the Nitrogen Cycle? An engineer is designing a fountain that shoots out drops of water. The nozzle from which the water is launched is 3 meters above the ground. It shoots out a drop of water at a vertical velocity of 14 meters per second. Function h models the height in meters, h, of a drop of water t seconds after it is shot out from the nozzle. The function is defined by the equation h(t)=5t2+14t+3. How many seconds until the drop of water hits the ground? 16. On June 8, 1992, a crop circle with an 18-meter radius was found in a wheat field near Szekesfehervar,43 miles southwest of Budapest, Find its circumference,a. 112.06b. 113.04 mC, 124,45 md116,34 m I dont know this and I need help its due tomorrow just got it today I need to know what the question is asking please help The dimensions of a triangular prism are shown in the diagram.What is the volume of the triangular prism in cubic centimeters?A1,360 cm3BCD408 cm31,632 cm3816 cm3 Answer the question in the picture? 23) Atlanta Olympic planners were critized for the lack of infrastructure. What is "infrastructure"?A) Roads and bridgesB) Safety and policeC) Housing developmentsD) Sales and advertising SHOW WORK FOR BRAINLISTA $55 sweater is on sale for 20% off. Today only, you can take an additional 10% off the sale price. How much does the sweater cost today? the sum of 4 and 6 times a number z Select all the equations where r 3 is a solution. One way for an author to entertain a reader is toa)include some humor.b)suggest a way to act.c)quote an expert opinion.d)recommend a way to think. Victor drew trapezoid PQRS on acoordinate plane. The coordinates of eachvertex are:P(8,4) Q(10, 4) R(13, -1) S(8, -1)tionWhat is the length, in units, of side PS?A. 2B. 3C. 4D. 5 Compose a paragraph response thatexamines one of the claims discussed in the discussion activity today. Examineand support this claim using relevant and sufficient evidence found in thetext. "The Immortal Life of Henrietta Lacks" What is one disadvantage of hydroelectric energy? PLEASE HELP I FAILED DIS