2. Write an equation to represent f(e)










Absolute Value Functions

Dion will make $16381.2 in a year.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The formula for simple interest is:

S = p*t*r/100

where P is the principal amount of money, R is the interest rate as a decimal, T is the time.

Dion gave $12, 848 to his local church

which he calculated as 27.5 % of his yearly salary.

S = 12, 848 * 1*27.5 /100 = 3533.2

Total = 3533.2+12, 848 = $16381.2

Hence Dion will make $16381.2 in a year.

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Answer:

see below

Step-by-step explanation:

7300 investment

annual rate 6.6% compounded monthly = 6.6/12 months = 0.55% per month

t years = t*12 months

so function is = 7300 * (1+6.6%/12)^12t

APY = (1+0.55%)^12 - 1 = 1.068-1 = 0.068 = 6.8%

The exponential function [tex]Y=21{(1.44)}^x[/tex] represents growth when x ∈ N.

The formula for exponential growth is [tex]y = y_0.e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_0.e^{(-kt)}.[/tex].

Given, An exponential function [tex]Y=21{(1.44)}^x[/tex].

Now, This function can represent growth or decay depending upon the values of 'x'.

If x ∈ N, Then this exponential function [tex]Y=21{(1.44)}^x[/tex] represents growth.

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a) The table is given below..

b) x + y = 45

c) 5.20x + 9y = 291

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

Cost of small box x = $5.20

Cost of large box y = $9

Now,

Number of boxes sold in one hour = 45

Total amount earned = $291

We can make two equations.

x + y = 45

x = 45 - y

Substituting

5.20x + 9y = 291

5.20 (45 - y) + 9y = 291

234 - 5.20y + 9y = 291

234 + 3.8y = 291

3.8y = 291 - 234

3.8y = 57

y = 15

Now,

x = 45 - y

x = 45 - 15

x = 30

Table:

Categories     Value   Number     Amount

Small box       5.20         30          30 x 5.20 = 156

Large box        9              15          15 x 9 = 135

Thus,

The table is given above.

The equation is x + y = 45

The equation is 5.20x + 9y = 291

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The Length of RS = 7 units.

The set of points that lie on a straight line is known as Collinear points. In other words, two or more points that lie on the same straight line are said to be Collinear points.  

Here we have

RS = x + 5, ST = 14x − 15, and RT = 20  

When R, S, and T are considered as 3 collinear points

=> RT = RS + ST

From the given data,

=> 20 = x + 5 + 14x − 15  

=> 15x − 10 = 20

=> 15x = 30

=> x = 2

Length of RS = x + 5 = 2 + 5 = 7

Therefore,

The Length of RS = 7 units

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Answer:

4 × 5p = 20p

(Multiply the terms; don't have to be like terms)

Reason:

I'm assuming the x refers to multiplication. If so, then 4 x 5 = 4 times 5 = 20. The p doesn't change.

A real world example would be that 5p represents a box with 5 pens inside it. Then imagine 4 such boxes to get 4 x 5 = 20 pens total.

In a case whereby One number is 11 less than another ,If their sum is increased by eight, the result is 81 the numbers will be 42.

The concept that will be used here is summation. A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.

Let the first number be wriiten as = x

second number = x-11

The we can add up as :

(x + x -11 + 8) =81

2x -3 =81

2x =84

x = 42

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Two compound propositions p and q are logically equivalent if p↔q is a tautology. Alternatively,  p and q are equivalent if and only if the columns in a truth table giving their truth values agree.

Two compound propositions p and q are logically equivalent if and only if p logically implies q and q logically implies p. In other words: two compound propositions are logically equivalent if and only if they have the same truth table.

let us consider,

       T be the truth and F be the false of a problem statement.

Then the compound propositions p and q are logically equivalent if :

                 P                           q               P→q

                  T                             T                  T

                  F                             F                   T

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The complete question is :

What is the correct way of determining of two compound propositions p and q are equivalent.

construct a truth table for p→q if the proposition is tautology.

The numbers in order from smallest to in largest are 65.6, 66.6. and 67.6 respectively

Algebraic expression are expressions comprising of terms, variables, coefficients, constants and factors.

