simplify the following indices :
6²×3²×3³×6⁴
​

9x²-16x(3x+11)(7x-5)

9x²-48x²-176x(7x-5)

9x²-48x²-1232x²+880

-1271x²+880

Answer:

slope = -3

Step-by-step explanation:

⭐ What is the equation of a line in slope intercept form?

The given line of best fit is written in slope-intercept form. All we have to do is identify which term is the slope.

[tex]y = -3x + 5[/tex]

-3 is the coefficient of x. Therefore, -3 is the slope.

Given the set of data, we can calculate that the mean is 9.5, the variance is 17.58 and the standard deviation is 4.19

Mean, variance, and standard deviation

The concepts of mean, variance and standard deviation are very basic but very important in statistics.

Mean is the average of all data in a sample group, which is obtained by adding up all the data values, then dividing by the number of samples.

[tex]mean = \frac{sum all of the data}{size of data}[/tex]

Variance is a value that describes the variation of data, by measuring how far each piece of data is spread from the average of a data set.

[tex]variance = \frac{sum (x_{i} - mean)^{2} }{n}[/tex]

Standard Deviation is a measure of the spread of observations in a data set relative to their mean. it measures how many observations in a data set differ from the mean and is the square root of the variance.

σ = [tex]\sqrt{variance}[/tex]

Now we can calculate the mean of the given data as follows:

[tex]mean = \frac{sum all of the data}{size of data}[/tex]

         = (3 + 6 + 8 + 12 + 13 + 15) / 6

         = 57 / 6

         = 9.5

Then we can calculate the variance as follows:

[tex]variance = \frac{sum (x_{i} - mean)^{2} }{n}[/tex]

              = [tex]\frac{((3-9,5)^{2} + (6-9,5)^{2} + (8-9,5)^{2} + (12-9,5)^{2} + (13-9,5)^{2} + (15-9,5)^{2} )}{6}[/tex]

              = (42,25 + 12,25 + 2,25 + 6,25 + 12,25 + 30,25) / 6

              = 105.5 / 6

              = 17.58

Standard deviation can be calculated from the variance:

σ = [tex]\sqrt{variance}[/tex]

  = [tex]\sqrt{17.58}[/tex]

  = 4.19

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The result of DNA replication, given the fact that most cancer cases came as a result of DNA replication errors, is C. A chromosome with two identical DNA strands is formed.

The biological process of creating two identical copies of DNA from a single original DNA molecule is known as DNA replication.

After this process is complete and all the DNA has been copied, the cell actually has twice as much DNA as it needs, which it can then divide and parcel into the daughter cell, resulting in the daughter cell and the mother cell being nearly genetically identical in many cases.

Sometimes however, there will be errors in DNA replication, and this can lead to things like cancer as shown by Dr. Bert Vogelstein.

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The linear equation that represent the total cost after x month is y = 35 + 29.95x.

What is linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given that, a cable operator offer at $29.95 per month plus a one-time installation fee.

Assume that, a be one time installation fee.

After x month, they need to pay without one-time installation fee is 29.95x.

The total amount that need to pay after x month is a + 29.95x

The linear equation that represents total cost after x month is

y = a +  29.95x

Putting y = 214.70 and x = 6

214.70 = a +  29.95 × 6

214.70 = a +  179.70

a = 35.

Putting a = 35 in y = a +  29.95x

y = 35 +  29.95x

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The difference between Tom and Alfie is  1 kg

Let's call the weight of Tom T, the weight of Harry H, the weight of Freddie F, and the weight of Alfie A. We are given that T = H + 5, H = F + 3, and F = A - 2.

Substituting the second and third equations into the first equation gives us:

T = (A - 2) + 3 + 5

T = A - 2 + 3 + 5

T = A + 1

So the difference between Tom and Alfie is T - A = A + 1 - A = 1 kg.

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Answer:

Anna needs 801 boxes.

Step-by-step explanation:

You need to know how many groups of 9 are in 7209.

Use division to find this answer.

7209 ÷ 9 = 801

Anna needs 801 boxes.

