lim ₓ→∞ (x+4/x-1)∧x+4​

Answers

Answer 1

It looks like the limit you want to find is

[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4}[/tex]

One way to compute this limit relies only on the definition of the constant e and some basic properties of limits. In particular,

[tex]e = \displaystyle\lim_{x\to\infty}\left(1+\frac1x\right)^x[/tex]

The idea is to recast the given limit to make it resemble this definition. The definition contains a fraction with x as its denominator. If we expand the fraction in the given limand, we have a denominator of x - 1. So we rewrite everything in terms of x - 1 :

[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \left(\dfrac{x-1+5}{x-1}\right)^{x-1+5} \\\\ = \left(1+\dfrac5{x-1}\right)^{x-1+5} \\\\ =\left(1+\dfrac5{x-1}\right)^{x-1} \times \left(1+\dfrac5{x-1}\right)^5[/tex]

Now in the first term of this product, we substitute y = (x - 1)/5 :

[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \left(1+\dfrac1y\right)^{5y} \times \left(1+\dfrac5{x-1}\right)^5[/tex]

Then use a property of exponentiation to write this as

[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \left(\left(1+\dfrac1y\right)^y\right)^5 \times \left(1+\dfrac5{x-1}\right)^5[/tex]

In terms of end behavior, (x - 1)/5 and x behave the same way because they both approach ∞ at a proportional rate, so we can essentially y with x. Then by applying some limit properties, we have

[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4} = \lim_{x\to\infty} \left(\left(1+\dfrac1x\right)^x\right)^5 \times \left(1+\dfrac5{x-1}\right)^5 \\\\ = \lim_{x\to\infty}\left(\left(1+\dfrac1x\right)^x\right)^5 \times \lim_{x\to\infty}\left(1+\dfrac5{x-1}\right)^5 \\\\ =\left(\lim_{x\to\infty}\left(1+\dfrac1x\right)^x\right)^5 \times \left(\lim_{x\to\infty}\left(1+\dfrac5{x-1}\right)\right)^5[/tex]

By definition, the first limit is e and the second limit is 1, so that

[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4} = e^5\times1^5 = \boxed{e^5}[/tex]

You can also use L'Hopital's rule to compute it. Evaluating the limit "directly" at infinity results in the indeterminate form [tex]1^\infty[/tex].

Rewrite

[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \exp\left((x+4)\ln\dfrac{x+4}{x-1}\right)[/tex]

so that

[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4} = \lim_{x\to\infty}\exp\left((x+4)\ln\dfrac{x+4}{x-1}\right) \\\\ = \exp\left(\lim_{x\to\infty}(x+4)\ln\dfrac{x+4}{x-1}\right) \\\\ =\exp\left(\lim_{x\to\infty}\frac{\ln\dfrac{x+4}{x-1}}{\dfrac1{x+4}}\right)[/tex]

and now evaluating "directly" at infinity gives the indeterminate form 0/0, making the limit ready for L'Hopital's rule.

We have

[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\ln\dfrac{x+4}{x-1}\right] = -\dfrac5{(x-1)^2}\times\dfrac{1}{\frac{x+4}{x-1}} = -\dfrac5{(x-1)(x+4)}[/tex]

[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1{x+4}\right]=-\dfrac1{(x+4)^2}[/tex]

and so

[tex]\displaystyle \exp\left(\lim_{x\to\infty}\frac{\ln\dfrac{x+4}{x-1}}{\dfrac1{x+4}}\right) = \exp\left(\lim_{x\to\infty}\frac{-\dfrac5{(x-1)(x+4)}}{-\dfrac1{(x+4)^2}}\right) \\\\ = \exp\left(5\lim_{x\to\infty}\frac{x+4}{x-1}\right) \\\\ = \exp(5) = \boxed{e^5}[/tex]


Related Questions

calculate the area of the following figure.​

Answers

Answer:

77 cm²

Step-by-step explanation:

The figure can be decomposed into two rectangles.

✔️Area of rectangle 1:

Area of rectangle 1 = length * width

length = 3.5 cm

width = 8 cm

Area of rectangle 1 = 3.5*8 = 28 cm²

✔️Area of rectangle 2:

Area of rectangle 2 = length * width

length = 14 cm

width = 3.5 cm

Area of rectangle 2 = 14*3.5= 49 cm²

✔️Area of the figure = 28 + 49 = 77 cm²

A rectangular board is 1400 millimeters long and 900 millimeters wide. What is the area of the board in square meters? Do not round your answer.

