write an equation of the line that passes through point p and is perpendicular to the line with the given equation.

30 boxes of popcorn and 20 free DVD rentals were given away.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

let a variable represent the number of the highest-cost item (boxes of popcorn). If that is p, then the number of DVD rentals is (53-p) and the total cost is ...

 2p +(50 -p) = 80

 p = 80 -50 = 30 . . . . . . . boxes of popcorn

50-p= (50 -30) = 20 . . . DVD rentals

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The inverse of the function is, [tex]f^-^1(x)=x^2+4x+4[/tex].

What is inverse of the function?

The inverse function of a function f in mathematics is a function that reverses the operation of f. If the inverse of f exists, it is denoted by f-1 and exists only if f is a bijective function.

Given that f(x) = √x - 2

We have to find the value of f-¹(x).

Let, y = √x - 2

Replace x with y.

⇒ x = √y - 2

Adding 2 on both sides,

x + 2 = √y - 2 + 2

x + 2 = √y

Taking square on both sides,

(x + 2)^2 = (√y)^2

x^2 + 4x + 4 = y

y = x^2 + 4x + 4

Rewrite y as .[tex]f^-^1(x)[/tex]

So, we get [tex]f^-^1(x)[/tex] = x^2 + 4x + 4

Hence, the inverse of the function is, [tex]f^-^1(x)=x^2+4x+4[/tex].

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The answer of the given multiplication is, 30.935.

What is multiplication?

A mathematical formula that specifies the objects to be multiplied, known as a factor, produces a product. For instance, the product of x and is cdot, while the product of x and is 30.

Consider, the product

          1  1.  5

   x     2.  6  9

__________________

           1  0  3  5

+         6  9  0  0

+      2  3  0  0  0

____________________

       3  0  9  3  5

There is one after after decimal point in 11.5, and there are two digits after decimal point in 2.69

So, there are total three digits after decimal point.

Therefore, we place the decimal after 0.

Hence, the multiplication of given numbers is, 30.935

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Answer:

$4.21

Step-by-step explanation:

6*70+1=421

There are total 246 ways to select a committee of 3 from a gorup of 13.

What is Combination?

A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant. You can choose the components in any order in combinations.

Solution:

Given that,

Total Number of Applicants = 13

Total Seats Available for the Committee = 3

Since, the order of selection is not relevant in the given question we will use combination.

13C3 = 13! / (10! * 3!)

13C3 = 13*12*11*10!/(10! * 6)

13C3 = 286

This means there are total 246 ways to select a committee from a gorup of 13.

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The amount that the customer be charged before tax and tip is $25.55

Given,

The markup on a restaurant = 250%

The cost of a meal to produce = $7.30

We have to find the amount will the customer be charged before tax and tip;

The markup price = 250/100 × 7.30 = 5/2 × 7.30 = 2.5 × 7.30 = 18.25

The Markup price on a restaurant is $18.25

Now,

The amount that the customer be charged before tax and tip = The cost of a meal to produce + The markup price

= 7.30 + 18.25

= 25.55

That is,

The amount that the customer be charged before tax and tip is $25.55

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The first four terms are -4 , -1 , 4, 11 respectively

Sequence is the arrangement of set of number in a particular order.

A se.q.u.e.n.c.e. can be defined based on the number of terms.

The function f (n) =n^2-5, where n is the number of term

therefore, when n= 1, (first term)

f (n) = 1^2-5= -4

when n= 2 (second term)

f (n) = 2^2-5=4-5= -1

when n= 3 (Third term)

f (n)= 3^2-5=9-5= 4

when n = 4 (fourth term)

f (n)= 4^2-5=16-5= 11

therefore the first four term of the sequence are -4 , -1 , 4, 11 respectively

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Answer:

Below

Step-by-step explanation:

= 2000 (.9)^2 (.9)^t

    = 2000(.81)(.9)^t

         = 1620 (.9)^t

Answer:

[tex]K(t)=1620(0.9)^{t}[/tex]