Answer:

[tex]y = x^2 + 6x + 8[/tex]

Step-by-step explanation:

⭐What is the equation of a parabola in standard form?

⭐Whenever you factorise a quadratic (parabola), you are writing the parabola in terms of its x-intercepts.

⭐ Therefore, the expressions of the x-intercepts are the factors of your quadratic.

⭐What are factors of a number?

We have to reverse-engineer this problem to find the quadratic by:

1. Re-write the quadratic in terms of its factors

If one of the x-intercepts is -2, then the expression for said x-intercept is: [tex](x+2)[/tex]

If one of the x-intercepts is -4, then the expression for said x-intercept is:

[tex](x+4)[/tex]

2. Multiply the factors

[tex]y = (x+2)(x+4)[/tex]

[tex]y = x^2 + 4x + 2x + 8[/tex]

3. Simplify the products

[tex]y = x^2 + 6x + 8[/tex]

Cindy was able to make $837 in commission thanks to her commission rate, which equates to $104.62 per hour.

Cindy is a travel agent. She receives a 9% commission based on the value of the trips she books. Today she spent eight hours arranging a $9,300 cruise for a newlywed couple

The commission that Cindy received can be determined by:

= Commission % x Price of booked trip

= 9% x 9,300

= $837

Consequently, the following is her hourly wage:

= Commission received / Hours worked

= 837 / 8

= $104.62

The bottom line is that  made $104.62 per hour plus $837 in commission.

Cindy was able to make $837 in commission thanks to her commission rate, which equates to $104.62 per hour.

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The expression 10% of 40 is 4 and 10% more than 40 is 44

From the question, we have the following parameters that can be used in our computation:

10% of 40

Express "of" as products

So, we have

10% of 40 = 10% * 40

Evaluate

10% of 40 = 4

In this case, we have:

10% more than 40

This means that

10% more than 40 = 40 * (1 + 10%)

Evaluate

10% more than 40 = 44

Hence. 10% more than 40 is 44

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The value of x in the algebraic equation is -1/2 and using system of linear equation to solve the problem, the cost of DVD and blue-ray are 84.3 and 178.6 respectively

This is a mathematical statement that represent an algebraic problem. It often two expression equating with one another.

8)

1/4 [(-2x - 7) / 8] = x / 2

Multiply through by 1/4

(-2x - 7) / 32 = x / 2

Cross multiply both sides

2(2x - 7) = 32x

4x - 14 = 32x

collect like terms

32x - 4x = - 14

28x = -14

x = -14 / 28

x = - 1/2

9)

To solve this problem, we should write a system of linear equations;

Let;

3x + 2y = 610 ...eq(i)

y - 10 = 2x ...eq(ii)

From equation (ii)

y = 2x + 10 ...eq(iii)

Put eq(iii) into equ(i)

3x + 2(2x + 10) = 610

3x + 4x + 20 = 610

x = 590/7 = 84.3

Put x = 84.3 into equ(ii)

y - 10 = 2(84.3)

y = 1250 / 7

y = 178.6

The cost of DVD is 84.3 and the cost of blue-ray is 178.6

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1. The solution to the quadratic equation, x² - 14x + 49 = 40, is x = 13.32 and x = 0.68

2. The solution to the quadratic equation, x² - x = 12, is x = -3 and x = 4

3. i. The factors of 2x² - 15x - 8 = 0 are (2x +1) and (x - 8)

ii. The x-intercepts of 2x² - 15x - 8 = 0 are x = -1/2 and x = 8

From the question, we are to solve the given quadratic equation by completing the square.

