As a town gets smaller, the population of its high school decreases by 8% each year. The senior class has 320 students now. In how many years will it have about 100
students? Write an equation. Then solve the equation without graphing.

The value of the absolute expression |a - b| + |b - a| will be 1.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The equation is given below.

a = b - 1/2

The expression is given as,

⇒ |a - b| + |b - a|

The value of (a - b) is given as,

a = b - 1/2

a - b = - 1/2

And the value of (b - a) is given as,

a = b - 1/2

b - a = 1/2

Then the value of the expression is calculated as,

⇒ |a - b| + |b - a|

⇒ |-1/2| + |1/2|

⇒ 1/2 + 1/2

⇒ 1

The worth of the outright articulation |a - b| + |b - a| will be 1.

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The two ways that sequences can be defined include the following: Arithmetic Sequences and Geometric Sequences.

A sequence is defined as the collection of items in such a way that repetitions can be observed.

There are two major ways the sequence can be defined in arithmetics and this includes the following:

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Answer:

31800.997945142

or

31800 24407400⁄24457657

S

The triangle ADE is similar to the triangle ABC.

What are congruent triangles?

The triangles are congruent if two sides and the included angle of one triangle match the corresponding sides and angle of another triangle.

It is given that triangle ABE is congruent to triangle ACD, which can also be written as ΔABE≅ΔACD.

So, according to the Corresponding parts of Congruent triangles (CPCT) property:

AB=AC...........(1)

AE=AD...........(2)

By dividing 2 and 1 we will get:

[tex]\frac{AD}{AB} =\frac{AE}{AC}[/tex]........(3)

In the triangles ADE and ABC, ∠A is the common angle and according to this and 3,

ΔADE is similar to ΔABC by side angle side criterion.

Therefore hence it is proved that ΔADE and ΔABC are similar.

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In geometry, parallel lines are the lines which maintain the same distance apart from each other and never intersect at any point.

What is parallel class 6?

In geometry, parallel lines are the lines which maintain the same distance apart from each other and never intersect at any point.

All rungs are perpendicular to the left post is a line perpendicular to one of a set of parallel lines, it is perpendicular to all parallel lines.

The rungs are parallel

lines that are perpendicular to the same line are parallel.

The rungs are perpendicular to both posts and the posts are parallel  to each other.

if a line is perpendicular to one of a set of parallel lines, it is perpendicular to all the parallel lines.

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To solve a 7 step equation, identify the equation, isolate the variable to one side of the equation, simplify the equation if necessary, divide both sides of the equation by the coefficient of the variable.

1. Identify the equation.

2. Limit the variable to only one side of the problem.

3. Simplify the equation, if necessary.

4. Divide both sides of the equation by the coefficient of the variable, if necessary.

5. Continue carrying out steps 2-4 until the equation is resolved.

6. Check your solution by substituting the solution back into the equation.

7. Write the solution in the form of an equation.

To solve a 7 step equation, identify the equation, isolate the variable to one side of the equation, simplify the equation if necessary, divide both sides of the equation by the coefficient of the variable, repeat steps 2-4 until the equation is solved, check your solution by substituting it back into the equation, and then write the solution in the form of an equation.

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The function rule that represents each situation is $8.75 * n.

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Here, we have

A worker's earnings E are a function of the number of hours N worked at a rate of $8.75 per hour.

We have to create an incognita that represents a worker's salary based on how many hours he or she works.

G: Worker's salary

n: number of hours worked

G=f(n)

Then using the data that the worker earns $8.75 per hour worked, we must formulate f(n) so that with this data we can calculate G.

G = f(n) = $8.75 * n

If the worker performs 1 hour of work (n=1), then his salary will be:

G = $8.75 * 1 = $8.75

If the worker performs 10 hours of work (n=10), then his salary will be:

G=$8.75 * 10 = $87.5

Hence, the function rule that represents each situation is $8.75 * n.

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The probability of the card being a queen, given that it is a face card is; 33%

The probability of an event is simply the number of favorable outcomes divided by the total number of outcomes possible.

In a  standard deck of cards, we know that there are 52 cards in total and that out of those 52 cards, there are 12 face cards.

Now, One-third of those face cards are always queens, due to the fact that there are 4 queens in a deck of cards.

This means that the probability using the formula of;

Probability = number of favorable outcomes/number of expected outcomes

Probability = 4/12 = 1/3 = 0.33 = 33%

Therefore, we conclude that there is a 33% chance that the card Luke holds is a queen.

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Answer:

orthocentre

Step-by-step explanation:

A triangle's three altitudes intersect at the orthocentre

As asked by the question, the value of K for a given equation of a line is equal to the slope of the line.

A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.

A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).