These algebraic expressions are also composed of arithmetic operation, such as;

From the information given as;

x+1 + 2x + 4 + 2x + 6 = 334

collect like terms

x + 2x + 2x = 334 - 11

add or subtract like terms

5x = 323

Make 'x' the subject of formula

x = 64. 6

The numbers are;

x + 1 = 65.6

x+ 2 = 66. 6

x + 3 = 67. 6

Hence, the numbers are 65.6, 66.6. and 67.6

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Yes, you can distinguish the two components if you have two detectors. The detectors can measure different properties of the components, such as:

By using the two detectors and measuring different properties of the components, you can identify which components belong to which state. For example, a detector can measure the size of the components, and another detector can measure the density of the components. If the components from one state have a larger size or a higher density than the components from another state, then the detectors can distinguish between the two components.

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When a fifth degree polynomial with a root of multiplicity 3 at x = 2, and a root of multiplicity to at x = -3. The polynomial can be written in the form

Each zero's multiplicity is the quantity that indicates how frequently its corresponding factor appears. In other words, the powers are the multiplicities.

The polynomial is expressed as  y = (x - 2) ^a (x - b)^c

for x = 2, x - 2, and the multiplicity is 3 hence

(x - 2)³

for x = -3, x + 3 and the multiplicity is will be 2 hence

(x + 3)²

Because of this we can say that

a = 3, b = -3 and c = 2

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The number of hours that Alonso would have to work to earn $ 554. 40, given the same hourly wage, is 37.9 hours

To find the number of hours that Alonso needs to work in the week to make $ 554. 40, you first need to find the hourly wage :

= Amount earned / Hours worked

= 204. 40 / 14

= $ 14. 60 per hour

If Alonso wants to earn $ 554 .40 then the number of hours he would need to work is:

= Amount to be earned / Hourly wage

= 554. 40 / 14. 60

= 37.9 hours

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The dimension of the largest possible rectangular area that can be fenced for $4800 is 300 yard × 150 yard. The area, A of the rectangle as a function of its width, w is A = 300w - 1.5w².

Let the width of the rectangular area be "w" and its length be "l".

The cost of the east-west direction fencing is

2w * 12 = 24w

and the cost of the north-south direction fencing is

2l * 8 = 16l

Since the rancher wants to spend exactly $4800 on fencing, we can write an equation to represent the cost:

24w + 16l = 4800

Divide by 8

3w + 2l = 600

Therefore, l = 300 - 1.5w

The area of the rectangle is given by "lw", so

A = lw

Substituting the value of "l" from the first equation into this second equation:

A = (300 - 1.5w)w

A = 300w - 1.5w²

Thus, the area of the rectangle is a function of its width and can be expressed as Area = 300w - 1.5w².

To find value of w with maximum area, dA/ dw = 0

300 - 3w = 0

w = 100

Therefore, l = 300 - 1.5*100

l = 150

--The question is incomplete, answering to the question below--

"A rancher who wishes to fence off a rectangular area finds that the fencing in the east-west direction will require extra reinforcement due to strong prevailing winds. Because of this, the cost of fencing in the east-west direction will be $12 per (linear) yard, as opposed to a cost of $8 per yard for fencing in the north-south direction. Find the dimensions of the largest possible rectangular area that can be fenced for $4800, express the area of the rectangle as a function of its width."

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The correct orientation and location of triangle DEF is option B (as shown in the attachment to this answer).

Rotation is one of the types of solid transformation which involves turning a given object about a reference point or line at a certain required measure of angle. Other types of transformation are: dilation, translation and reflection.

Dilation: This is a process in which the dimensions of an object is either increased or decreased to produce its image.

Translation: This is a procedure that requires moving a given object a number of units in a specified direction.

Reflection: This requires flipping an object over a line to produce an image.

In the question, after rotating triangle ABC 90^o clockwise; the correct orientation and location of triangle DEF is option B.

A sketch of this is attached to this answer for clarity.

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Answer:

how would i know the closing price ...

If an oil change at city auto is regularly $30 Mr. Allen has a coupon for 15% off. The  equation that can be used to find the sale price, S, of an oil change is: 3. s=0.85(30).

First step is to find the percentage left if he has a coupon for 15% off.

Percentage left = ( 1- 0.15)

Percentage left  = 0.85 or 85%

Now let find the sales price

Sales price = 0.85(30)

Sales price = $25.50

Therefore the  equation that can be used to find the sale price, S, of an oil change is: 3. s=0.85(30).

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The complete question is:

An oil change at city auto is regularly $30 Mr. Allen has a coupon for 15% off. Which equation can be used to find the sale price, S, of an oil change?

