y=4x^2-8x+3
find the vertex form

He may keep 82 movies on each shelf, using up to 492 movies and leaving 3 movies to retain.

Arithmetic operations is a field of mathematics that studies numbers and the operations on numbers that are helpful in all other disciplines of mathematics. It consists mostly of operations like addition, subtraction, multiplication, and division. Arithmetic Operator is used to conduct mathematical operations on the supplied operands such as addition, subtraction, multiplication, division, modulus, and so on. Arithmetic operators carry out operations on numbers. Variables are assigned values using assignment operators. Logical operators compare two values and return either "true" or "false" depending on whether the comparison is true (or false).

Here,

Movies that movie store has=495 movies

Number of shelves=6

If the owner wanted to make sure each shelf had the same number of movies,

=495/6

=82.5

He can keep 82 movies in each shelf that will use up to 492 movies and 3 movies will be left to keep.

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Based on the information illustrated, the analysis implies the following:

a. nonstatistical.

b. statistical.

c. nonstatistical

d. statistical

A statistical question is one that can be answered by collecting varying amounts of data. A statistical question is one that does not have a single answer. Instead, you should expect a range of responses.

Identifying a statistical question necessitates knowledge of statistics. Statistics is a mathematical study that involves the collection, analysis, and interpretation of changing data. A statistical question will ask a question with a variable answer; data must be collected and analyzed, and the answer will provide an explanation of the information.

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statistical or nonstatistical  What's the difference? is that statistical is of or pertaining to statistics while nonstatistical is not statistical.

Statistical sampling is more objective and uses probability to determine the appropriate sample size. While it is does not eliminate sampling risk, statistical sampling allows the auditor to measure sampling risk and take steps to control it. Nonstatistical sampling relies more on the auditor's judgment.

Thus, the correct answer is nonstatistical statistical nonstatistical statistical

The probability that the married couple will have adjacent desks is 0.2857and the probability that the married couple will have non-adjacent desks is 0.7143.

Probability is synonymous with potential. It is a branch of mathematics that studies the occurrence of a random event. The number ranges from 0 to 1. In mathematics, probability has been introduced to predict how likely events are to occur.

Given that

Of 7 new employees, 2 employees are married to each other; these 7 employees are to be assigned 7 desks that are lined up in a row.

If the assignment of the employees to the desks is made randomly, we have to find the probability that the married couple will have adjacent desks and will have non-adjacent desks.

Now, the event that the couple has non-adjacent desks is the complement of the event that they have adjacent desks.

Now, first, let us determine in how many ways can the couple have adjacent desks.

Let us consider the married couple as a single entity, that always stays together.

Then, in total, there are 6 entities; 5 non-related employees and 1 married couple.

Now, these 6 can be arranged among themselves in 6! number of ways.

The married couple can have adjacent desks in 2! ways.

So, the favorable number of cases, in which the couple has adjacent desks, is 6!*2!.

Again, 7 employees can be assigned desks in 7! number of possible ways.

That is, the number of all possible cases is 7!.

This means that

P(The couple has adjacent desks)

=6!*2!/7!

=0.2857.

Now,

P(The couple will have non-adjacent desks)

=1-P(The couple will have adjacent desks)

=1-0.2857

=0.7143

Therefore the probability that the married couple will have adjacent desks is 0.2857and the probability that the married couple will have non-adjacent desks is 0.7143.

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The expected value of a player's winnings on each roll is equal to: D. $30.00

In order to determine the expected value of a player's winnings on each roll, we would list all of the outcomes that are associated with rolling a fair six-sided die.

By rolling a fair six-sided die, we would obtain the following outcomes:

Outcomes = 1, 2, 3, 4, 5, and 6.

Generally speaking, there are only two (2) numbers that are multiples of three (3) in a fair six-sided die and these include the following:

Multiples of three (3) = 3 and 6

When a player rolls a three (3), the player's possible winning is giving by:

Player's winning = 3 × 20 = $60

When a player rolls a three (3), the player's possible winning is giving by:

Player's winning = 6 × 20 = $120

Total winnings = $60 + $120

Total winnings = $180

Now, we can determine the expected value of a player's winnings on each roll:

Expected value = 1/6 × 180

Expected value = $30.

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Complete Question:

A game involves rolling a fair six-sided die. If the number facing upward on the die is a whole number multiple of three, the player wins an amount equal to the number on the die times $20. If the number is not a multiple of three, the player gets nothing. What is the expected value of a player's winnings on each roll?

A. $3.33

B. $6.66

C. $8.50

D. $30.00

E. $40.00

The area of wallpaper required is 0.98 [tex]m^{2}[/tex]

Mensuration is a division of mathematics that studies geometric figure calculation and its parameters such as area, length, volume, lateral surface area, surface area, etc. It outlines the principles of calculation and discusses all the essential equations and properties of various geometric shapes and figures. 

Mensuration is a subject of geometry. Mensuration deals with the size, region, and density of different forms both 2D and 3D. Now, in the introduction to Mensuration, let’s think about 2D and 3D forms and the distinction between them.

d = 0.26m

h = 1.2m

s = pi * d * h

 = 0.98 square meter

the area of wallpaper required is 0.98 [tex]m^{2}[/tex]

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Answer:

0.98 m²

Step-by-step explanation:

I got it right hope this helps.

When charging $15 for a key chain, it is discovered that his maximum profit is $75 using the vertex of the quadratic function.

The vertex of a quadratic equation,

A quadratic equation is given by, [tex]ax^{2} +bx +c[/tex]

The vertex is given by [tex]A (x_{1} ,y_{1} )[/tex]

[tex]x_{1} = \frac{-b}{2a}\\ \\y_{1} = \frac{-b^{2} +4ac }{4a}[/tex]

Considering the coefficient a, we have that:

If a < 0, the vertex is a maximum point.

If a > 0, it will be a minimum point.

The function given is (x -10 ) (60 -3x)

f(x) = (x -10 ) (60 -3x)  = 60x -3[tex]x^{2}[/tex] -600 +30x = -3[tex]x^{2}[/tex] +90x -600

So, here a = -3, b = 90 and c = -600

So,

[tex]x_{1} = \frac{-b}{2a}\\ \\x_{1} = \frac{-90}{2*(-3)} = 15[/tex]

[tex]y_{1} = \frac{-b^{2} +4ac }{4a} = \frac{(-90)^{2} + 4*(-3)*(-600) }{4*(-3)} = 75[/tex]

Hence, He can make up to $75 in profit when he charges $15 for a key chain.

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Centriod!

A centroid is also known as the centre of gravity.

Hope this answers your question!

Answer: centroid

Step-by-step explanation:

There are 102 grams of copper in 12 cm³ of copper.

A unit rate means a rate for one of something.

Given that 1 cm³ of copper have mass of 8.5 grams

Therefore, 12 cm³ = 12*8.5 = 102 grams

Hence, There are 102 grams of copper in 12 cm³ of copper.

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Answer:

I think that the answer is going to be 34-21+6=19

Answer:

(0, 6)

Step-by-step explanation:

Given function:

[tex]y=\log_4(2x+64)+3[/tex]

The y-intercept of a function is the point at which the curve crosses the y-axis, so when x = 0.

Therefore, to find the y-intercept, substitute x = 0 into the function:

[tex]\implies y=\log_4(2(0)+64)+3[/tex]

[tex]\implies y=\log_4(64)+3[/tex]

Rewrite 64 as 4³:

[tex]\implies y=\log_4(4)^3+3[/tex]

[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies y=3\log_4(4)+3[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies y=3(1)+3[/tex]

[tex]\implies y=3+3[/tex]

[tex]\implies y=6[/tex]

Therefore, the y-intercept of the given function is (0, 6).

The solution of the exponential expression will be a⁹.

Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied.

Given exponential expression is (a⁻¹ x a⁻²)⁻³. The expression will be solved as below,

E = (a⁻¹ x a⁻²)⁻³

The base is the same and the variables are in multiplication with powers then the powers will be added,

E = (a⁻³)⁻³

E = a⁹

Therefore, the solution of the exponential expression will be a⁹.

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Answer:

x=5

Step-by-step explanation:

Follow the steps in the image.

-Hope this helped

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{70\% of 30}}{\left( \cfrac{70}{100} \right)30}\implies 21[/tex]

Answer: 21

Step-by-step explanation:

70% of 30 students is 21

Hope this helped :)

The solution to the points are:

This is the point where the curve or curves of the graph changes direction.

In this case, the turning point in the vertex

The graph has its vertex at (1, -3.2)

This means that

Turning point = (1, -3.2)

This is the point where the curve or curves of the graph touches the x-axis i.e. f(x) = 0

In this case, the points are: (-1, 0) and (3, 0)

This means that

The roots are (-1, 0) and (3, 0)

This is the point where the curve or curves of the graph passes through x = 2.5

In this case, the points are: (2.5, -1.4)

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The correct answer is Option B. Parameters are defined as a group of numerical characteristics of a population.

Parameters are generally the numbers or values that represent the whole population's numerical characteristics. There is a difference between Statistics and Parameters.

Statistics is generally defined as the numerical characteristics of a sample. For example, a sample of standard mean or a sample of standard deviation is an example of statistics.

Parameters are the numerical representation of the characteristics of a population. For example, Population mean or Population standard deviation are examples of Parameters. These represent the data or the characteristics of the population in numerical.

Hence, the correct answer is Option B.

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The correct answer is Parameters are described as a group of numerical characteristics of a population.

In general, Parameters are the numerical values that represent the entire population's numerical characteristics. There is a variation between Statistics and Parameters. Statistics are defined as the numerical characteristics of a sample. A sample of standard mean deviation or a sample of standard deviation are examples of statistics.

               Parameters are the numerical portrayal of the characteristics of a population.  Population mean deviation or Population standard deviation are examples of Parameters. These depict the information or the characteristics of the population in a numerical way.

Hence, the correct answer is Parameters are described as a group of numerical characteristics of a population.

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The number of communication channels, 10 channels would five people require.

To find number of communication channels, we use;

On the other hand, it might be a sign of the scope and intensity of the project communication management needed in huge projects and so-called megaprojects. This could, for example, entail allocating specific resources to project communication responsibilities in accordance to the number of available channels for communication. These factors may be especially important for teams working on sensitive projects and projects where information flow may be unclear or even fraudulent.

Number of potential communication channels = n x (n-1)/2

Given n = 5;

→ x = 5*(5 - 1)/2

     = 5*2

     = 10

The number of communication channels, 10 channels would five people require.

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The greatest percent error among the predictions is of:

2.23%.

The percent error of a measure is obtained by the division of the difference between the actual value and the estimated value by the actual value, and multiplied by 100%, hence the equation is:

Percent error = |Actual - Estimate|/Actual x 100%.

From the given dot plot, we have that the farthest measure from 22.4 seconds is of 22.9 seconds.

The difference between the actual time and the estimate time is of:

22.9 seconds - 22.4 seconds = 0.5 seconds.

Applying the presented division, the percent error is given as follows:

Percent error = 0.5/22.4 x 100% = 2.23%.

The dot plot is given by the image at the end of the answer.

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A sample to have a standard deviation of zero means the score has no variability.

When the score has no variability it points towards the standard deviation being zero, This is the case where all the scores in the sample have the exact same value. This means there is no spread in the data set at all. The data set is combined in a single clumped value. Since there is only one value it would be the mean of the data set. The standard deviation measures the spread of a quantitative data set. This number cannot be a non-negative real number.

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Answer:

the answer is 350

Step-by-step explanation:

if it increased by 200% that means it doubled

so when x is doubled we get 700

so: 2x=700

       x=700/2

       x=350

The solution of the algebraic equation is x = -2. The proof is elaborated below.

The algebraic equation given to us is 14(x + 1) = -7(4 + x). An equation is a mathematical statement that proves the equality of two mathematical expressions. The first step is to simplify the brackets. The equation becomes 14x + 14 = -28 - 7x. Now, we will add 7x to both sides of the equation. The equation is modified as 21x + 14 = -28. Now, we will subtract 14 from both sides of the equation. The equation is modified as 21x = -42. Now, we will divide both sides of the equation by 21. The equation is modified as x = -2.

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Answer:

Slope is equal to the change in y y over the change in x x, or rise over run. m = change in y change in x m = change in y change in x. The change in x x is equal to the difference in x-coordinates (also called run ), and the change in y y is equal to the difference in y-coordinates (also called rise ). m = y2 −y1 x2 −x1 m = y 2 - y 1 x 2 - x 1.

The inequality expression of the volume of the balloon is V < 4,400

From the question, we have the following statement:

The initial volume of the balloon is 4,400 cubic centimeters

Also, we understand that:

The balloon leaks out over time

This means that the volume of air in the balloon decreases over time.

So, we have the following representation

V = Less than the initial volume

Rewrite as

V < 4400

Hence, the volume of the balloon at any time after it starts leaking is V < 4,400

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Answer:

Step-by-step explanation:

can’t be determined

Answer:

50 mins

Step-by-step explanation:

80 percent=40 mins

100 percent=50 mins

Step-by-step explanation:

Equation of the line which passes through the given points (-p ,-q) and

(p, q) where p ≠ q ≠ 0 is given by y = (q/p)x.

As given in the question,

Given condition is :

p ≠ q ≠ 0

Equation of the line which passes through the given points (-p ,-q) and

(p, q) is given by:

(x₁ , y₁) = (-p ,-q)

(x₂ , y₂) = (p, q)

(y -y₁)/ (x -x₁) = (y₂ -y₁)/ (x₂ -x₁)

⇒(y +q)/(x+ p) = (q +q)/(p +p)

⇒(y +q)/ (x +p) = 2q /2p

⇒p(y+ q) =q( x +p)

⇒yp + pq = qx +pq

⇒yp = xq

⇒y = (q /p)x

Therefore, equation of the line which passes through the given points (-p ,-q) and (p, q) where p ≠ q ≠ 0 is given by y = (q/p)x.

The complete question is :

Given p ≠ q ≠ 0, what is the equation of the line that passes through the points (–p, –q) and (p, q)?

A. y = –x

B. y = q/px

C. y = q

D. y = 2x + (2p – q)

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Answer:

b

Step-by-step explanation:

just did it

Step-by-step explanation:

[tex]\sf 12 \times \cfrac{12}{2} + 13[/tex]

First, let's divide 12 by 2:-

Multiply 12 × 6 :-

Add 72 + 13:-

Therefore, your answer is 85!!

____________________

Hope this helps!

Have a great day!!

Answer:

y=6x+2

Step-by-step explanation:

y=mx+c

8=6(1)+c

8=6+c

c=2

y=6x+2

The vertex of the curve will be at (-2, -4) and the axis of symmetry is at -2

From the graph, the roots of the equation are -4 and 0, therefore, (x + 4) is a factor and x is also a a factor.

The equation of the curve is the product of the factors of the curve which is y = x(x + 4)

y =  + 4x

The x coordinate of the vertex =

will be illustrated as:

-b/2a = axis of symmetry

a and b is the coefficient of x

so a = 1, b = 4

x coordinate of vertex = -4/2 = -2

Then, substitute x = -2 into y =   + 4x to find the y-coordinate of the vertex

y = (-2)² + 4(-2)

y = 4 -8

y = -4

vertex  = (-2, -4)

The axis of symmetry is -b/2a which is -2

Therefore, the vertex is at (-2, -4).

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We need to add 81 as the constant term to the binomial (n² - 18n) so that the resulting trinomial is a perfect square, and factorization of that resulting trinomial will be (n - 9).

As per the question statement, we are provided with a binomial (n² - 18n),

And we are required to add a proper constant to the above mentioned binomial so that the resulting trinomial is a perfect square, and then factorise the resulting trinomial.

To answer question, first we need to know the standard form of expanding a perfect square into a trinomial, which goes as,

[(a - b)² = {(a)² + (b)² - (2 * a * b)]

Here, if we compare our concerned binomial (n² - 18n), or, [(n)² - (2 * n * 9)], with the above mentioned standard expansion of a perfect square into a trinomial, we get, (a = n) and (b = 9), and the (b²) term is missing.

Adding [(b²) = (9²) = 81] which is a constant term, to our concerned binomial (n² - 18n), we get, (n² - 18n + 81),

Or, [(n)² + (9)² + (2 * n * 9)],

Which is a trinomial and matches with the standard expansion of a perfect square into a trinomial, and hence,

[(n² - 18n + 81) = (n - 9)²]

That is, we need to add 81 as the constant term to the binomial (n² - 18n) so that the resulting trinomial is a perfect square, and factorization of that resulting trinomial will be (n - 9).

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