Why is it important to have a control group in an experiment of investigation?
Answer choices-
•To show what happens when the dependent variable is not changed.
•To see how the dependent variable changes the dependent variable is not involved.
•To compare the results when the independent variable is not involved.
•To allow the researchers to change the dependent variable as they wish.

Answer: lived 48 years

              reigned for 15 years

Step-by-step explanation:

Let x represent the number of years he reigned.

Let y represent Alexander's age.

Use the given information to create a system of equations:

Equation 1:      x + 9 = (1/2)y

Equation 2:     x - 9 = (1/8)y

Multiply the second equation by -1 and add the equations to eliminate x:

 [tex].\quad x+9=\dfrac{1}{2}y\\\\\underline{-x+9}=\underline{-\dfrac{1}{8}}y\\\\.\qquad 18=\dfrac{3}{8}y\\\\.\qquad 48=y[/tex]  

Input y = 48 into either equation to solve for x:

[tex].\quad x+9=\dfrac{1}{2}(48)\\\\.\quad x+9 = 24\\\\.\qquad x = 15[/tex]    

Answer:

x^3-64y^3

Step-by-step explanation:

(x-4y)^3

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

x^3-64y^3

Hope this helps ;) ❤❤❤

Greetings from Brasil...

As said:

1° angle: X

2° angle: 2X

3° angle: 20 + 5X

"...The sum of the measures of the angles of a triangle is 180 degrees..."

(1° angle) + (2° angle) + (3° angle) = 180

X + 2X + (20 + 5X) = 180

X + 2X + 5X = 180 - 20

8X = 160

X = 160/8

X = 20

But the problem asks for the value of each angle. Thus

1° angle: X

as X = 20, so

1° angle: X = 20

2° angle: 2X

as X = 20, so

2° angle: 2.20 = 40

3° angle: 20 + 5X

as X = 20, so

3° angle: 20 + 5.20 = 20 + 100 = 120

The values of the first, second, and third angles are 20°, 40° and 120° respectively.

Let the first angle = x

Let the second angle = 2 × x = 2x

Let the third angle = 20 + (5 × x) = 20+5x

Total angles in the triangle = 180°

Based on the information above, the angles will be calculated thus:

x + 2x + 5x + 20 = 180

Collect like terms

8x = 180 - 20

8x = 160

x = 160/8

x = 20

First angle = 20°

Second angle = 2x = 2 × 20° = 40°

Third angle = 5x + 20 = (5 × 20°) + 20° = 120°

The angles are 20°, 40°, and 120°

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Rayne sell each desk at the price of $125.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given the following information;

The Number of desks sold = 3

The Amount of rent paid = $4

The Amount paid to carpenter = 1/2 of revenue

The Amount left = $185.50

If Rayee gave half of his revenue to the carpenter and then had $185.50 left.

The his revenue before paying the carpenter will be twice what he has left will be;

($185.50 * 2) = $371

Hence, the total revenue from the sale of 3 desk = ($371 + rent)

= (371 + 4)

= $375

Then each desk cost :

$375 / 3 = 125

Hence, Rayne sell each desk at the price of $125.

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The addition is one of the four fundamental mathematical operations. The selling price of each desk is $122.33.

The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

Revenue generated = Revenue left with Rayne + Revenue with carpenter

Since Rayne gave half of his revenue to the carpenter, therefore, both of them will have the same revenue will them

Revenue generated = Revenue left with Rayne + Revenue left with Rayne

Revenue generated = 2(Revenue left with Rayne)

Revenue generated = 2($185.50)

Revenue generated = $371

Also, Rayne paid a booth rent of $4. Therefore, the total revenue generated will be,

Total revenue generated = Revenue generated + $4

                                          = $371 + $4

                                          = $367

Since Rayne sell 3 desks, therefore, the selling price of each desk will be,

Selling price = $367 / 3

                     = $122.33

Hence, the selling price of each desk is $122.33.

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===================================================

Work Shown:

b = 5

(2b)^2 = (2*5)^2 = 100

So we want the expression a^2+3b to be less than (2b)^2 = 100

We need to solve a^2 + 3b < 100 which turns into

a^2 + 3b < 100

a^2 + 3(5) < 100

a^2 + 15 < 100

after substituting in b = 5.