=__M

Answers

Answer:

1260000 millimeters

Step-by-step explanation:

You multiply 1400mm x 900mm and this is the correct answer.

Hope it helps c:

The area of the rectangular board which is 1400 millimeters long and 900 millimeters wide is 1.26 square meters.

What is the area of a rectangular board?

If x and y be the length and width of a rectangular board respectively, then the area of that rectangular board is xy square unit.

How to solve this problem?

Since 1000 millimeters = 1 meter.

i.e. 1 millimeter = 1/1000 meter.

Now, length of the board = 1400 millimeters = 1400/1000 meters = 1.4 meters

Width of the board = 900 millimeters = 900/1000 meters = 0.9 meter

Area of the board = 1.4 * 0.9 = 1.26 square meters.

Therefore, the area of the rectangular board which is 1400 millimeters long and 900 millimeters wide is 1.26 square meters.

Learn more about area here -

https://brainly.com/question/6843862

#SPJ2

Solve: 1/3a^2-1/a=1/6a^2

Answers

Step-by-step explanation:

there are two answers for a

Answer:

The ANSWER IS 1/6

Step-by-step explanation:

I need to know what goes in the periods rate total amount and total interest boxes in why

Answers

9514 1404 393

Answer:

periods: 4rate: 1%total amount: 598.35total interest: 23.35

Step-by-step explanation:

"Periods" will be filled with the number of years (1) times the number of periods per year (quarterly = 4). periods = 4

"Rate" is likely filled with the rate of interest divided by the number of periods per year. rate = 4%/4 = 1%

Then the total amount is found by ...

  total amount = principal × (1 + rate)^(periods)

  = 575 × (1.01^4) = 598.35

The total interest is the difference between this amount and the principal.

  total interest = total amount - principal

  = 598.35 -575 = 23.35

_____

We believe we have made reasonable assumptions regarding the intent of the columns in the table. Your best bet is to compare this problem to the worked examples in your curriculum materials.

If an author wanted to inform readers about the different types of advertisements, how would this shape his essay’s content and delivery? He would take an explanatory tone with readers to reveal the different categories of advertisements. He would take a factual tone to show readers why most advertising is exaggerated or even false. He would take a formal, technical tone telling readers about the amount of advertising they see every day without even noticing it half the time. He would take an amusing tone showing readers the worst advertisments ever created.

Answers

Answer:

a  He would take an explanatory tone with readers to reveal the different categories of advertisements

Step-by-step explanation:

a is formal and is the  best tone for the paper

Please help! Identify the recursive formula for the sequence 20, 28, 36, 44, . . . .
Answers below in picture:

Answers

Option A

Answered by GauthMath if you like please click thanks and comment thanks

A committee of 3 is to be selected randomly from a group of 3 men and 2 women.
Let X represent the number of women on the committee. Find the probability
distribution of X.

Answers

Total number of ways to select 3 people from the 5 total: 5!/(3! (5 - 3)!) = 10

• Number of ways of picking 0 women:

[tex]\dbinom20\times\dbinom33 = 1\times1 = 1[/tex]

• Number of ways of picking 1 woman:

[tex]\dbinom21\times\dbinom32 = 2\times3 = 6[/tex]

• Number of ways of picking 2 women:

[tex]\dbinom22\times\dbinom31 = 1\times3 = 3[/tex]

• Number of ways of picking 3 women: 0, since there are only 2 to choose from

Then X has the probability mass function

[tex]P(X=x) = \begin{cases}\frac1{10}&\text{if x=0}\\\frac6{10}=\frac35&\text{if }x=1\\\frac3{10}&\text{if }x=2\\0&\text{otherwise}\end{cases}[/tex]

A candidate running for public office receives 2,000 of the 8, 000 total votes cast from an election. Name the numerator and denominator
of the fraction that represents the candidate's fraction of the total votes.

Answers

Numerator: 2000
Denominator: 8000

Hope this helps lol

A class of kindergarteners is making get well cards for children in the houses how many different cards can be made from 2 shapes 4 card colors 3 colors of glitter and 8 colors of markers

Answers

Answer:

192

Step-by-step explanation:

Multiply all numbers together.