The value of K for a given line is equal to the slope of the line. Since lines are generally expressed in the form of y = mx +b , where m is the slope of the line and b is the y-intercept of the line. Here , the value of K will be equal to the slope m of the line.

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The symbol of a linear inequality is: " ≤ " or " ≥ "

The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.

It's a line with a shaded side on one side to show which xy pairings are the inequality's solutions.

For example -

Let us take a equation, 4x + 8y ≤ -24

Now, solve the above equation in the form of slope-intercept.

4x + 8y ≤ -24

or, 8y ≤ - 4x - 24

or, y ≤ -(1/2)x - 3

Now, the graph becomes according to the slope-intercept form is:

Here we noticed that,

This side of the inequality is shaded below (instead of above) because y is lower than (or equal to) the other side.

Because working with a "or equal to" inequality, draw a solid line rather than a dashed one. Points on the solid line denote locations where the inequality has been solved.

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The top 25% of cars have a typical gas mileage of at least 33.5 miles per gallon.

To calculate this, you need to use the interquartile range (IQR) formula.

The IQR is calculated by subtracting the 25th percentile (Q1) from the 75th percentile (Q3).

IQR = Q3 - Q1

In this case, the 25th percentile (Q1) is 28.4, and the 75th percentile (Q3) is 37.9. So:

IQR = 37.9 - 28.4 = 9.5

The top 25% of cars have a gas mileage of 33.5 miles per gallon, which is Q3 + 1.5*IQR.

33.5 = Q3 + 1.5*IQR

33.5 = 37.9 + 1.5*9.5

33.5 = 37.9 + 14.25

33.5 = 52.15

Therefore, the top 25 percent of cars have a typical gas mileage of at least 33.5 miles per gallon.

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Answer:

D, [tex]y=\frac{-5}{2x}+3[/tex]

Because the equation depicts a straight line in the Cartesian plane, it is called a linear equation.

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.

In the variable separation if the unknown function and its derivatives have no exponent larger than one and there are no cross-expressions—that is, terms like f f′ or f′f′′ in which the function or its derivatives appear more than once—the partial differential equation is said to be linear.

Because the equation depicts a straight line in the Cartesian plane, it is called a linear equation. Through the use of logical and mathematical tools, it enables us to solve issues in a variety of scientific fields and academic disciplines as well as in real-world circumstances.

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An observational study is used to answer a research question based purely on what the researcher observes.

An observational study is a statistical study that does not have any treatment or intervention done by the researchers.

Observational research allows the researcher to see what their subjects really do when confronted with various choices or situations. The term refers to the study of non-experimental situations in which behaviour is observed and recorded.

Statistics is the process of collecting data about a group of objects to draw conclusions about populations of those objects. For example, a statistician may take a sample group of workers from company XYZ and have them rate their job satisfaction with the company. Based on the results of that sample, the statistician can make educated assumptions about all the employees of company XYZ and their job satisfaction.

However, observational studies can only establish that significant associations exist between predictor and outcome variables. Observational studies cannot establish that the associations identified represent cause-and-effect relationships.

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Answer:

y=0

Step-by-step explanation:

The graph of the function f(x) = x^4 - 6*x^7 + 5 crosses the x-axis at x = 0 and x = 5.

The graph of the function f(x) = x^4 - 6*x^7 + 5 is a polynomial function. The roots of a polynomial are the values of x for which the polynomial is equal to zero. To find the roots of the polynomial, we must solve the equation f(x) = 0. To solve this equation, we will use polynomial division.

We will divide the polynomial by (x - 5), which will give us the following result:

f(x) = x^4 - 6*x^7 + 5 = (x - 5)(x^3 + 7x^2 - 5x + 25).

We can now solve for the roots of the polynomial. Since (x - 5) is a factor of the polynomial, the root is x = 5. We can also solve for the other roots by setting the remainder of the polynomial division equal to 0. This gives us the equation x^3 + 7x^2 - 5x + 25 = 0. This equation can be solved by factoring and the result is x = 0, 1, and 5. Therefore, the graph of f(x) = x^4 - 6*x^7 + 5 crosses the x-axis at x = 0 and x = 5.

f(x) = x^4 - 6*x^7 + 5

Divide f(x) by (x-5):

f(x) = (x-5)*(x^3 + 7x^2 - 5x + 25)

Set remainder equal to 0:

x^3 + 7x^2 - 5x + 25 = 0

Factor:

x^3 + 7x^2 - 5x + 25 = (x - 5)*(x^2 + 5x + 5)

x = 0, 1, 5

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Critical values of the function f(θ) = 2cos(θ) +(sin(θ))² on the interval 0≤ θ < 2π is 0 and π.