------------------

Let's isolate 'a'

a^2 + 15 < 100

a^2 < 100-15

a^2 < 85

a < sqrt(85)

a < 9.2195

'a' is an integer, so we round down to the nearest whole number to get [tex]a \le 9[/tex]

So the greatest integer possible for 'a' is a = 9.

------------------

Check:

plug in a = 9 and b = 5

a^2 + 3b < 100

9^2 + 3(5) < 100

81 + 15 < 100

96 < 100 .... true statement

now try a = 10 and b = 5

a^2 + 3b < 100

10^2 + 3(5) < 100

100 + 15 < 100 ... you can probably already see the issue

115 < 100 ... this is false, so a = 10 doesn't work

Answer:

9

Step-by-step explanation:

I just did the question on AOPS, please see the attachment down below.

Hope this helped! :)

Answer:

(C) [tex]3x + 7 > 4x[/tex]

Step-by-step explanation:

Let [tex]x[/tex] represent the number that is unknown.

Using the words, we can write out each equation.

"The sum of three times a number and seven" will be adding 7 to 3x. So [tex]3x + 7[/tex].

"is greater than four times the number." will include a greater than sign and then 4 times the number, x. So:

[tex]> 4x[/tex]

Combining these, we get [tex]3x + 7 > 4x[/tex].

Hope this helped!

===============================================

Work Shown:

x = a number (something unknown)

3x = 3 times a number

3x+7 = the sum of 3 times a number and 7

4x = 4 times a number

3x+7 > 4x is the inequality that forms because the "the sum of 3 times a number and 7" portion is greater than the "4 times a number" portion

Answer:

Option (C)

Step-by-step explanation:

           Statements                                 Reasons

1). EG = FH                               1). Given information

2). EG = EF + FG                      2). Segment addition postulate

3). FH = FG + GH                      3). Segment addition postulate

4). EF + FG = FG + GH             4). Definition of congruent segments

5). EF = GH                               5). Subtraction property of equality

Therefore, reasons given in Option (C) will be the answer.

Part (a)

------------------

Explanation:

You use the compound interest formula

A = P(1 + r/n)^(n*t)

where

After plugging those values in, you would go from A = P(1 + r/n)^(n*t) to

A = P(1 + r/n)^(n*t)

A = 5000(1 + 0.016/1)^(1*x)

A = 5000(1.016)^x

Since you're using x for the input, it's possible your teacher wants you to use y for the output. So replace A with y to get y = 5000(1.016)^x

==============================================

Part (b)

--------------------------

Explanation:

Plug x = 15 into the equation we found back in part (a). Use your calculator to simplify. Round to the nearest hundredth which is rounding to the nearest penny.

y = 5000(1.016)^x

y = 5000(1.016)^15

y = 6344.1818561953

y = 6344.18

Answer:

girlie u gotta chill

Step-by-step explanation:

Answer:

7 + 8i

Step-by-step explanation:

Conjugate of 7 - 8i is 7 + 8i

Answer:

Step-by-step explanation:

7+8i

Answer:

52.38%

Step-by-step explanation:

Given that,

Total number of students in the class is 42

Out of 42, 10 like hamburgers, 22 like pizza, 8 like french fries, and 2 like salad.

We need to find the percentage of the class chose pizza. There are 22 student who like to have pizza. Required percentage is given by :

[tex]P=\dfrac{22}{42}\times 100\\\\P=52.38\%[/tex]

So, 52.38% of students chose pizza.

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = - 4}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{3x - 5 = 2x - 9}[/tex]

Move 2x to left hand side and change it's sign

⇒[tex] \sf{3x - 2x - 5 = - 9}[/tex]

Move 5 to right hand side and change it's sign

⇒[tex] \sf{3x - 2x = - 9 + 5}[/tex]

Collect like terms

⇒[tex] \sf{x = - 9 + 5}[/tex]

Calculate

⇒[tex] \sf{x = - 4}[/tex]

Hope I helped!