The given equation is

x² - 14x + 49 = 40

Solving the equation

x² - 14x + 49 = 40

x² - 14x = 40 - 49

x² - 14x = -9

Multiply the coefficient of x by 1/2 square and add to both sides

x² - 14x + (-7)² = -9 + (-7)²

(x - 7)² = -9 + 49

(x - 7)² = 40

x - 7 = ±√40

x = 7 ± √40

x = 7 ± 6.32

x = 7 + 6.32 OR 7 - 6.32

x = 13.32 OR 0.68

Solving x² - x = 12 by factoring

x² - x = 12

x² - x - 12 = 0

x² -4x + 3x - 12 = 0

x(x - 4) + 3(x - 4) = 0

(x + 3)(x - 4) = 0

x + 3 = 0 OR x - 4 = 0

x = -3 OR x = 4

Determining the factors of 2x² - 15x - 8 = 0

2x² - 15x - 8 = 0

2x² - 16x + x - 8 = 0

2x(x - 8) + 1(x - 8) = 0

(2x + 1)(x - 8) = 0

The factors are (2x +1) and (x - 8)

Determining the x-intercepts

(2x + 1)(x - 8) = 0

2x + 1 = 0 and x - 8 = 0

2x = -1 and x = 8

x = -1/2 and x = 8

Hence, the x-intercepts are -1/2 and 8

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no 48 es un numero irracional

Cualquier número real que no se puede escribir como el cociente de dos números enteros, p/q, donde p y q son ambos números enteros, se denomina número irracional. Por ejemplo, la raíz cuadrada de 2 no se puede expresar como un número entero o una fracción.

Explicación detallada:

48 se puede expresar como [tex]\frac{48}{1}[/tex] aquí se puede ver que la forma p/q está presente. Entonces es un número racional.

no 48 es un numero irracional.

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48 is not an irrational number

Any real number that cannot be written as the quotient of two integers, p/q, where p and q are both integers, is called an irrational number. For example, the square root of 2 cannot be expressed as a whole number or a fraction.

48 can be expressed as  [tex]\frac{48}{1}[/tex] here you can see that the p/q form is present. So it is a rational number.

48 is not an irrational number.

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Volume of solid generated by revolving the region bounded by the graph is 3817.53 unit

A volume is created while a plane figure rotating about an axis or around any straight line situated on the same plane.

We apply definite integration to calculate the required volume.

we are given the equation y = 5x² and y =0, x= 3

volume is calculated by using the formula, V = ∫π y² dx

                                                                      V = ∫₀³π (5x²) ² dx

On the y-axis x = 0 so upper limit x = 3 and lower limit x= 0

                                                          V= π × 25/5 [x⁵] ³₀

                                                        V = 15.71 [3⁵- 0]

  hence, the volume of solid = 3817.53 unit

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commission = 250,000×4/100

commission = $10,000

Answer:

$10,000

Step-by-step explanation:

because of acom by Jill one GB cb to be yes we will i you and the ward off Luth you sir ma we have in mind the customer service is not available for is it possible to you IJN you and the ward screen shot of a quick response because I am not you sir I am not sure if my proposal sounds interesting for you ma I will send it to u the picture

The response will be -10 if the stated statement is accurate.

This same square root and cubed root are the two radicals we see most frequently. Since the square root is so often employed, it is customary to presume that any radical written without the need for an index is a square root. The figure above constitutes a radical taken as a whole.

An phrase that has a root, often a square or cube root, is referred to as a radical. A radical is made up of three main parts, namely: It expresses the degree of radicand multiplication. If the root symbol's numeric component is absent, it is assumed as 2 (square root). The symbol √ means “root of”.

= 6 - 4²

= 6 - 16

= - 10

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The correct questions are-

6 - 4²

Answer:

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

x=7-2

x=5

Answer:

x=5

Step-by-step explanation:

5+2=7  or 7-2=5

The simple formula or rule that generates the terms of an integer sequence that begins with the given list is given below.