Step-by-step explanation:

Given function:

[tex]K(t)=2000(0.9)^{t+2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]

[tex]\implies K(t)=2000(0.9)^{t}\cdot(0.9)^2[/tex]

Simplify:

[tex]\implies K(t)=2000(0.9)^{t}\cdot0.81[/tex]

[tex]\implies K(t)=0.81 \cdot 2000(0.9)^{t}[/tex]

[tex]\implies K(t)=1620(0.9)^{t}[/tex]

The graph of the inequality y < -1

In the below, See the attachment

Given,

In the question:
The equation is :

y< -1

To graph the above equation:

What is graph explain?

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node.

Now, According to the question:

y is less than -1

The graph will be :

In the below, See the attachment .

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a) The number of students studying abroad in the year 2001 is; 150.38 thousand

b) The number of students studying abroad in the year 2018 is; 467.53 thousand

An exponential growth or decay function is defined as a function that grows or shrinks at a constant percent growth rate.

We are given the equation as;

y = 123.1(1.069)ˣ

This equation models the number of students who studied abroad each year from 1998 to 2013

where;

y is the number of students from a certain country studying abroad

x is the number of years after 1998

a) In the year 2001, this is 3 years after 1998 and so we have;

y = 123.1(1.069)³

y = 150.38 thousand

b) In the year 2018, it will have been 20 years after 1998. Thus, we have;

y = 123.1(1.069)²⁰

y = 467.53 thousand

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The total time it will take to to read a book that has 305 pages is 167.75 minutes.

The time it takes to read 10 pages of a book can be represented with the equation y equals 5.5 divided by 10 times x, where y represents the total time in minutes and x represents the number of pages read.

Therefore, the equation is as follows

[tex]y = \frac{5.5}{10}x[/tex]

where

Hence, let's find how long it will take to read a book that has 305 pages.

Therefore,

[tex]y=\frac{5.5}{10}(305)[/tex]

[tex]y = \frac{1677.5}{10}[/tex]

y = 167.75 minutes

Therefore, it will take 167.75 minutes.

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The set of factors of 16 is={1,2,4,8,16}.So option(1) is correct

Natural numbers are those that start with 1 and go on indefinitely. In other words, natural numbers are counting numbers that do not include 0 or any negative or fractional numbers. Natural numbers are numbers like 1, 6, 89, 345, and so on.

What exactly are the factors?

A factor is a number that divides another number with no remainder. In other words, if multiplying two whole numbers results in a product, the multiplied numbers are factors of the product because the product is divisible by them. There are two methods for locating factors: multiplication and division.

Given in the question that, N is the set of natural numbers that are factors of 16

factors of 16 are = 1,2,4,8,16

so the set of factors of 16 is={1,2,4,8,16}

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The graph of the polynomial f(x) is added as an attachment

From the question, the equation of the polynomial is given as

f(x) = x^3 + 3x^2 – 4x – 12

To start with, we need to represent the function of the polynomial properly

So, we have the following representation

f(x) = x³ + 3x² – 4x – 12

Solving further, we need to factorize the function

This gives

f(x) = x²(x + 3) - 4(x + 3)

Factor out x + 3

f(x) = (x² - 4)(x + 3)

Express as difference of two squares

f(x) = (x - 2)(x + 2)(x + 3)

When the above equation is solved, we have

x = 2, x = -2 or  = -3

This means that the intercepts of the function are -3, -2 and 2

Next, we plot the polynomial function using the above intercepts and the end behavior

See attachment for the graph of the function

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Answer:

i need help please by german

The diameter of this circle has length of 65 when it is inscribed in a circle is a quadrilateral.

The straight line that runs through the center of a round shape or object from one point on one edge to another: The diameter is twice as large as the radius. The pond is six feet across. Both definitions hold true for the diameter of a sphere.