Best regards!!

Answer:

Step-by-step explanation:

7 quarter mile laps totals 7/4 miles, or 1 3/4 miles.

1 3/4 miles is between 1 and 2, a subset of real numbers.

Answer:

(c) (x+3)(x+4)=5

Step-by-step explanation:

It's in factored form, and you would use the method of finding the perfect square to get the equation set to zero and find the solutions.

Answe:

27

Step-by-step explanation:

Let total children =x

when x divide by 6 we got 3

and when divide by 8 we also got 3

since x divided by both 6 and 8 got 3, we can use LCM to find the number to children in the club exclude the 3 player. you will get 24 and by adding 3 the total players that you will get is 27

Answer:

x₁ = 0.6

x₂ = 1.07

Step-by-step explanation:

36x² + 23 = 60x

36x² - 60x + 23 = 0

x = {-(-60)±√((-60²)-(4*36*23))} / (2*36)

x = {60±√(3600-3312)} / 72

x = {60±√288) / 72

x = {60±16.97) / 72

x₁ = {60-16.97} / 72 = 43.03/72 = 0.6   aprox.

x₂ = {60+16.97} / 72 = 76.97/72 = 1.07    aprox.

verify:

x₁

36*0.6² + 23 = 60*0.6

36*0.36 + 23 = 36

13 + 23 = 36

x₂

36*1.07² + 23 = 60*1.07

36*1.145 + 23 = 64.2

41.2 + 23 = 64.2

Answer:

h=4 and k=-4....

Step-by-step explanation:

hopevit helps you

Step-by-step explanation:

[tex]A^2= \begin{bmatrix} 4 & 0 \\ 4 & 4 \end{bmatrix}[/tex]

Equate this to $hA + kI$

Thus,

[tex] A^2= h \begin{bmatrix} 2 & 0 \\ 1 & 2 \end{bmatrix} + k \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}[/tex]

Hence we have the following equations (by equating corresponding terms on both sides):

$2h+k=4$

$h=4$

Solve these to get $h=4$ and $k=-4$

Answer:

A = 2/4

B = 1.25

C = 11/4 , 2.75

Step-by-step explanation:

Answer:

20 m

Step-by-step explanation:

The maximum height is given by the vertex form of the equation, that is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given

h(t) = - 5t² + 20t ← factor out - 5 from each term

      = - 5(t² - 4t)

Using the method of completing the square

add/subtract ( half the coefficient of the t- term)² to t² - 4t

h(t) = - 5(t² + 2(- 2)t + 4 - 4 )

      = - 5(t - 2)² + 20 ← in vertex form

with vertex = (2, 20 )

The maximum height is at the value of k = 20

That is the maximum height is 20 m

16/9

1,7777777777777 =

= 1,(7)

= (17 - 1)/9

= 16/9

Answer:

first term= -42

common difference= 24

10th term= 174

Answer:

x = -16/5  or

x = 6/5

Step-by-step explanation:

[tex]-\left|5+5x\right|-9=-20\\\\\mathrm{Add\:}9\mathrm{\:to\:both\:sides}\\-\left|5+5x\right|-9+9=-20+9\\\\Simplify\\-\left|5+5x\right|=-11\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\\\frac{-\left|5+5x\right|}{-1}=\frac{-11}{-1}\\\\\left|5+5x\right|=11\\\\\mathrm{Apply\:absolute\:rule}:\\\\\mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a\\5+5x=-11\quad \mathrm{or}\quad \:5+5x=11\\\\5+5x=-11\quad :\quad x=-\frac{16}{5}\\\\5+5x=11\quad :\quad x=\frac{6}{5}\\[/tex]

[tex]x=-\frac{16}{5}\quad \mathrm{or}\quad \:x=\frac{6}{5}\\[/tex]

The value of x after solving the expression -|5 + 5x| - 9 = -20 is equal to x  = -16/5 or x = 6/5.

What do you mean by algebraic expressions ?

Algebraic expression is an equation which consists of variables and the arithmetic operations such as division , multiplication , etc.

