Which expression is
equivalent to the following complex fraction?

Answer:

You can find the mean, by adding all the terms in each data set and dividing by the number of terms.  For example, if there were four data points, you would add them all up and divide by four.

hope this helps!

Answer:

12

Step-by-step explanation:

because it digit havbeen given ad k

Answer:

Whats the question then?

Step-by-step explanation:

An equation is formed of two equal expressions. The sum of all possible values of x is 16.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

3x + 2y = 21

3x = 21 - 2y

x = (21-2y)/3

Since the value of x is needed to be positive, the value of 2y must not exceed 21. Also, the value of (21-2y) must be a multiple of two.

Now, the values of y that will satisfy the given condition in the equation are 0, 3, 6, and 9.

Further, the sum of the possible values of x are,

Sum = 7 + 5 + 3 + 1 = 16

Hence, the sum of all possible values of x is 16.

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Answer:

4

Step-by-step explanation:

When we substitute the blank for 4 and divide by 4, 7,504,124/4 is 1,876,031 :)

Have an amazing day!!

Please rate and mark brainiest!!

Step-by-step explanation:

[tex]( \sec(x) + \tan(x) )( \frac{1 - \sin(x) }{ \cos(x) } )[/tex]

[tex]( \frac{1}{ \cos(x) } + \frac{ \sin(x) }{ \cos(x) } )( \frac{1 - \sin(x) }{ \cos(x) } )[/tex]

[tex]( \frac{1 + \sin(x) }{ \cos(x) } )( \frac{1 - \sin(x) }{ \cos(x) } )[/tex]

[tex] \frac{1 - \sin {}^{2} (x) }{ \cos {}^{2} (x) } [/tex]

[tex] \frac{ \cos {}^{2} (x) }{ \cos {}^{2} (x) } [/tex]

[tex] = 1[/tex]

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. The given triangle can be solved as shown below.

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,

[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ B}{\beta} =\dfrac{Sin\ C}{\gamma}[/tex]

where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,

Sin B is the angle and β is the length of the side of the triangle opposite to angle B,

Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.

For the given triangle, using the sine rule the ratio of the angle and the sides of the triangle can be written as,

[tex]\dfrac{Sin\ A}{18} =\dfrac{Sin\ B}{11} =\dfrac{Sin\ C}{c}\\\\\dfrac{Sin\ 72^o}{18} =\dfrac{Sin\ y^o}{11} =\dfrac{Sin\ x^o}{c}[/tex]

Taking the first two ratios,

[tex]\dfrac{Sin\ 72^o}{18} =\dfrac{Sin\ y^o}{11}\\\\y = 35.54^o[/tex]

The sum of all the angles of a triangle is 180°.

72° + 35.54° + x° = 180°

x = 72.46°

Now, using the sine ratio,

[tex]\dfrac{Sin\ 72^o}{18} =\dfrac{Sin\ 72.46^o}{c}\\\\c = 18.046[/tex]

Hence, the given triangle is solved.

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Sam paid $ 124.032 as tax deduction each week.

An equation is a mathematical statement formed when an algebraic expression is equated by an equal sign by a constant or algebraic expression.

It is given that

weekly earnings of Sam is $912

Tax deduction is 13.6 %

Let the amount of Tax deduction is represented by $x

Then the equation formed is

x = 13.6 % 912

x = 13.6 *912 /100

x = $ 124.032

Therefore Sam paid $ 124.032 as tax deduction each week.

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Answer:

Infinitely many solutions.

Step-by-step explanation:

Let's solve your system by elimination.

x−3y=9;−x+3y=−9

x−3y=9

−x+3y=−9

Add these equations to eliminate x:

0=0

Answer:

Infinitely many solutions.

Answer:

[tex]3x^{2} +2x[/tex]

Step-by-step explanation:

Using the rainbow expansion method:

[tex]x(3x+2)=3x*x+x*2\\ = 3x^{2} +2x[/tex]

Answer:

3x² + 2x

Step-by-step explanation:

x (3x + 2)

= x*3x + x*2

= 3x² + 2x

if the perimeter=s+s+s+s

=x+x+x+x

Answer:

the answer is 3power 7

3^7

Answer:

3^8

Step-by-step explanation:

All the options are incorrect. the required average is (3x-9)/2.

Thermometer A reads xº.
Thermometer B reads 2° below the reading on thermometer A = x-2
Thermometers C and D each read 4° less than twice the reading on thermometer  = 2(x-2)-4

Average of the values is the ratio of total sum of values to the number of values.

As per question,
A=x
B = x-2
C.D = 2(x-2)-4= 2x-8
Average = A + B + C + D /4
= x+x-2+2x-8+2x-8/4
= 6x-18/4
= 3x-9/2

Thus, the required average of temperature = 3x-9/2.

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Event A and Event B are events that do not overlap. This statement is false.

Two events overlap if there is a chance that both events occur together. A spade has a number 2. Thus, it is possible to pick a spade that has the number 2 on it. Thus, these events are dependent events.

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Answer:

  $7800

Step-by-step explanation:

The total interest earned can be found by summing the earnings from each of the investments.

Let x represent the total amount invested. Then Jessica's earnings are ...

  (x/2)(0.07) +(x/2)(0.13) = 780

Simplifying the equation gives ...

  (x/2)(0.07 +0.13) = 780

  0.10x = 780

  x = 7800 . . . . . . . . divide by 0.10

Jessica has $7800 invested.

A function assigns the value. The function f(g(x)) represents the amount that Sonia will earn per hour by baking bread.