We note that 25²+60²=65² and 39²+52²=65²

Let [tex]\bar{AB}[/tex]=25, [tex]\bar{BC}[/tex]=39, [tex]\bar{CD}[/tex]=52, [tex]\bar{DA}[/tex]=60

Let [tex]\bar{BD}[/tex]=x and ∠DAB=y

x²=25²+60²-3000cos(y)

x²=39²+52²-4056cos(180-y)

We obtain by performing some computation x²=4225-3000cos(y) and x²=4225-4056cos(y).

4056cos(y)=3000cos(180-y)

cos(180-y)=-cos(y)

So, by substituting we get 4056cos(y)= -3000cos(y)

cos(y)=0 or y=90.

∠BAD=90 and ∠BCD=90.

The diameter of a right triangle inscribed in a circle is the hypotenuse.

This means that the diameter is √4225=65

Therefore, the diameter of this circle has length of 65.

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5+-13/2

x= -b ±√b²-4ac÷2a

x^{2}-5x+3=0

a=1

b=-5

c=3

x=-(-5±√(-5)²-4.1.3÷2.1

Evaluate the exponent

Multiply the numbers

Subtract the numbers

Multiply the numbers

x=5±√13÷2

To solve for the unknown variable, separate it into two equations: one with a plus and the other with a minus.

x=5+√13÷2

x=5-√13÷2

Rearrange and isolate the variable to find each solution

x=5+√13÷2

x=5-√13÷2

x=5±√13÷2

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Answer: 714 and 715

Step-by-step explanation:

In mathematics, a Ruth–Aaron pair consists of two consecutive integers (e.g., 714 and 715) for which the sums of the prime factors of each integer are equal: 714 = 2 × 3 × 7 × 17, 715 = 5 × 11 × 13, 2 + 3 + 7 + 17 = 5 + 11 + 13 = 29.

Hope this helps!!! :)

Answer: 30.4

Step-by-step explanation:

After some work this is my final answer.

Answer: for the first it is not direct varition while for the second one it i s

Step-by-step explanation:

Factor:

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product. There are two methods of finding factors: multiplication and division.

Multiple:

multiple in math are the numbers you get when you multiply a certain number by an integer. For example, multiples of 5 are: 10, 15, 20, 25, 30…etc. Multiples of 7 are: 14, 21, 28, 35, 42, 49…etc.

How to find hcf of two or more numbers :

Steps 1:

Find all the factors of each given number.

Step 2:

Find common factors of the given number.

Step 3:

The greatest of all the factors obtained in Step 2, is the required highest common factor (H.C.F).

I'm only writing the answers below as I already told how to find it.

Highest common factor:

1. The factors of 18 are: 1, 2, 3, 6, 9, 18

The factors of 20 are: 1, 2, 4, 5, 10, 20

Then the greatest common factor is 2.

2. The factors of 15 are: 1, 3, 5, 15

The factors of 15 are: 1, 3, 5, 15The factors of 20 are: 1, 2, 4, 5, 10, 20

The factors of 15 are: 1, 3, 5, 15The factors of 20 are: 1, 2, 4, 5, 10, 20Then the greatest common factor is 5.

3. 8

4. 12

5. 10

6. 14

How to find lcm. of numbers :

Step 1: Find the prime factors of the given numbers by repeated division method.

Step 2: Write the numbers in their exponent form. Find the product of only those prime factors that have the highest power.

Step 3: The product of these factors with the highest powers is the LCM of the given numbers.

I'm only writing the answers below as I already told how to find it.

Lowest common multiple :

1. 42

2. 12

3. 40

4. 20

5. 80

6. 42

hope it helps you..

Answer:

s = 16

Step-by-step explanation:

4s+s+36+4s =180  The sum of the interior angles of a triangle is 180  Combine like terms.

9s + 36 =180  Subtract 36 from both sides

9s = 144  Divide both sides by 9+

s = 16

Answer:

s = 16

Step-by-step explanation:

the three angles of a triangle should add up to 180 degrees.

If you have 5 qualified candidates to fill the positions of president and vice president, then their have 20 ways to be fill the positions.