The algebraic expression given is -|5 + 5x| - 9 = -20

We know that a modulus sign is a representation of  ran absolute value which has two values either a positive or negative value.\

After solving the expression we get :

-|5 + 5x| - 9 = -20

So , after removing the modulus sign we will get two expressions :

-(-(5 + 5x) - 9 = -20

5 + 5x = -11

or

-(5 + 5x) - 9 = -20

-(5 + 5x) = -11

Solving the two expressions we get the value of x as :

x  = -16/5

or

x = 6/5

Therefore , the value of x after solving the expression -|5 + 5x| - 9 = -20 is equal to x  = -16/5 or x = 6/5.

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Answer:

line: y = (1/8)x - 17/4

Step-by-step explanation:

To find perpendicular of line (negative reciprocal the given slope)

y = -8x-5

Perpendicular slope = (1/8)x

-4 = (1/8)(2) + b

-4 = 1/4 +b

Multiply everything by 4 to make it eaiser

-16 = 1 -+4b

-17 = 4b

b = -17/4

Answer:

r = 4.

Step-by-step explanation:

0.4r = 1.6

4r = 16

2r = 8

r = 4.

0.4(4) = 1.6

1.6 = 1.6

Hope this helps!

Answer:

All whole numbers are integers. AND All natural numbers are rational numbers.

Step-by-step explanation:

Answer:

The answer is D and E

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex] \sf{6(4 - y) = 5 + 3}[/tex]

Distribute 6 through the parentheses

[tex] \sf{24 - 6y = 5 + 3}[/tex]

Add the numbers

[tex] \sf{24 - 6y = 8}[/tex]

Move constant to right hand side and change it's sign

[tex] \sf{ - 6y = 8 - 24}[/tex]

Calculate

[tex] \sf{ - 6y = - 16}[/tex]

Divide both sides of the equation by -6

[tex] \sf{ \frac{ - 6y}{ - 6} = \frac{ - 16}{ - 6} }[/tex]

Calculate

[tex] \sf{y = 2.6}[/tex]

Hope I helped!

Best regards!!

Answer: Hi!

First, we need to distribute 6 to the terms inside of the parentheses, 4 and -y.

6 * 4 = 24

6 * (-y) = -6y

Our equation now looks like this:

24 - 6y = 5 + 3

We can now combine like terms.

24 - 6y = 5 + 3

5 + 3 = 8

Our equation now looks like this:

24 - 6y = 8

We can now use inverse operations to get rid of 24. Remember, our goal is to isolate the x. The inverse operation for addition (24 is positive) is subtraction, so we subtract 24 on both sides:

 24 - 6y = 8

- 24       - 24

Our equation now looks like this:

-6y = -16

Last step! We now use inverse operations to get rid of -6. The inverse operation for multiplication is division (-6 is being multiplied by y); so we divide -6 on both sides.

-6y/-6 = y

-16/-6 = 8/3 = 2 2/3

Our equation now looks like this:

y = 2 2/3

Therefore, your solution is 2 2/3.

Hope this helps!

Answer:

SO 18²⁴ IS GREATER

Step-by-step explanation:

24×36=864

18²⁴=1.3382588×10³⁰

HOPE IT WILL HELP ^_^

Answer:

24*26

Step-by-step explanation:

18/24ths doubled will result in a fraction while 24*26 is going to be an integer (864) much larger than 3/2= (18/24)*2

========================================

Work Shown:

LK = 65

LR = 52

RK = LK - LR = 65 - 52 = 13

The triangles are similar, so the corresponding sides form equal ratios

LK corresponds to RK as they are both on the same side

LK/RK is one ratio and it is equal to MK/SK

----------------

LK/RK = MK/SK

65/13 = 60/x

65x = 13*60 ... cross multiply

65x = 780

x = 780/65 ... divide both sides by 65

x = 12

SK = 12

Answer:

12

Step-by-step explanation:

RK = 65- 52= 13

similar triangle (∆RKS and ∆LKM)

[tex] \frac{13}{65} = \frac{x}{60} [/tex]

[tex]x = \frac{60 \times 13}{65} [/tex]

[tex]x = 12[/tex]