Mathematics Middle School

Organize the following expressions from greatest to least by number of terms:
I. x + 2xyz
II. 3x + y + z
III. 2x2y + x2 − 3x + 4
IV. 9x2yz

Answers

Answer 1
the order is III, II, I, IV
Answer 2

Answer:

[tex]2x^2y + x^2 - 3x + 4~ (4)>3x + y + z ~(3)>x + 2xyz ~(2)>9x^2yz~ (1)[/tex]  

Step-by-step explanation:

We are given expressions in the question.

Term in an expression:

Each expression constitute terms.A term can be a number, a variable, or a constant multiplied by a variable or variables.Each term in an algebraic expression is separated by a + sign or - sign.

We need to find the number of terms in each expression:

1)

[tex]x + 2xyz\\\text{Number of terms}= 2[/tex]

2)

[tex] 3x + y + z\\\text{Number of terms}= 3[/tex]

3)

[tex]2x^2y + x^2 - 3x + 4\\\text{Number of terms} = 4[/tex]

4)

[tex]9x^2yz\\\text{Number of terms} = 1[/tex]

Arranged  from greatest to least by number of terms:

[tex]2x^2y + x^2 - 3x + 4~ (4)>3x + y + z ~(3)>x + 2xyz ~(2)>9x^2yz~ (1)[/tex]

Related Questions

for every pound a company spends on advertising it spends £0.64 on its websites. express the amount spent on advertising to the amount on its website it's website as a ratio it's in its simplest form

Answers

The ratio expression is £ 1.00 : £0.64 =  100:64
                                       = 25:16

Solution:

we are given that

For every pound a company spends on advertising it spends £0.64 on its websites.

we have been asked to express the amount spent on advertising to the amount on its website it's website as a ratio it's in its simplest form.

We can find the required ratio as below

[tex]Ratio=\frac{1}{0.64} \\ \\ Ratio=\frac{100}{64} \\ \\ Ratio=\frac{25}{16} \\[/tex]

Hence the required ratio is 25:16.

According to the Transitive Property of Congruence: If CD≅EF and EF≅GH, then _____


A. CD≅EF

B. EF≅EF

C. CD≅GH

D. EF≅GH

If you're reading this the answer is C

Answers

Transitive Property of Congruence. the answer is C.

Answer:

The answer is the option C

CD≅GH

Step-by-step explanation:

we know that

The Transitive Property of Congruence states that

If [tex]a=b[/tex] and [tex]b=c[/tex]

then

[tex]a=c[/tex]

In this problem we have

CD≅EF  and EF≅GH

therefore

CD≅GH -------> by Transitive Property of Congruence

A machinist creates a washer by drilling a hole through the center of a circular piece of metal. If the piece of metal has a radius of x + 7 and the hole has a radius of x + 6, what is the area of the washer?

Answers

The area of the washer (which is a circle, but the inner part cut out) is given by:
[tex]A_c = \pi r^2[/tex]

Now, we need to find the radius of the entire metal circle which the hole was drilled on:
[tex]R_w = (x+7) - (x+6) = 1[/tex]

Plug it in to find the area of the metal plate:
[tex]A_p = \pi (1)^2 = \pi [/tex]

Now, you subtract the area of the hole from the area of the plate. The area of the hole will be:
[tex]A_h = \pi (x+6)^2[/tex]
[tex]A_h = \pi (x^2+12x+36) =  [/tex]

Subtract the area of the hole from the metal plate to get:
[tex]A_w = \pi - (\pi x^2+12 \pi x+36 \pi) = \pi x^2+12 \pi x -35 \pi[/tex]

That's your answer, although it looks wrong because not much information was provided. 

Harry’s pizzeria is having a sale on medium and large pizzas. Medium pizzas are 10 inches in diameter and cost $7.99. Large pizzas are 14 inches in diameter and cost $14.99 Which size pizza is the better deal? Explain

Answers

Area = pi * r^2
.
A pizza with a 7-inch diameter has a radius of 3.5 inches.
Area = pi*3.5^2 = 38.48 sq. in.
.
A pizza with a 14-inch diameter has a radius of 7 inches.
Area = pi*7^2 = 153.93 sq. in.