A function assigns the value of each element of one set to the other specific element of another set.

Given f(x)=9x²+1 and g(x)=√(2x³). Therefore, the value of f(g(x)) will be,

[tex]f(g(x)) = 9(\sqrt{2x^3})^2 + 1[/tex]

            = 9(2x³) + 1

           = 18x³ + 1

The function f(g(x)) represents the amount that Sonia will earn per hour by baking bread.

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The equation that can be used for finding the lengths in the Pythagoras theorem include:

b² = c² - a²

a² = c² - b²

c² = a² + b²

It should be noted that a Pythagoras theorem is simply the theorem that's used in finding the missing length of a right angled triangle.

In this case, the equation that can be used to find the sides in a Pythagoras theorem has been given.

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Answer: -10x+1.5

Step-by-step explanation:

[tex]-2(5x-0.75)=-10x+1.5[/tex]

Answer:

  (a)  (5, -3)

Step-by-step explanation:

The "substitution method" for solving a system of equations requires that you write an expression that can be substituted for a variable in one or more of the other equations in the system.

The given equations are ...

We notice the first equation gives an expression for y. This is exactly what we want to substitute for y in the second equation.

When the expression (x-8) is substituted for y in the second equation, you get ...

  2x +3(x -8) = 1

This simplifies to ...

  5x -24 = 1

This 2-step equation can now be solved in the usual way:

  5x = 25 . . . . . . add 24 to isolate the variable term

  x = 25/5 = 5 . . . . . divide by the coefficient of x

Note that we now know what the correct answer choice is.

Using the expression for y, we find ...

  y = x -8 = 5 -8 = -3

The solution is (x, y) = (5, -3).

__

The attached graph confirms this solution.

Answer:

36

Explanation:

Multiples of 4 are:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64,...

Multiples of 18 are:

18, 36, 54, 72, 90, 108, 126, 144,...

The least common multiple of 4 and 18 is 36.

Answer:

Step-by-step explanation:

[tex]\frac{a+b}{a^2b} +\frac{a-b}{ab^2} \\=\frac{b(a+b)+a(a-b)}{a^2b^2} \\=\frac{ab+b^2+a^2-ab}{a^2b^2} \\=\frac{b^2+a^2}{a^2b^2} \\or\\=\frac{1}{a^2} +\frac{1}{b^2}[/tex]

Answer:

He have to invest $527.777778 .

Step-by-step explanation:

X : 4.75% = $10,000 : 90

Answer:

The volume = 5 276.66928645188 cm³

Step-by-step explanation:

let V be the volume of the given sphere.

V = (4/3)×π×r³ ,where r is the radius of the sphere

r = 21.6÷2 = 10.8 cm

Then

V = (4÷3)×π×(10.8)³

   = 5 276.66928645188 cm³

Hello,

if :

[tex] \frac{16}{4(3 - 1)} = \frac{16}{4 \times 2} = \frac{16}{8} = 2[/tex]

if :

[tex] \frac{16}{4} \times (3 - 1) = 4(3 - 1) = 4 \times 2 = 8[/tex]

Answer:

Hello! The answer is c) 8.

Step-by-step explanation:

To solve this question, we need to follow the order of operations. This can be done through PEMDAS - parentheses, exponents, multiplication, division, addition, and subtraction.

First, we need to solve what's in the parentheses:

[tex]\frac{16}{4} * 2[/tex]

Now we can multiply and we get:

[tex]\frac{32}{4}[/tex]

This can be further simplified by doing 32 ÷ 4 to get 8.

Therefore, the answer is c) 8

Answer:

26

Step-by-step explanation:

7(4)+-2

28-2=26

Step-by-step explanation:

y = 4 and z = -2

[tex] = 7y + z[/tex]

[tex] = 7 \times 4 + ( - 2)[/tex]

[tex] = 28 - 2[/tex]

[tex] = 26...[/tex]

Her boss would give Kim a total of $2x

The given parameters are:

Distance = 26 km

Assume that the amount raised during the marathon is

Amount = x

From the question, we have:

Boss = Double the amount

This means that:

Boss = 2 * Amount

Substitute Amount = x

Boss = 2x

Hence, her boss would give Kim a total of $2x

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Answer:

3081.24 cm³ (nearest hundredth)

Step-by-step explanation:

Formulas

[tex]\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}[/tex]

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

If a rectangular piece of paper is rolled along its length to form a cylinder:

To calculate the volume of the formed cylinder, determine the radius by using the circumference formula:

[tex]\implies \sf 2 \pi r = 44[/tex]

[tex]\implies \sf r = \dfrac{44}{2 \pi}[/tex]

[tex]\implies \sf r =\dfrac{22}{\pi}[/tex]

Substitute the round radius into the formula for Volume and solve for V:

[tex]\implies \sf V=\pi \left(\dfrac{22}{\pi}\right)^2(20)[/tex]

[tex]\implies \sf V=\pi \left(\dfrac{484}{\pi^2}\right)(20)[/tex]

[tex]\implies \sf V=\left(\dfrac{484}{\pi}\right)(20)[/tex]

[tex]\implies \sf V=\dfrac{9680}{\pi}[/tex]

[tex]\implies \sf V=3081.239698...cm^3[/tex]

Therefore, the volume of the cylinder is 3081.24 cm³ (nearest hundredth).

The sample standard deviation is 2.45.

Standard deviation measures the spread of a dataset around its mean. The variance measures the average degree to which each data point differs from the mean.

The standard deviation is the square root of the variance.

Standard deviation = √6 = 2.45

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