John read 7 and 1/2 pages in 2/5 of an hour at what rate in pages per hour did he read?

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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Answer: always, always

Step-by-step explanation:

Every circle is similar to every other circle.

The probability that the number is a multiple of four is 0.25.

we know that if a number is multiple of four then its last 2 digits must be divisible by four.( i.e. ten's and one's places)

We are given only four numbers 1,2,3,4 , which can't be repeated.

So here , in this case , such numbers with last two digits divisible by four are 12,24 and 32 only

Having last two digits ‘12’ ;

the first two digits can be formed using 3 and 4 only . This can be done in (2!) = 2 ways.

Similar case will be happening with 24 and 32 as well.

So the total ways of getting a multiple of four will be = 2 + 2 + 2

                                                                                        = 6 ways

Now total numbers that can be made from given four digits = [tex]P_{4} ^{4}[/tex]

                                                                                                  = 24

So the probability of getting a multiple of four is = 6/ 24

                                                                                 = 0.25

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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 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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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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Step-by-step explanation:

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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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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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

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).

Answer:

y = -2x + 1

Step-by-step explanation:

y = mx + b  you must find the m (slope) and the b (y intercept) to write the equation for the graph.

The slope is negative.  If you start on the very left side of the graph and follow it, you will see that it goes in a down hill direction.  That means that the slope is negative.  If I start on the very left and the line goes up from there, the slope is positive.  If the line is a straight horizontal line, then the slope is zero, it does not go up or down.

The slope is -2.  Select one of the dots and travel to the next dot, but you can only move horizonaly and vertically.  You cannot move diagonally.  You will notice that the two closes dots are two units up (or down) and only 1 unit left (or right) depending on which dot you start at.  Since you move 2 units up and 1 unit left that is a slope of 2.  2/1 = 2.

The b (y-intercept) is just where you see the line cross the y axis.  It crosses it at 1.

Answer:

  y = -2x + 1

Step-by-step explanation:

Here m is the slope and b is y-intercept.

Pick any two points on the line.

(-1,3) & (2,-3).

Find the Slope.

     [tex]\sf \boxed{Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

                 [tex]\sf = \dfrac{-3-3}{2-[-1]}\\\\=\dfrac{-6}{2+1}\\\\=\dfrac{-6}{3}\\\\=-2[/tex]

m = -2.

Equation of the line:

     y = -2x + b

Substitute any one point in the above equation and find the y-intercept. (-1,3)

     3 = -2*(-1) + b

     3 = 2 + b

3 - 2  = b

      b = 1

Equation of the line:

        y = -2x + 1

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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21 is  missing  length of parallel lines.

What is an example of parallel lines?

Because lines are parallel

so they cut into equal proportion

 then ,         4/10  = x/15

                  4 * 15/10 = x

                     x = 6

length of line  = 15 + 6 = 21

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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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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.

Answer: 120

explanation: We already have our first value 36 and the second value 30. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

STEP 136 = 30% × Y

STEP 236 =

30

100

× Y

Multiplying both sides by 100 and dividing both sides of the equation by 30 we will arrive at:

STEP 3Y = 36 ×

100

30

STEP 4Y = 36 × 100 ÷ 30

STEP 5Y = 120

Finally, we have found the value of Y which is 120 and that is our answer.

You can easily calculate 36 is 30 percent of what number by using any regular calculator, simply enter 36 × 100 ÷ 30 and you will get your answer which is 120

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

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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a) a/5 + 3 = 8

Step 1 : Minus both sides by 3

a/5 + 3 - 3 = 8 - 3 -> a/5 = 5

Step 2 : Multiply both sides by 5

a/5 x 5 = 5 x 5 -> a = 25.

b) (3b)/7 - 1 = 5

Step 1 : Add both sides by 1

(3b)/y - 1 +1 = 5 + 1 -> (3b)/7 = 6

Step 2 : Multiply both sides by 7

(3b)/7 x 7 = 6 x 7 -> 3b = 42

Step 3 : Divide both sides by 3

3b : 3 = 42 : 3 -> b = 14.

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 simple interest using I = prt if Oliver borrowed $1,500 to purchase a riding lawn mowerat the rate of f 12% for 6 monthsis

The concept that will be used is the concpt of simple interest and thei can be calculates using the simple interst formular which is

I = [(prt)/100]

where p = principal =  $1,500

     I = intereste rate

     t=time

Then this can be expressed as

I= (prt)/100

I =  ($1,500* 6/12 * 12 )/100

=  $90

In conclusion the simple interest is now  $90 which is the second option that is given.

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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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Answer:

VA: x = 1, x = -1

HA: y = 0

x-int: (4, 0)

y-int: (0, 4)

Step-by-step explanation:

x-int:

0 = (x-4)/((x-1)(x+1))

0 = (x-4) because the (x-1)(x+1) are multiplied by 0

4 = x

x = 4

(4, 0)

y-int:

y = (0 - 4)/((0 - 1)(0 + 1))

y = (-4)/((-1)(1))

y = (-4)/(-1)

y = 4/1 = 4

(0, 4)

The angle amount of m is 128⁰

Angle can also refer to the length of a rotation or an angle. The Greek word , which means "crooked, curled," and the English word "ankle," are related words. Both stem from the Proto-Indo-European root  which means "to bend" or "bow," in some way.

A plane angle, according to Euclid, is the inclination to each other of two intersecting lines in a plane that are not perpendicular to one another. Proclus asserts that an angle must be either a quality, a number, or a connection. Eudemus used the first idea, viewing an angle as a departure from a straight line; Carpus of Antioch used the second idea, viewing an angle as the distance or space between intersecting lines; and Euclid used the third idea. Vertical angles, opposing angles, or vertically opposite angles refer to a pair of angles that are directly across from one another and are created by two straight lines meeting to form a "X". Vert is the shorthand for them. opp.

The vertical angle theorem states that angles that are vertically opposing are equal. The assertion shown that since both of a pair of vertical angles are supplementary to both of the neighboring angles, the vertical angles are equal in measure, according to Eudemus of Rhodes' attribution of the proof to Thales of Miletus. When Thales visited Egypt, it is recorded in history[9] that he noticed the Egyptians measuring the vertical angles whenever two intersecting lines were drawn to ensure that they were equal. Thales came to the conclusion that one might establish

4x+6=7x-21

3x=27

x=9

x+x+42+42=360

2x+84=360

x=128⁰

Therefore, the angle amount of m is 128⁰

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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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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

The corresponding sides and angles of both the triangles [pre-image and the image] are congruent

Hence,The corresponding sides and angles of both the triangles [pre-image and the image] are congruent

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