.
The smaller pizza costs $5 = 500 cents, so it costs 500/38.48 = about 13 cents per sq. in.
.
It costs $12 = 1200 cents, so it costs 12/153.93 = about 8 cents per sq in.
.
The larger pizza is a better buy in terms of the cost per sq. in.
.
Done, hope that helped
The pizza that is the better deal is Large.

Medium Pizza : 
A^m = (3.14)*(5)^2
A^m= 78.5in^2
$7.99 / 78.5in^2 = $.10/1in^2

Large Pizza :
A^l = (3.14)*(7)^2
A^l = 153.86in^2
$14.99/153.86in^2 = $.09/1in^2


A square has an area of 49 square inches. Explain how to find the perimeter of the square.

Answers

It is a square, so you know the sides are equal. You also know that 49 is a squared number. so you do 49 square rooted and you get 7. the perimeter is adding all the side lengths. So you take 7 and multiply it by 4 since a square has 4 sides. and u have your perimeter. 28!

You are a farmer and want to spend under $35,000 on farm equipment. You need a hay bailer that costs $6,250 and several plowing disks cost $2,500 each. Write an inequality that models how many plowing disks could be purchased within your budget. What is the maximum number of plowing disks you can buy?

Answers

Inequality: $6,250+$2,500p > $35,000

Maximum plowing disks: 10 which would cost you $31, 250

Answer:

A) 2,500x + 6,250 < 35,000; 11 plowing disks

Step-by-step explanation:

Figure 1 is dilated to get Figure 2.

What is the scale factor?

Enter your answer, in simplest form, in the box.

Answers

I believe the answer is 2.4, because 24/10= 2.4. To check this answer, multiply 10 by 2.4. :) 

140 fluid ounces increased by 45%

Answers

Hello!

"Increase" means to add. We must find out what 45% of 140 fluid ounces is, and to do that we must first convert the percentage to a decimal and then multiply it by the amount of fluid ounces.

I know, that's probably a lot to take in! :D

45% ÷ 100 = 0.45 as a decimal

0.45 × 140 = 63

Add this to the amount of fluid ounces:

140 + 63 = 203

Final Answer:

203 fluid ounces.
Multiply it by 1.45 and it should work.

Chris is making a poster for Bike Safety Week. The diameter of circle A is 14 in.

If the area of circle B is the area of circle A, what is the area of circle B? (Use 3.14 for .)

Answers

Answer:

30.772 in2.

Step-by-step explanation:

First, find the radius of circle A.

* in picture*

Next, use the formula and the radius of circle A to find the area of circle A.

*in picture*

Last, multiply the area of circle A by  to find the area of circle B.

*in picture*

Therefore, the area of circle B is 30.772 in2.

31000 people attended a ballgames at a stadium that offers two kinds of seats; The day's receipts were $200000. How many people paid $14.00 for reserved seats, and how many paid$5.00 for general admission?

Answers

x= # of reserved seating
y= # of general admission

QUANTITY EQUATION:
x + y= 31,000

COST EQUATION:
14x + 5y= $200,000

STEP 1:
solve for either variable in quantity equation
x + y= 31,000
subtract both sides by y
x= 31000 -y


STEP 2:
substitute x=31000-y in cost equation
14x + 5y= $200,000

14(31000-y) +5y= 200000
434000 -14y + 5y= 200000

434000 - 9y= 200000
add 9y to both sides

434000= 200000 + 9y
subtract 200000 from both sides
234000= 9y

divide both sides by 9
26,000= y general admission


STEP 3:
substitute y answer in either equation
14x + 5y= $200,000
14x + 5(26000)= 200000
14x + 130000= 200000
14x= 70000
x= 5,000 reserved seats


CHECK:
14x + 5y= $200,000
14(5000) + 5(26000)= 200000
70000 + 130000= 200000
200000= 200000


ANSWER: There were 5,000 reserved seats and 26,000 general admission seats.

Hope this helps! :)
Final answer:

To solve this problem, we can use a system of equations to find the number of people who paid $14 for reserved seats and the number of people who paid $5 for general admission.

Explanation:

To solve this problem, we can use a system of equations. Let's say the number of people who paid $14 for reserved seats is 'x', and the number of people who paid $5 for general admission is 'y'.

We know that the total number of people who attended the ballgame is 31,000, so we can write the equation:

x + y = 31,000

We also know that the total receipts from the day were $200,000, so we can write another equation:

14x + 5y = 200,000

Now we can solve this system of equations to find the values of 'x' and 'y'.