Sequence is the order in which elements, such as numbers, letters, or symbols, follow one another in a specific order. It is a fundamental concept in mathematics and computer science, and is used in many other areas including music, language, and art. In mathematics, it is often used to describe patterns or to represent numerical values. In computer science, it is used to represent data structures, such as lists and arrays.
a. The sequence can be expressed as 3x2^n, where n is the position of the number in the sequence. The next three terms are 127, 162, and 201.

b. The sequence can be expressed as 4n+3, where n is the position of the number in the sequence. The next three terms are 47, 51, and 55.

c. The sequence can be expressed as 2^n+n-1, where n is the position of the number in the sequence. The next three terms are 1111, 10000, and 10011.

d. The sequence can be expressed as the number of times the previous value is repeated, starting with 1. The next three terms are 5, 5, and 8.

e. The sequence can be expressed as 4x3^n, where n is the position of the number in the sequence. The next three terms are 5906, 17718, and 53154.

f. The sequence can be expressed as (n+1)!+(n-1)!+2, where n is the position of the number in the sequence. The next three terms are 27027025, 94594500, and 34459425.

g. The sequence can be expressed as the number of times the previous number is repeated, starting with 1. The next three terms are 0, 0, and 1.

h. The sequence can be expressed as 4^n, where n is the position of the number in the sequence. The next three terms are 4294967296, 17179869184, and 68719476736.

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Complete questions as follows-
For each of these lists of integers, provide a simple formula or rule that generates the terms of an integer sequence that begins with the given list. Assuming that your formula or rule is correct, determine the next three terms of the sequence.
a. 3, 6, 11, 18, 27, 38, 51, 66, 83, 102, . . .
b. 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, . . .
c. 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, . . .
d. 1, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, . . .
e. 0, 2, 8, 26, 80,242,728,2186,6560,19682, . . .
f. 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425, . . .
g. 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, . . .
h. 2, 4, 16, 256, 65536, 4294967296, . . .

Answer: 54

Step-by-step explanation: bc ? you just divid 54 by 3 and 6 then you divid 77 by 4 and 9 then divide them both tada

Answer:

sodas cost $5 and a large popcorn costs $8

create formulas out of the situations making the variable p=popcorn and s=soda

so,

3p + 6s = 54

and

4p + 9s = 77

then choose one variable to solve for

3p = 54 - 6s

divide both sides by 3

p = 18 - 2s

then plug your answer for p into the other equation:

4(18 - 2s) + 9s = 77

finally, solve for s

72 - 8s + 9s = 77

s = 5

if s=5 then

3p + 6(5) = 54

p = 8

The decimal point can be removed by dividing 10 with each numerator and denominator of 6.1/0.1

(61/10)/(1/10) = 61/10 x 10 = 61

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

6.1/0.1

We will remove the decimal point by dividing 10 with both the numerator and denominator.

(61/10)/(01/10)

= 61/10 x 10/1

= 61/1

= 61

Thus,

The value of 6.1/0.1 is 61.

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The cost of one chair is [tex]x=54.75[/tex] $ and the cost of one table is [tex]y=49.5[/tex] $.

What is the total cost?

The total cost formula is used to combine the variable and fixed costs of providing goods to determine a total. The formula is:

Total cost = (Average fixed cost x average variable cost)

Let cost of one chair is [tex]x[/tex]

Let cost of one table is [tex]y[/tex]

So,

[tex]5x+3y=31[/tex]       ...(1)

[tex]2x+6y=52[/tex]      ......(2)

Solving equation (1) and (2) we get

[tex]a_1x+b_1y+x_1=0\\\\a_2x+b_2y+c_2=0[/tex]

[tex]\frac{x}{b_1c_2-b_2c_1}=\frac{y}{c_1a_2-c_2a_1}=\frac{1}{a_1b_2-a_2b_1}\\\\\frac{x}{3(31)-6(52)}=\frac{y}{31(2)-52(5)}=\frac{1}{5(2)-2(3)}\\\\\frac{x}{93-312}=\frac{y}{62-260}=\frac{1}{10-6}\\\\\frac{x}{-219}=\frac{y}{-198}=\frac{1}{-4}\\\\x=54.75,y=49.5[/tex]

Hence, the cost of one chair is [tex]54.75[/tex] $ and the cost of one table is [tex]49.5[/tex] $.

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Chorus over all view is about love, magic and war and following is the summary of his theme.

In the chorus, it is stated that "everything but death" has been vanquished by man, hinting at what Antigone will experience. Additionally, they sing of "unsavory ambition," or inordinate pride, which alludes to Creon's terrible fault, or hamartia.

The chorus in "Oedipus Rex" serves as the voice of the common people and offers perspective that the other characters in the play are unable to express. The chorus advances the plot by introducing new characters and providing answers to issues that arise.

The chorus declares that this play will not be about love, war, or valiant acts. Instead, it will detail the successes and failures of Dr. John Faustus, a German native of humble origins who attends the University of Wittenberg to study philosophy and divinity. He is so good at theology that he finally gets haughty, which is what brings him to ruin. In the end, Faustus decides to research necromancy, or magic.

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Answer:

sorry i messed up my first calculations, currently recalculating

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the number of $30 advance tickets and $35 same-day tickets sold, when a total of 55 tickets were sold for $1825.

Let s represent the number of same-day tickets sold. Then 55-s is the number of advance tickets sold, and total revenue is ...

  35s +30(55 -s) = 1825

  5s = 175 . . . . . . Simplify, subtract 1650

  s = 35

  55-s = 30

35 same-day and 30 advance tickets were sold.

The answer of the given pattern is 38564.11

The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.

If we have a^b then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).

We are given the expression as

"-6000(1+1.1+1.1^2+...+1.1^7)"

Using the power series we get;

= -6000(1.1^8/0.1)

After the complete solution the answer is 38564.11

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Answer: 20

Step-by-step explanation:

x = 2

6(2)+8 = 20

Answer: 20

Step-by-step explanation:

f(2)= 6(2)+8

=20

 plug in x with 2

the equilibrium constant for this reaction in terms of the equilibrium constants is Knet = √Ka/Kb

and for the reactions below:

2 S(s) + 3 O2(g) 2 SO3(g) is √Ka

S(s) + O2(g) SO2(g) is 1/Kb

A reversible reaction mechanism progresses from initial conditions to chemical equilibrium at a constant temperature, with all reactants and products present in constant non-zero amounts. At this temperature, an equilibrium constant "K" exists. It is frequently followed by a subscript to indicate the type of equilibrium constant that it considers depending on the phases of reaction species that it considers. The expression for each type of equilibrium constant differs with the direction and stoichiometry of the balanced reaction equation. This enables existing equations with known "K" values to be exploited in order to derive new "K" values for related systems.

SO2(g) + 1/2 O2(g)SO3 (g) is the desired reaction equation

We consider the first given reaction system at the bottom. We divide its coefficients by two to get the square root of the initial equilibrium constant: 2 S(s) + 3 O2(g) (g) 2 SO3(g) = √Ka

Then we reverse the second given reaction system at the bottom. Its current equilibrium constant is the reciprocal of the predecessor: S(s) + O2(g) SO2(g) is 1/Kb

The above two equations total to yield our target equation. The product of the two values obtained above yields the target equilibrium constant: Knet = √Ka/Kb

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Total  no. of cups of baking soda used for the experiment in improper fraction is [tex]\frac{91}{8}[/tex].

Initial no. of cups of baking soda used for an experiment = [tex]1\frac{3}{4}[/tex]

Converting mixed fraction to improper fraction,

[tex]1\frac{3}{4}=\frac{7}{4}[/tex]

No. of times the experiment performed by students = [tex]6\frac{1}{2}[/tex]

Converting mixed fraction to improper fraction,

[tex]6\frac{1}{2} = \frac{13}{2}[/tex]

Total  no. of cups of baking soda  =(Initial no. of cups)* (No. of times)

                                                        [tex]=\frac{7}{4} *\frac{13}{2} \\\\=\frac{91}{8} \\\\[/tex]

                                                        = 11.4 (decimal form)

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The equation of line in slope in intercept form will be equal to y = 4x - 4.

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the data provided in the question,

The formula for a line is y = mx + b, where m denotes the slope and b the y intercept.

So,

The equation can be written as,

y = 4x + b

As per the given point (2, 4),

4 = 4(2) + b

b = 4 - 8

b = -4

So, the final equation will be,

y = 4x - 4

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Answer: 7

Step-by-step explanation:

x=12-5

x=7

Answer:

x=7

Step-by-step explanation:

12-5=7 or 7+5=12