Therefore, the answer is 0 and π.

f(θ) = 2cos(θ) +(sin(θ))²

f'(θ) = -2sin(θ) +2sin(θ)cos(θ)

Critical values of f are points at which f' is zero or not defined.

For all values of θ, we can find that f'(θ) is defined.

f'(θ) = 0

-2sin(θ) +2sin(θ)cos(θ) = 0

cos(θ) - 1 = 0 or sin(θ) = 0

cos(θ) = 1

θ = nπ, n = 0, 1, 2, ...

sin(θ) = 0

θ = nπ, n = 0, 1, 2, ...

Therefore in the interval 0 ≤ θ < 2π, critical values are 0 and π.

2π is not there as it is not included in the interval.

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The equation of the parabola y = 5 · x² + 15 · x - 25 in vertex form is y + 145 / 4 = 5 · (x + 3 / 2)².

Herein we find the equation of a parabola in standard form, that is, an equation of the form:

y = a · x² + b · x + c

Where:

From this equation we must derive the vertex form, whose definition is shown below:

y - k = C · (x - h)²

Where:

The vertex form is found by algebra properties. First, write the equation of the parabola:

y = 5 · x² + 15 · x - 25

Second, use algebra properties until the vertex form is found:

y + 25 = 5 · x² + 15 · x

y + 25 = 5 · (x² + 3 · x)

y + 25 + 45 / 4 = 5 · (x² + 3 · x + 9 / 4)

y + 145 / 4 = 5 · (x + 3 / 2)²

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This is based on Conditional Probability.

P(a football, then a baseball) is 0.08333 and P(two baseballs)

is 0.15

The chance of an event happening given that another event has already occurred (via assumption, supposition, statement, or evidence) is known as conditional probability in the field of probability theory.  This particular approach depends on event B happening in some way connected to another event A. In this case, a conditional probability analysis with respect to event B is possible. The probability of A under the condition B is typically expressed as P(A|B) or PB if the event of interest is A and the event B is known to have occurred or is assumed to have done so (A). This can alternatively be thought of as the percentage of probability that B crosses A:

P(A|B)=P(A∩B)/P(B)

1) P(a football, then a baseball)= ([tex]\frac{5}{25}[/tex])×([tex]\frac{10}{24}[/tex]) =0.08333

2) P(2 Baseballs) = ([tex]\frac{10}{25}[/tex])×([tex]\frac{9}{24}[/tex]) = 0.15

This is based on Conditional Probability.

P(a football, then a baseball) is 0.08333 and P(two baseballs)

is 0.15

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Answer:

x = 4.5

Step-by-step explanation:

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we need to get rid of the 5 that is multiplying the expression 2x + 1.

One way to do this is to divide both sides of the equation by 5. This gives us:

(5(2x + 1))/5 = 50/5

Simplifying the left side of the equation gives us:

2x + 1 = 10

Now, we just need to get x by itself on one side of the equation. To do this, we can subtract 1 from both sides of the equation. This gives us:

2x = 9

Finally, we can divide both sides of the equation by 2 to solve for x. This gives us:

x = 9/2

Therefore, the solution to the equation is x = 9/2, or x = 4.5.

I hope this helps! Let me know if you have any other questions.

Answer:

x = 9/2 or 4.5

Step-by-step explanation:

5(2x + 1) = 50

10x + 5 = 50

10x = 50 -5

x = 45 /10

x = 9/2 or 4.5

I hope my answer helps you.

The discriminant of the quadratic equation 2x² + 3x - 5 = 0 is 49 and the nature of the roots are -3/4 + 7/4 and -3/4 - 7/4.

The discriminant of the quadratic equation 2x² + 3x - 5 = 0 is b² - 4ac = 9 - 4(2)(-5) = 49.

The nature of the roots of the equation can be determined by the discriminant. If the discriminant is positive, then the roots are real and distinct; if it is zero, then the roots are real and equal; and if it is negative, then the roots are complex and conjugate. In this case, the discriminant is positive, so the roots are real and distinct.

To calculate the roots, we use the quadratic formula:

x = [-b ± √b² - 4ac]/2a.

For this equation, a = 2, b = 3, and c = -5,

so x = [-3 ± √49]/2(2) = [-3 ± 7]/4 = -3/4 ± 7/4.

This means the two roots of the equation are -3/4 + 7/4 and -3/4 - 7/4.