Multiplying the first equation by 5, we can eliminate 'y' by subtracting the second equation from it:

5x + 5y = 155,000

-(14x + 5y = 200,000)

Simplifying, we get:

-9x = -45,000

Dividing both sides of the equation by -9, we find that 'x' = 5,000.

Substituting this value back into the first equation, we can solve for 'y':

5,000 + y = 31,000

Simplifying, we get 'y' = 26,000.

Therefore, 5,000 people paid $14 for reserved seats and 26,000 people paid $5 for general admission.

Number 14
I need help with this

Answers

n is five more than twelve should be n=12+5 the example out the 5 in the wrong side of the equation

A ________ is a monomial or the sum or difference of two or more monomials. Base, polynomial, linear term,quadratic equation

Answers

The answer is:

 "A polynomial is a monomial or the sum or difference of two or more monomials".

 By definition, the terms of a Polynomial Function have the form ax^n, where "n" is a natural number. 

 To classify a polynomial, you must count the number of its terms. For example:

 5x²-2x  (This is a binomial, because it is formed by two terms).
 x³-3x+1 (This is a trinomial, because it has three terms):

 To identify the degree of a polynomial, you must see the term which has the highest exponent. For example, the degree of following polynomial is 2.

 4x²-x+3 

 The degree of this polynomial is 3:

 x³+2x²-x+10

What does the y-intercept have to do with the graph?

Answers

It gives the other half of the coordinates.
Ex:(3, 6)
The y is the 6 the 6th number up the line.

Principle = $15,500 Interest Rate = 8.75% Time = ? Years Simple Interest = $5425.00

Solve for the Time in Years

Answers

We must find time by using the simple interest formula:

I = P x i x t

I is the interest
P is the total principal 
i is the rate of interest per year
t is the total time in years

In this example, when we plug our known values in, our formula looks like this: 

t = [tex] \frac{I}{i*p} [/tex]

t = [tex] \frac{5425}{0.0875 * 15500} [/tex]

t = 4

So time (in years) would be 4 years. 

PLEASE HELP ME!!!!!!!!!!! FAST PLEASE ITS URGENT!!!!!!!! WILL GIV BRAINLIEST!!!

The golf scores for the 32 members of the Belmont Country Club were 108, 89, 74, 115, 92, 86, 103, 107, 94, 89, 111, 78, 116, 82, 99, 107, 74, 78, 101, 93, 85, 98, 109, 82, 83, 105, 91, 106, 97, 84, 92, 96. Which histogram correctly shows the frequency distribution of the scores using ten-point intervals?

Answers

Histogram options for golf scores: (a) 3,9,8,9,2; (b) 5,7,10,7,4; (c) 4,8,9,8,3; (d) 5,8,9,8,5. Correct choice (d) accurately represents the frequency distribution of scores in ten-point intervals.

To create a histogram with ten-point intervals for the given golf scores, we need to organize the scores into ranges and determine the frequency of scores within each range. Let's examine each option:

a. 70-80: 3 scores, 80-90: 9 scores, 90-100: 8 scores, 100-110: 9 scores, 110-120: 2 scores.

b. 70-80: 5 scores, 80-90: 7 scores, 90-100: 10 scores, 100-110: 7 scores, 110-120: 4 scores.

c. 70-80: 4 scores, 80-90: 8 scores, 90-100: 9 scores, 100-110: 8 scores, 110-120: 3 scores.

d. 70-80: 5 scores, 80-90: 8 scores, 90-100: 9 scores, 100-110: 8 scores, 110-120: 5 scores.

The correct histogram is option (d) with scores in the 70-80, 80-90, 90-100, 100-110, and 110-120 ranges having frequencies of 5, 8, 9, 8, and 5, respectively. This accurately represents the distribution of golf scores in ten-point intervals among the members of the Belmont Country Club.

Kade makes 5/6 cup salad dressing. He uses 2/3 cup dressing on a salad. How much salad dressing is left

Answers

To solve [tex] \frac{5}{6} - \frac{2}{3} [/tex], we need to find a common denominator. If we multiply [tex] \frac{2}{3} [/tex] by [tex] \frac{2}{2} [/tex], we get [tex] \frac{4}{6} [/tex]. The reason we can do this is because two over two is really just equivalent to 1, and multiplying a number times one equals the original number. So if you're subtracting  [tex] \frac{4}{6} [/tex] from [tex] \frac{5}{6} [/tex], you have


[tex] \dfrac{5}{6} - \dfrac{4}{6} = \dfrac{5-4}{6} = \dfrac{1}{6} \ cups[/tex].