2 * 4 * 3 * 8 = 192

Answer:

it's 192 because you have to multiply all of the numbers to get 192

Use the unit circle to find tan 60°.
a. square root 3/3
c. 2 square root 3/3
b. square root 3/2
d. square root 3



Please select the best answer from the choices provided


A
B
C
D

Answers

the answer is d ( square root 3 )

tan = oposite / adjacent

tan 60° = √3 / 1

= √3

Find an odd natural number x such that LCM (x, 40) = 1400

Answers

Answer:

175.

Step-by-step explanation:

40 = 2*2*2*5

1400 = 2*2*2*5*5*5*7

So by inspection we have x = 5*5*7 = 175

Solve the function.
Plz Help!!

Answers

[tex]1\pm\sqrt{2}i[/tex]

Step-by-step explanation:

We already know that one of the roots is x = -4 so we can factor this out to get

[tex]x^3+2x^2-5x+12=(x+4)(x^2-2x+3)[/tex]

Using the quadratic equation on the 2nd factor, we find the roots are

[tex]x= \dfrac{2\pm\sqrt{(2)^2 - 4(1)(3)}}{2}=1\pm\sqrt{2}i[/tex]

Seth and Ted can paint a room in 5 hours if they work together. If Ted were to work by himself, it would take him 1 hours longer than it would take Seth working by himself. How long would it take Seth to paint the room by himself if Ted calls in sick

Answers

Answer:

Seth would need 10 hours to paint the room.

Step-by-step explanation:

Let's define:

S = rate at which Seth works

T = rate at which Ted works

When they work together, the rate is S + T

And we know that when they work together they can pint one room in 5 hours, then we can write:

(S + T)*5 h = 1 room.

We also know that Ted alone would need one hour more than Seth alone.

Then if Seth can paint the room in a time t, we have:

S*t = 1room

and

T¨*(t + 1h) = 1room

Then we have 3 equations:

(S + T)*5 h = 1

S*t = 1

T¨*(t + 1h) = 1

(I removed the "room" part so it is easier to read)

We want to find the value of S.

First, let's isolate one variable (not S) in one of the equations.

We can isolate t in the second one, to get:

t = 1/S

Now we can replace it on the third equation:

T¨*(t + 1h) = 1

T¨*( 1/S + 1h) = 1

Now we need to isolate T in this equation, we will get:

T = 1/( 1/S + 1h)

Now we can replace this in the first equation:

(S + T)*5h = 1

(S + 1/( 1/S + 1h) )*5h = 1

Now we can solve this for S

(S + 1/( 1/S + 1h) )= 1/5h

S + 1/(1/S + 1h) = 1/5h

Now we can multiply both sides by (1/S + 1h)

(1/S + 1h)*S + 1 = (1/5h)*(1/S + 1h)

1 + S*1h + 1 = 1/(S*5h) + 1/5

S*1h + 2 = (1/5h*S) + (1/5)

Now we can multiply both sides by S, to get:

(1h)*S^2 + 2*S = (1/5h) + (1/5)*S

Now we have a quadratic equation:

(1h)*S^2 + 2*S  - (1/5)*S -  (1/5h) = 0

(1h)*S^2 + (9/5)*S - (1/5h) = 0

The solutions are given by the Bhaskara's formula:

[tex]S = \frac{-(9/5) \pm \sqrt{(9/5)^2 - 4*(1h)*(-1/5h)} }{2*1h} = \frac{-9/5 \pm 2}{2h}[/tex]

Then the solution (we only take te positive one) is:

S = (-9/5 + 2)/2h

S = (-9/5 + 10/5)/2h = (1/5)/2h = 1/10h

Then Seth needs a time t to paint one room:

(1/10h)*t = 1

t = 1/(1/10h) = 10h

So Seth would need 10 hours to paint the room.

Use the Distributive property to solve this equation

-2(x-4)+8=2

Answers

Answer:

x=7

Step-by-step explanation:

-2(x-4)+8=2(remove brackets by multiplying with -2)

-2x+8+8=2(group like terms and simply)

-2x=2-16(change side change sign)

-2x = -14(divide both sides by -2)

x=7

generate a table of values for the equation y = -4.5x - 0.5. Use values for x from -2 to 2, increment by 1 in each row

Answers

Answer:

x = -2: y = 8.5

x = -1: y = 4

x = 0: y = -0.5

x = 1: y = -5

x = 2: y = -9.5

Step-by-step explanation:

We find the numeric values for the function from x = -2 to x = 2.

x = -2:

[tex]y = -4.5(-2) - 0.5 = 9 - 0.5 = 8.5[/tex]

x = -1:

[tex]y = -4.5(-1) - 0.5 = 4.5 - 0.5 = 4[/tex]

x = 0:

[tex]y = -4.5(0) - 0.5 = 0 - 0.5 = -0.5[/tex]

x = 1:

[tex]y = -4.5(1) - 0.5 = -4.5 - 0.5 = -5[/tex]

x = 2:

[tex]y = -4.5(2) - 0.5 = -9 - 0.5 = -9.5[/tex]

By examining past tournaments, it's possible to calculate the probability that a school wins their first game in the national college basketball tournament. Each school's rank going into the tournament is a strong indicator of their likelihood of winning their first game.

Find the linear regression equation that models this data.

Answers

The linear regression model which models the data is :

y = -6.41053X + 103.83509

Obtaining the regression equation could be performed using either the formula method or using technology (excel, calculator, online regression calculators )

Using technology :

• Enter the data into the columns provided ;

The regression equation obtained for the data is : y = -6.41053X + 103.83509

Where ;

Slope = -6.41053

Intercept = 103.83509

X = Rank

y = probability percentage

Hence, from the linear regression equation obtained, we could see that a negative linear relationship exists between rank and probability as implied from it's negative slope value.

Learn more on linear regression : https://brainly.com/question/12164389

Given the equation y/x = -6/7 the constant of variation is:

Answers

Answer:

[tex]{ \tt{ \frac{y}{x} = - \frac{6}{7} }} \\ { \tt{y = - \frac{6}{7}x }} \\ { \boxed{ \bf{constant = - \frac{6}{7} }}}[/tex]

Question 8 of 53
How much would $700 be worth after 8 years, if it were invested at 5%
interest compounded continuously? (Use the formula below and round your
answer to the nearest cent.)
A(t) = P•e^rt
A. $5887.12
B. $1044.28
C. $6432.11
D. $38,218.71

Answers

9514 1404 393

Answer:

  B. $1044.28

Step-by-step explanation:

Putting the given numbers into the given formula, we have ...

  A(8) = $700•e^(0.05•8) ≈ $1044.28

Ibrahim wants to give each of his six friends 1 2/3 candy bars. How many candy bars does he need to buy?

Answers

Answer:

10 candy bars

Step-by-step explanation:

Since each of his friends needs a candy bar, you need to multiply 6 and 1 ⅔ together.

First, convert 1 ⅔ into an improper fraction: this gives us ⁵⁄₃.

Next, multiply ⁶⁄₁ and ⁵⁄₃ together. To do this, you can visualize 6 as ⁶⁄₁ (which is the same thing). Now you have ⁶⁄₁ x ⁵⁄₃.

Simplify:

The 6 in the numerator and the 3 in the denominator cancel out. This gives us ²⁄₁ x ⁵⁄₁ , which is 2 x 5.

2 x 5 = 10

30 POINTS PLEASE HELP

Answers

Answer:

Answer:

Solution given:

f(x)=5x-3

let

y=f(x)

y=5x-3

interchanging role of x and y

x=5y-3

x+3=5y

y=[tex]\frac{x+3}{5}[/tex]

$o,

f-¹(x)=[tex]\frac{x+3}{5}[/tex]

we conclude that

f-¹(x)≠g(x)

Each pair of function are not inverses.

g(x)=x/5+3

let g(x)=y

y=x/5+3

interchanging role of x and y

x=y/5+3

x-3=y/5

doing crisscrossed multiplication

5(x-3)=y

y=5x-15

g-¹(x)=5x-15

So

g-¹(x)≠f-¹(x)

Each pair of function are not inverses.

PLEASE HELPPP ASAPPPPP

Answers

the answer is permutation !

Answer:

combination  91 ways

Step-by-step explanation:

This is a combination since order doesn't matter

Permutation are when order matter

14 choose 2 order doesnt matter

14*13

--------

2*1

91 different ways

The area of a rectangle is 3,878 square centimeters. If the rectangle has a width of 14 centimeters, what is its length?

Answers

Answer:

277 cm

Step-by-step explanation:

[tex]A=l*w\\3,878=l*14\\l=\frac{3,878}{14} \\l=277[/tex]

A test has 6 multiple choice questions , each with four possible answers . How man different answer keys are possible?