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Answer:

The linear equation is y = 450 - 30 x, where y is the number of pages

Lourdes has left to read after x days

Step-by-step explanation:

Each day, Lourdes reads 30 pages of a 450-page book

- We need to write a linear equation to represent the number of pages

 Lourdes has left to read after x days

∵ Lourdes reads 30 pages each day

∵ Lourdes will read for x days

∴ The number of pages Lourdes will read in x day = 30 x

- The left pages will be the difference between the total pages of the

 book and the pages Lourdes read

∵ The book has 450 pages

∵ Loured will read 30 x in x days

∴ The number of pages left = 450 - 30 x

- Assume that y represents the number of pages Lourdes has left

 to read after x days

∴ y = 450 - 30 x

The linear equation is y = 450 - 30 x, where y is the number of

pages Lourdes has left to read after x days

Answer:(-1,2)

Step-by-step explanation:

-(6x+y=-4)

6x+5y=4

------------------

-6x-y=4

6x+5y=4

--------------

4y=8

y=2

6x+2=-4

6x=-6

x=-1

Harvard in-text citations allow for the inclusion of up to three authors. When there are four or more authors, et al. is used to shorten the citation.

In-text citations in APA style are used to quickly describe the sources of your information within the text of your research report.

The reader is directed to more detailed information in the Reference list by succinct in-text citations.

The author's last name and the year of publication are used in APA in-text citations,: (Field, 2005). Include the page number when using direct quotations, as in the following example: (Field, 2005, p. 14).

Reduce the source title or organization name, excluding any articles, to the first word or phrase in the in-text citation if it is longer than four words (a, an, and the).

The alphabetized word for the source in the Works Cited should be the first word in the abbreviated title or organization name.

Therefore, Harvard in-text citations allow for the inclusion of up to three authors. When there are four or more authors, et al. is used to shorten the citation.

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If the limit is infinity minus infinity it is undefined because the result would be a number that is not a real number.

In mathematics, a limit is the value that a function approaches as the independent variable approaches a certain value. Limits are used to study the behavior of a function as the independent variable approaches a certain point.When the limit is infinity minus infinity (∞ - ∞), it is undefined because the result is not a real number. Infinity minus infinity is an indeterminate form, which means that the limit could approach any real number or it could approach infinity or negative infinity. In other words, the result of infinity minus infinity is an unknown quantity.To understand why infinity minus infinity is undefined, you must understand the concept of infinity. Infinity is not a number, but rather an idea of something that is larger than any number. Therefore, when subtracting infinity from infinity, there is no set answer since the two concepts are not numbers. To calculate the limit, the two infinities must be replaced with real numbers. In conclusion, when the limit is infinity minus infinity, it is undefined because the result is not a real number. Infinity is an idea and not a number, so the result of infinity minus infinity can not be determined. To calculate the limit, the two infinities must be replaced with real numbers.

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A transition of AB6 units to the right followed by a transition 6 unit down this transformations could be used to prove that the line segments are congruent.

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The geometric mean of 4 and 25 is 10.

When a positive value is repeated in either the means or extremes position of a proportion, that value is referred to as a geometric mean (or mean proportional) between the other two values.

The Geometric Mean (GM) is the average value or mean that, by taking the product of a set of numbers' values as its root, indicates the collection's central tendency.

Let x = the geometric mean.

4/x = x/25 (by the definition of geometric mean)

x²=100

x=√100 (cross-product property)

x=10

Hence, The geometric mean of 4 and 25 is 10.

Complete question: What is the geometric mean of 4 and 25?

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Jing's initial pay rate is $12.50 per hour. She will receive a pay raise of $0.50 per hour every year.

Max's initial pay rate is 10 dollars per hour. He will receive a pay raise of 1 dollar per hour every year.

To determine how many years it will take for Max to earn more per hour than Jing, we need to find the point at which the two linear equations intersect. This can be done by setting the two equations equal to each other and solving for x.

Jing's equation is: $12.50 + 0.50x

Max's equation is: x + 10

Setting the equations equal to each other and solving for x, we get:

$12.50 + 0.50x = x + 10

This simplifies to:

$0.50x = -2.50

Dividing both sides by 0.50, we get:

x = -5

Since the value of x cannot be negative, this means that Max will never earn more per hour than Jing.

If the function for the total rental cost for vacuum cleaner is f(x) = 6x + 14 , then the cost for using it for 10 hours is  $74   .

A hardware store rents vacuum cleaner for a part of a day ,

the function that models the total rental cost for the vacuum cleaner is given as : f(x) = 6x + 14 ;

where , x is the number of hours the cleaner is used .

given that the vacuum cleaner is used for 10 hours , So x = 10 .

the total cost is f(10) = 6×10 + 14  ;

f(10) = 60 + 14 ;

f(10) = 74 ;

Therefore , the total rental cost for using the vacuum cleaner for 10 hours is $74  .

The given question is incomplete , the complete question is

A hardware store rents vacuum cleaners that customers may use for part of a day before returning. The function f(x) = 6x + 14 models the total rental cost of a vacuum cleaner. What is the total cost for using the vacuum cleaner for 10 hours  .

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