Kade has 1/6 cup of salad dressing left after using some on a salad. We found this by converting 2/3 cup to 4/6 cup and then subtracting it from the 5/6 cup he initially had.

To find out how much salad dressing Kade has left after using some on a salad, we need to subtract the amount used from the total amount he made. Kade made 5/6 cup of salad dressing and used 2/3 cup on a salad. To perform the subtraction, both fractions need a common denominator. The smallest common denominator for 6 and 3 is 6. The fraction 2/3 can be converted to 4/6 so that both fractions have the same denominator. Now we can subtract:

Convert 2/3 cup to 4/6 cup (Since 3*2 = 6, and 2*2 = 4).Subtract 4/6 cup from 5/6 cup: 5/6 - 4/6 = 1/6 cup.

Hence, Kade has 1/6 cup of salad dressing left after using it on the salad.

The hypotenuse of a right triangle is 37 mm. One leg of the right triangle is 12 mm. What is the length of the other leg? 30 mm 35 mm 40 mm 47 mm


The legs of a right triangle are 10 cm and 24 cm. What is the length of the hypotenuse?

 22 cm 26 cm 30 cm 34 cm

Answers

leg=35 hypotenuse=26

PLEASE HELP!!!! THANK YOU!!!

The graph of the function y = x2 is shown. How will the graph change if the equation is changed to y = 2x2?
A) The parabola will become wider.
B) The parabola will become narrower.
C) The parabola will move up 2 units.
D) The parabola will move down 2 units.

Answers

The equation describes a relationship between the variables A and B. The graph is a visual representation of this on a Cartesian plane. The parabola will become narrower in this case as the equation is changing from a smaller relative value of Y to a larger relative value of Y.

The parabola will become narrower, the correct option is B.

How the graph will change?

For a function f(x), we define a vertical stretch of scale factor k as:

g(x) = k*f(x).

If k > 1, we have a stretch, if 0 < k < 1, we have a contraction.

In this case, we have:

f(x) = x^2g(x) = 2*x^2

So we have a vertical stretch of scale factor 2, this means that we are stretching our function vertically, so it will become narrower, meaning that the correct option is B.

If you want to learn more about transformations, you can read:

https://brainly.com/question/4289712

Help me with this one question and think closely it is not 8 or 800 question 36

Answers

(1 L)/(100 ft^2) * (800 m^2) * (0.26417205236 gal/L) * ((1 ft)/(0.3048 m))^2
≈ 22.75 gal

___
The conversion from liters to gallons is accurate to the digits shown, but is not exact.

Simplify the expression. 6k – 1 + 6k

Answers

12k-1 is the simplified answer
The two 6ks will add together.
6k + 6k - 1
12k - 1

What are the measures of two complementary angles if the difference in their measures is 18?

Answers

Complementary angles = 90°
x= angle 1
(90-x)= angle 2

Subtract the two angles to get the difference between them (18°).

(90-x) - x= 18
combine like terms

90 - 2x= 18
subtract 90 from both sides

-2x= -72
divide both sides by -2

x= 36° angle 1


Substitute answer in to find angle 2:
=90 - x
=90 - 36
=54° angle 2

Hope this helps! :)

Round 3,942,588 to the nearest thousand.

Answers

Hey there! :D

3,942,588

The thousandths is where the 2 is. 

If the number behind the 2 is 5 or greater, we round up to 3.

It is, so round up:

3,943,000 <== rounded number

I hope this helps!
~kaikers

graphing system y=2x-2 2y=4x- 4

Answers

These two equations describe the same line.

___
In the graph here, the graph of one equation is shown as a dotted line, not be cause those are the only points on the graph, but because I wanted you to see the other equation describes exactly the same line.

Answer:

These two equations describe the same line.

___

In the graph here, the graph of one equation is shown as a dotted line, not be cause those are the only points on the graph, but because I wanted you to see the other equation describes exactly the same line.

The sum of two numbers is -1. When twice the first number and four times the second number are added, it equals -10. What are the two numbers?