Answers

Answer:

24

Step-by-step explanation:

6 x 4 = 24

Answer:

Step-by-step explanation:

4⁶=4096

Please help, I really need this

Answers

9514 1404 393

Answer:

  (a) -- the correct choice is highlighted

Step-by-step explanation:

The units of specific heat tell you what quantities make up the ratio.

  [tex]\dfrac{390\text{ J}}{1\text{ kg$\cdot^\circ$C}}=\dfrac{-12.0\text{ J}}{0.012\text{ kg}\cdot\Delta T}\\\\\Delta T=\dfrac{-12.0}{0.012\cdot390}\ ^\circ\text{C}\approx-2.56\text{ $^\circ$C}[/tex]

The temperature will decrease by 2.56 C.

Supposed we saved 55$ and we saved 6$ each week what’s the total amount of t we will have after w weeks

Answers

Answer:

t=55+6w

Hope This Helps!!!

Rationalize the denominator of $\displaystyle \frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}$, and write your answer in the form\[
\frac{A\sqrt{2} + B\sqrt{3} + C\sqrt{7} + D\sqrt{E}}{F},
\]where everything is in simplest radical form and the fraction is in lowest terms, and $F$ is positive. What is $A + B + C + D + E + F$?

Answers

9514 1404 393

Answer:

  57

Step-by-step explanation:

Apparently, you want to simplify ...

  [tex]\displaystyle \frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}[/tex]

so the denominator is rational. It looks like the form you want is ...

  [tex]\dfrac{A\sqrt{2} + B\sqrt{3} + C\sqrt{7} + D\sqrt{E}}{F}[/tex]

And you want to know the sum A+B+C+D+E+F.

__

We can start by multiplying numerator and denominator by a conjugate of the denominator. Then we can multiply numerator and denominator by a conjugate of the resulting denominator.

  [tex]\displaystyle =\frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}\cdot\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{\sqrt{2} + \sqrt{3} - \sqrt{7}}=\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{2\sqrt{6}-2}\\\\=\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{2\sqrt{6}-2}\cdot\frac{\sqrt{6}+1}{\sqrt{6}+1}=\frac{(1+\sqrt{6})(\sqrt{2}+\sqrt{3}-\sqrt{7})}{10}\\\\=\frac{\sqrt{2}+\sqrt{3}-\sqrt{7}+2\sqrt{3}+3\sqrt{2}-\sqrt{42}}{10}=\frac{4\sqrt{2}+3\sqrt{3}-\sqrt{7}-\sqrt{42}}{10}[/tex]

Comparing this to the desired form we have ...

  A = 4, B = 3, C = -1, D = -1, E = 42, F = 10

Then the sum is ...

  A +B +C +D +E +F = 4 + 3 -1 -1 +42 +10 = 59 -2 = 57

The sum of interest is 57.

If y is 2,851, 1% of Y is

Answers

Excellent question, but let's rephrase it.

Suppose you have a square of surface area of 2851.

What would be a hundredth of such square?

What would be surface area of that hundredth.

Why hundredth? Because percent denotes hundredths cent is a latin word for hundred. You would usually encounter similar word that describes 100 years: century.

Well it is actually very easy. Just divide 2851 into 100 pieces and look at what is the area of one piece.

[tex]2851/100=285.1=y[/tex]

So a single piece has an area of 258.1.

Hope this helps. :)

what is the minimum number of students who must be enrolledin a universitt to guarantee that there are at least two students from the same country

Answers

Answer:

Being that there are 195 countries, there would have to be 390 students

Step-by-step explanation:

Find the critical numbers (x-values) of the function y equals 2 x to the power of 5 plus 5 x to the power of 4 minus 19. Enter your answers as a comma-separated list. Round answers to 2 decimal places, if necessary.

Answers

Answer:

[tex]x=0,x=-2[/tex]

Step-by-step explanation:

From the question we are told that:

[tex]y=2x^5+5x^4-19[/tex]

Generally the equation if differentiated is mathematically given by

[tex]y'=10x^4+20x^3-0[/tex]

Where

y'=0

[tex]10x^4+20x^3=0[/tex]

Factorizing,We have

[tex]x=0,x=-2[/tex]

Therefore

The critical points are

[tex]x=0,x=-2[/tex]

20 bottles make 1 fleece jacket how much do 200 make ​

Answers

10,because 20 times 10 = 200
Answer: 10 jackets


Step 1: Write an equation

Before we can write an equation, it’s important to acknowledge what we are trying to solve at this point in the problem.

We should create an equation that will bring us from 20 bottles to 200 bottles. This will tell us how many jackets we will have, since 20 bottles make 1 jacket. This will bring us our answer. Let’s write an equation, with 200 equaling 20 times an unknown number.

20x= 200

Step 2: Solve equation

Now let’s solve for x which will tell us how many jackets we will get. Let’s solve now by isolating x. We need to divide each term by 20.

20x= 200
x= 10


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in this sermon John Winthrop writes both the consequences and benefits of following, or not following,"The lord our God" how does he see this as affecting the colony? Which of the following ideas was theresult of Jean-Jacques Rousseauexpanding on the social contract theoryfrom Locke's ideas?A. allowing the king to rule by divine rightB. letting the people decide on their own sovereignty C. allowing the monarchy to decide on the welfare of the people Qu aspectos consideras relevantes dentro de una mega tendencia?Ayuda porfavorr It is often the case that people with an Eating Disorder may change their diagnosis. For example, a person may first be diagnosed with Anorexia Binge Purge Subtype and progress to Bulimia Nervosa. This shift in diagnosis is referred to as _________________. a. Dystonic diagnosis b. Diagnostic Crossover c. Disordered Eating d. Syntonic Diagnosis PRESS THE PHOTO NEED HELP!!! 30 POINTS Explain the effects of force giving example The graph of h(x) = (x - 3)2 is a translation of thegraph of f(x) .. blank by. Blank units. What is the domain of the function graphed below? what is efficiency of a machine? what is the formula of water According to Zimmels (1983), the sizes of particles used in sedimentation experiments often have a uniform distribution. In sedimentation involving mixtures of particles of various sizes, the larger particles hinder the movements of the smaller ones. Thus, it is important to study both the mean and the variance of particle sizes. Suppose that spherical particles have diameters that are uniformly distributed between 0.02 and 0.08 centimeters. Find the mean and variance of the volumes of these particles. (Recall that the volume of a sphere is (4/3) r3) Round your answers to four decimal places.E(Y)= ___ x105 cm3V(Y) = ___ x109 can somene explain this to me please? 6. Technology can be used in various fields of __________A. educate B. education C. educator D. educated7. Space _________ plays an important role in the development of science.A. exploration B. exploraty C. explorers D. explore8. The ________ of steam engine has become a revolution in worlds transportation.A. invent B. invention C. inventor D. invented9. There are several aspects that need to be _________ in your project.A. improvement B. improving C. improved D. improve10. Our first try on the new medicine was ________, so we needed to make a lot of changes.A. successful B. succeed C. unsuccessful D. unsucceed11. A _______ is a scientist who studies the earth, including the origin and history of the rocks and soil of which the earth is made. A. geology B. geologist C. geography D. geographic12. We need ________ evidence to confirm the existence of aliens.A. science B. scientist C. scientific D. sci-fi13. The invention of the Internet ________ humans life.A. transform B. transformer C. overslept D. sleptover14. She came to class late today. She __________.A. oversleep B. sleepover C. overslept D. sleptover15. She is going to receive a _________ for her new invention.A. patent B. certificate C. degree D. lience A solution is made by dissolving 0.565 g of potassium nitrate in enough water to make up 250. mL of solution. What is the molarity of this solution? Please explain and show work. Name 3 Disadvantages of diversifying the local economy and revaaluate the role of the private sector. ANSWER PLEASE simplify 2n(n2+2n+3)-3(2n+7) and (-4n2-3n-8)+2(n+9) predict what happen to the human and the plants if the transport system are affected 8 cm 10 cm 15 cm surface area of a rectangle Super Garage was started on June 1 by Mr. Peter Thomson . A summary of June transactionsis presented below.June 1. Invested $25,000 cash to start the garage.2. Purchased repair equipment for $5,000 cash.4. Paid $500 cash for the space rent.4. Hired an employee5. Paid $700 for a one-year fire insurance policy.6. Received $10000 in cash from customers for repair service.10. Provided repair service on account to customers $1750.21. Collected cash of $5000 for services provided on June 6.27. Withdrew $1,000 cash for personal use.30. Paid employee salaries $3,000.30. Received an electricity bills $170.Required:i. Journalize the transactionsii. Post and balance the transactions to ledger accounts How Can We Obtain Divorce Certificate in Pakistan?