1. s=0.85 divided by 30

2. s=85 divided by 30

3. s=0.85(30)

4. s=85•30

To find the football field's area in square yards, we need to multiply the length by the width, both of which are given in different units of measurement (yards and feet).

Steps:

1. Convert the width of the field from feet to yards: 160 feet / 3 feet/yard = 53.33 yards

2. Multiply the length and width of the field to find its area: 100 yards * 53.33 yards = 5,333 square yards. Therefore, the area of the football field is 5333.33 square yards.

The room is square since the length and range of the room are the same. Hence, we can apply the area of the square formula to cipher the area of the given carpet demanded to cover the room. Hence, the answer is 16 square yards.

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The area of the field in square yards will be 16 sq. yards.

To calculate the size of a football field in square yards, multiply the length by the width, which are both given in separate units of measurement (yards and feet).

First, we'll convert the field's width from feet to square yards.

There are 3 feet in 1 yard,

So 160 feet is the same as 160 / 3 = 53.333 yards.

Then we'll multiply the length by the width: 100 * 53.333 = 5333.33 square yards.

Therefore, the area of the football field is 5333.33 square yards.

The room is square since its length and width are equal.

As a result, we can use the area of the square formula to calculate the area of the provided carpet required to cover the room.

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Note that:

There are three separate planes and three different lines in the diagram. Line X crosses two of the planes, whereas Line Z intersects just one of the planes, and Line Y has points on all three planes.

Line y has points A and B in each of the three planes.

A plane is a flat surface that can be sliced across by a straight line connecting any two locations on the plane.

As a result of the diagram, we may deduce that

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The completed proof for the two triangles is as follows -

ST bisects ∠UTV - Given

∠UTS ≅ ∠VTS - Angle Bisection Theorem

∠TUS and ∠TVS are right angles - Given

∠TUS ≅ ∠TVS - All right angles are congruent

ST ≅ ST - Reflexive property of congruence

ΔUTS ≅ ΔVTS - Angle Angle Side (AAS) Theorem

SU ≅ SV - CPCTC Rule

SU = SV - Congruence Theorem

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

Two right angle triangles ΔSUT and ΔSVT are given with line segment ST being the common.

It is given that line segment ST bisects ∠UTV as ST is the common line between the two triangles.

∠UTS ≅ ∠VTS as it is bisected by the line segment ST and it follows the rule of angle bisection theorem.

∠TUS and ∠TVS similar as they both are right-angles which is denoted by the small square symbol in the diagram.

∠TUS ≅ ∠TVS as they both are right-angles and all the right angles are equal and congruent having a measure of 90°.

ST ≅ ST since it is mid line segment of both the triangles and it follows the rule of reflexive property of congruency.

ΔUTS ≅ ΔVTS as they satisfy the AAS theorem, where two angles of a triangle and side between them are equal. Here, ∠UTS ≅ ∠VTS, ∠UTS ≅ ∠VTS and ST ≅ ST.

SU ≅ SV as corresponding parts of the congruent triangles are congruent. So, the CPCTC rule is applied.

SU = SV as they are part of the congruent triangles, so the line segments must be equal.

Therefore, ΔUTS is equal and congruent to ΔVTS.

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Answer:     Hope this helps sorry for answering late ^ ^

Step-by-step explanation: i got it right

The ratio of rubies to diamonds is equal to 1:4.

In Mathematics, a ratio simply refers to a mathematical expression that is typically used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In this scenario, we would assign variables to the number of rubies and number of diamonds as follows;

Since the number of rubies is four (4) times the number of diamonds, this can be represented as a ratio as follows;

R = 4D ⇒ R:D = 1:4.

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The value of x is 10.79

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

sin (tetha) = opp/ hyp

cos ( tetha) = adj/ hyp

tan ( tetha) = opp/ adj

tetha = 26

hyp = 12

adj = x

cos 26 = x/12

cos 26 × 12 = x

x = 0.899 × 12

x= 10.79

Therefore the value if x is 10.79

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The measure of angle K and L in the first figure is ∠L = 23 degrees and ∠K = 157. Second figure, the measure of ∠K = ∠L = 70 degrees.

A polygon's interior angle is the angle created between its two adjacent sides. Alternately, we may state that the internal angle of a polygon refers to the angle measured at the interior portion of a polygon.

For figure 2 the two lines are parallel to each other, and the line that meets the parallel line at points at M and L are from two equal lines.