Answers

let the two number be x and y.
x+y=-1......i
2x+4y=-10.....ii
solving the simultaneous equation we have:
from equation i, making x the subject we get:
x=-1-y........iii
substituting iii in ii we get:
2(-1-y)+4y=-10
-2-2y+4y=-10
2y=-10+2
2y=-8
y=-8/2=-4
substituting the value of y in iii we get:
x=-1-(-4)
x=-1+4
x=3
therefore the first number is 3 and the second number is -4


simplify the expression
(3x^4y^-5)3

Answers

To simplify the expression (3x^4y^-5)^3, apply the power rule to each term, calculate the result, and combine them. The simplified form is 27x^12y^-15.

How to Simplify the Expression (3x^4y^-5)^3:

Let's simplify the given expression step by step:

Apply the power rule of exponents to the entire expression. This means raising each term inside the parentheses to the given power:

(a^m * b^n)^p = a^(m*p) * b^(n*p)

So, (3x^4y^-5)^3 becomes:

(3^3) * (x^(4*3)) * (y^(-5*3))

Calculate each term separately:3^3 = 27x^(4*3) = x^12y^(-5*3) = y^-15

Putting it all together, we get:

27x^12y^-15

Simplified Form:

In conclusion, the simplified form of (3x^4y^-5)^3 is 27x^12.y^-15.

A triangle has a side lengths of (5.5x + 6.2y) centimeters, (4.3x+8.3z) centimeters and (1.6z -5.1y) cenrimeters which expression represents the perimeter,in centimeters of the triangle

Answers

Answer:

Perimeter of given triangle is ( 9.8x + 1.1y + 9.9z ) centimeters.

Step-by-step explanation:

Given : A triangle has a side lengths of (5.5x + 6.2y) centimeters, (4.3x+8.3z) centimeters and (1.6z -5.1y) centimeters  

We have to find the expression  that represents the perimeter (in centimeters)

of the triangle.

Perimeter of a figure is defined as the sum of all the sides.

Since given figure is triangle so perimeter of triangle is the sum of all the sides.

Given side lengths are

(5.5x + 6.2y) , (4.3x + 8.3z) and (1.6z -5.1y)

Thus, perimeter = (5.5x + 6.2y)  + (4.3x + 8.3z) + (1.6z - 5.1y)

Perimeter = 5.5x + 6.2y + 4.3x + 8.3z + 1.6z - 5.1y

LIKE TERMS are term with same variables.

Rearrange, we get

Perimeter = 5.5x + 4.3x + 6.2y - 5.1y + 8.3z + 1.6z

Adding like terms, we get,

Perimeter = (5.5 + 4.3)x + (6.2 - 5.1)y + (8.3 + 1.6)z

Perimeter = (9.8)x + (1.1)y + (9.9)z

Thus, Perimeter of given triangle is 9.8x + 1.1y + 9.9z centimeters.

A small plant is 212 inches tall. How tall will it be in 3 weeks if it grows 34 inch each week? Which method will NOT give the correct number of inches?

Answers

Answer:

Multiply [tex]2\frac{1}{2}[/tex] by [tex]3[/tex] and then add [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

we know that

using proportion

[tex]\frac{(3/4)}{1}\frac{in}{week}=\frac{x}{3}\frac{in}{weeks} \\ \\x=3*(3/4)\\ \\x=9/4\ in[/tex]

Find the height of the plant in [tex]3[/tex] weeks

[tex]2\frac{1}{2} +\frac{9}{4}=\frac{5}{2} +\frac{9}{4}\\ \\=\frac{19}{4}\ in[/tex]

therefore

The incorrect method is

Multiply [tex]2\frac{1}{2}[/tex] by [tex]3[/tex] and then add [tex]\frac{3}{4}[/tex]

because

[tex]2\frac{1}{2}*3+\frac{3}{4}=\frac{15}{2}+\frac{3}{4}\\ \\=\frac{33}{4}\ in[/tex]

A business owner purchases supplies for a laundromat and a car wash.

Part A

The owner purchases 6 cases of laundry soap, 8 cases of fabric softener, and 3 cases of bleach for the laundromat. Each case of laundry soap costs $68.45, eash case of fabric softener costs $39.71, and each case of bleach costs $52.25.

Which is the best estimate of the total cast, in dollars, of the laundry items?

Answers

To estimate the cost, you would round the numbers before doing any calculations. For this question you would have 6×70+8×40+3×50. This is 420+320+150. The total estimated cost would then be $890.