In the given question,

If you have 5 qualified candidates to fill the positions of president and vice president, then we have to find how many ways can the positions be filled.

We have total 5 qualified question.

Their have total 2 position president and vice president.

When the one position one of president filled then their one left 4 qualified candidate for the vice president position.

So the possible ways to fill the position is find by multiplying the 5 and 4. So

Possible ways=5*4

Possible ways=20

Hence, if you have 5 qualified candidates to fill the positions of president and vice president, then their have 20 ways to be fill the positions.

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The given sample is stratified sampling with topology as the stratum variable.

Archaeologists plan to examine a sample of two-meter-square plots near an ancient Greek site for artifacts visible in the ground. They choose separate samples of plots from the floodplain, coast, foothills, and high hills. We need to find the kind of this sample.

It is not a simple random sample since we cannot include just floodplains in the sample, for example. As a result, not all feasible subsets have an equal chance of being picked. This is stratified sampling with topology as the stratum variable.

Statistics is the study of data gathering, organization, analysis, interpretation, and presentation. It is customary to begin with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem.

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After one hour, there would be 337,500 bacteria in the hamburger.

This problem involves exponential growth relation, which is as below:

[tex]P(t)=P_{o}*e^{rt}[/tex]

where, [tex]P_{o}[/tex] is the initial value (i.e. at t=0), P(t) is the value at time 't' and r is the growth rate.

Usually, one perceives growth as linear, which might seem logical in unspecified cases. But, when specified exponential growth, the scenario changes. The difference between linear and exponential growth is like the difference between velocity and acceleration.

In case of above stated problem; [tex]P_{o}[/tex]=100,000 and P(20)=150,000

For calculating r, we substitute values:

[tex]150,000=100,000*e^{r*20}\\e^{20r}=1.5\\20r=ln(1.5)\\r=0.0202733[/tex]

Now we have our growth rate. Using the same formula for t=60, we have:

[tex]P(60)=100,000*e^{0.0202733*60}\\P(60)=100,000*3.375\\P(60)=337,500[/tex]

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Answer:
I agree due to everything stated there everything is perpendicular and is equal to the each other.

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By taking some simple quotients, we will see that a gold star gives 3 points more than a silver star.

First, we know that 80 silver stars are equivalent to 160 points, to get the number of points that each star gives, we need to take the quotient between the number of points and the number of stars.

160/80 = 2

Each silver star gives 2 points.

We also know that 30 gold starts give 150 points, then:

150/30 = 5

Each gold star gives 5 points.

The difference is:

5 - 2 = 3

A gold star gives 3 points more than a silver star.

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The perimeter of the parallelogram is 35 cm.

The length of the continuous line that a parallelogram's boundary forms are considered to be its perimeter. The same unit applies to it as it does to its sides. A closed shape made up of four line segments is referred to as a quadrilateral. If the opposing sides of a quadrilateral are parallel and the same length, the shape is referred to as a parallelogram.

Given, the area of the parallelogram = 62 cm²

We know the area of the parallelogram = base × height

62 = b × 6.2 cm

b = 62/6.2

b = 10 cm

So, the perimeter of the parallelogram is given by

P = 7.5 + 10 + 7.5 + 10 cm

P =  35 cm

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The cost of one text message is $0.04

Algebra is a branch of mathematics that helps with the representation of problems or situations through the use of mathematical expressions. We use definite or fixed numbers in algebra, such as -1,11, and so on. In algebra, in addition to numbers, we use variables such as x, y, and z.  Elementary algebra covers the fundamental concepts of algebra. It is frequently contrasted with arithmetic: arithmetic deals with fixed numbers, whereas algebra incorporates variables.

Given that $6. 32 to send 158 text messages

We have to determine the cost of one text message

158 = 6.32

1 = ?

= 6.32/158

= 0.04

Therefore the cost of one text message is $0.04

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Answer: For fiction Gabriel needs about 3 shelves with an extra 4 more books. For nonfiction books it's the same with 3 shelves with 1 more to put.