Hence, the angle suspended by both are equal, that is:

∠L = ∠M

∠L = 23 degrees.

Now, the ∠K and ∠J are created by two parallel lines; hence they are equal:

∠K = ∠J = x

The sum of interior angles of a quadrilateral is 360, so:

∠L + ∠M + ∠J + ∠K = 360

23 + 23 + x + x = 360

46 + 2x = 360

2x = 360 - 46

x = 157

Hence, the measure of angle K and L is 157 and 23 respectively.

For the second figure, the angle K and L are created by equal length of segments.

∠K = ∠L = x

The sum of interior angles of a quadrilateral is 360, so:

∠L + ∠M + ∠J + ∠K = 360

x + 90 + 130 + x = 360

2x + 220 = 360

2x= 360 - 220

x = 70

Hence, the angle of K and L is 70 degrees.

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hash functions are mathematical functions that create a hash value, also known as a message digest, by converting variable-length messages into a single fixed-length value.

A hash function converts a given numeric or alphanumeric key into a practical and controllable integer value. The mapped integer value acts as an index in the hash table.

A hash function, in its simplest form, converts a significant number or string into a tiny integer that can be used as the index in the hash table. The pair has the form (key, value), and one can find a value for a given key by using a "function" that converts keys to values.

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A possible equation to express the situation described is 2x + 4y = 110.

The word equation can be defined as a mathematical expression that uses numbers, symbols, and even letters to mathematically represent a situation.

Consider the variables:

Now relate these variables using letters and symbols

2x (number of tables that can fit two people) + 4y (number of tables that can fit four people) = 110

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Answer: x^3+3x^2+22x+66+234/x-3

Step-by-step explanation: I used synthetic division and this is what I got hope this helps

The value of sin(0) should be considered as the  [tex]\frac{\sqrt5}{5}[/tex] in second quadrant.

The values of all trigonometric functions' dependent on the value of the ratio of sides of a right-angled triangle are known as trigonometric ratios. The trigonometric ratios of a right-angled triangle's sides about any of its acute angles are known as that angle's trigonometric ratios.

Calculation of the value of sin(0):

Since the equation is [tex]cos(o)=\frac{-2\sqrt{5}}{5}[/tex]

by the Pythagorean theorem -

[tex]h^2=p^2+b^2[/tex]

value of perpendicular is = [tex]\sqrt5[/tex].

The trigonometry ratios for a specific angle ‘θ’ is given below:

Trigonometric Ratios:

Sin θ = Perpendicular/Hypotenuse

Cos θ = Base/Hypotenuse

Also in the case when 0 is an angle in quadrant II

So based on this, we can say that value of sin(0) should be considered

as the    [tex]\frac{\sqrt5}{5}[/tex].

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To the function u=I+6, for the output 20 input is 14.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

For the table 2, the rule is u=I+6

For output u=14, we get

14=I+6

I=8 (Input)

For output u=28, we get

28=I+6

I=22 (Input)

For input I=24, we get

u=24+6

u=30 (Output)

For output u=16

16=I+6

I=10 (Input)

For output u=20

20=I+6

I=14 (Input)

For input I=48

u=48+6

u=54 (Output)

Therefore, to the function u=I+6, for the output 20 input is 14.

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The number of people in the town in the next four years is 7610.

We know that the population growth rate can be obtained when we apply the exponential growth formula. In this case we would have;

P= Poe^rt

P = Population at time t

Po = Initial population

r = Population growth rate

t = time taken

3(4709) =4709e^9r

3 = e^9r

ln3 = 9r

r = ln3/9

r = 0.12 or 12%

In the next four years;

P =4709e^4 * 0.12

P = 7610

The population can be obtained as 7610.

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The number of arrivals who came in each day while this particular widget shop was open. Therefore, statement 2 is correct.

The process by which a sample of observations is selected from a population to assume the population is known as random sampling. This process ensures that the results we get from your sample should be close to what we would have gotten if we measured the complete population. So that all the units in the population have an equal chance of being chosen using the simplest random sample.

In the given scenario, the number of arrivals each day for the widget store should have equal chance. To be specific, we should only take into account the number of visitors on the days when the store is open.

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Answer:

9 cm

Step-by-step explanation:

cos B = adj/hyp

cos B = BC/AB

cos 25° = 8 m / AB

AB = 8 m / cos 25°

AB = 9 cm