The best estimate of the total cast, in dollars, of the laundry items is $885.

What is total?

A total is a whole or complete amount, and "to total" is to add numbers or to destroy something. In math, you total numbers by adding them: the result is the total.

Given that, the owner purchases 6 cases of laundry soap, 8 cases of fabric softener, and 3 cases of bleach for the laundromat.

Each case of laundry soap costs $68.45

So, the cost of 6 cases of laundry soap

= 6×68.45

= $410.7

Each case of fabric softener costs $39.71

So, the cost of 8 cases of fabric softener

= 8×39.71

= $317.68

Each case of bleach costs $52.25

So, the cost of 3 cases of bleach for the laundromat

= 3×52.25

= $156.75

Total =410.7+317.68+156.75

= $885.13

≈ $885

Therefore, the best estimate of the total cast, in dollars, of the laundry items is $885.

Learn more about the total here:

https://brainly.com/question/15842940.

#SPJ3

shannon uses 30 inches of ribbon to make one bow.how many feet are needed to make 10 bows?

Answers

30*10=300/12=25 ft hope i helped! 
she needs nearly 3 feet of ribbon
hope this helps

9. 10. 11. And need work or won’t get credit

Answers

Answer:

9) 22 - 5(6v - 1) = -63

22 - 30v + 5 = -63

27 - 30v = -63

-30v = -90

v = 3

10) 18x - (8x - 7) = 67

18x - 8x + 7 = 67

10x = 60

x = 7

11) 8(-2x - 4) + 12 = -52

8(-2x - 4) = -64

-2x - 4 = -8

-2x = -4

x = 2

Other Questions
Identify a sequence of transformation that maps triangle ABC onto A"B"C" in the image below.A. Clockwise 270 degrees rotation; reflection over the X-axisB. Counterclockwise 90 degrees rotation; reductionC. Counterclockwise 270 degrees rotation; reflection over the Y-axisD. Enlargement; clockwise 90 degrees rotation The three stages of moral development identified by kohlberg are ____. What would happen if there were no abiotic factors in an ecosystem The angles of triangle abc are in the ratio of 8:3:4. what is the maesure of the smallest angle After world war i, most european nations had what type of government, if only temporarily If i=Square root of -1, what is the value of i^3?A.-1B.iC.1D.-i It's okay for the shapes in a tessellation to overlap to cover up any gaps Read the passage from "Racing the Storm."Yeesh! Anastasia exclaimed. Finally giving her attention to the scene outside, she smiled. "Wow. Its beautiful, isnt it? she said.The author develops the character of Anastasia in this passage by using Anastasias dialogueto clarify Keris dialogue.to reinforce Keris dialogue.as a contrast to Keris dialogue.as an addendum to Keris dialogue. A vaccine has 90% probability of being effective in preventing a certain disease. the probability of getting the disease if the person is not vaccinated is 50%. in certain geographic region, 25% of the people get vaccinated. if a person is selected at random , find the probability that he or she will contract the disease What part of europe did the catholic church manage to hang on to? What two organ systems provide communication in thermoregulation? arespiratory and nervous bcirculatory and integumentary cintegumentary and muscular dnervous and endocrine David is filling five 3/4 quart bottles with a sports drink.His measuring cup only holds 1/4 quart.How many times will David need to fill tje measuring cup in order to fill the 5 bottels Which statement about the figure below is true?Select one:a. Points A, B, and E are not collinear. b. Points C, F, B, and E are coplanar. c. Points F, B, and C are collinear. d. Points C, D, B, and F are coplanar. Why did some states demand that the U.S. Constitution include a Bill of Rights? What were the early people of Colombia very good at? A checkpoint in the cell cycle has broken down. Which of the following results is possible?Any of these results is possible.The cell may contain damaged DNA and continue on to be reproduced with that DNA.The cell may continue to the M phase without having sufficient nutrients.The cell may not be large enough and contain enough cytoplasm to divide in the M phase. Which action is not part of the prewriting stage of the writing process? revising word choice identifying a main idea choosing a topic gathering details Who was the leader that introduced communism and central planning to the former soviet union? vladimir lenin friedrich engels karl marx joseph stalin? What is the primary source of population growth in most european countries? ? The person who prepares and abstract of title for a parcel of real estate: