Josiah bought a new car for $25,000. He did some research and found that the value of his car would depreciate at an average rate of $3,750 per year. The table shows data about the value of his car over the next 4 years.


Number of Years Owned 1 2 3 4

Car Value $ 25000 21250 13750 10000


Express the relation as a set of ordered pairs.


Identify the domain and range of this relation.


Is this relation a function?

The graph from the function is a linear graph

From the question, we have the following parameters that can be used in our computation:

g(x)=(x+2)(x−1)−x 2

Express properly

So, we have the following representation

g(x) = (x + 2)(x − 1) − x²

Next, we set x = 0, 1, 2 and 3 to determine the table of values

g(0) = (0 + 2)(0 − 1) − (0)² = -2

g(1) = (1 + 2)(1 − 1) − (1)² = -1

g(2) = (2 + 2)(2 − 1) − (2)² = 0

g(3) = (3 + 2)(3 − 1) − (3)² = 1

So, the table is

x        0         1        2        3

g(x)     -2      -1        0        1

From the table above, we can see that as x increases by 1, y constantly increase by 1

This means that the function is a linear function

See attachment for the graph

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The final answer after solving the given equation could be 14.

What is Linear Equation ?

Linear Equation can be defined as the equation in which the highest degree of the variable is one. Linear equations are generally three types , they are standard form , slope intercept form , point slope form and linear equation is also called as the equation of straight line.

Given,

Given equation,

2x + 6 = 3x -8

separating the value into a similar term:

2x-3x = -8 - 6

subtracting the equation:

-x = -14

remove negative sign:

x = 14

Therefore , the final answer could be 14.

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An absolute value equation is an equation that contains an absolute value expression. An inequality is a mathematical statement that compares algebraic expressions using greater than (>), less than (<), and other inequality symbols.

The absolute number of a number a is written as  |a|

And represents the distance between a and 0 on a number line.

An absolute value equation is an equation that contains an absolute value expression. The equation IxI = a

Has two solutions x = a and x = -a because both numbers are at the distance a from 0.

To solve an absolute value equation as

x+7|=14

You begin by making it into two separate equations and then solving them separately.

x+7=14

x+7−7=14−7

x=7

or

x+7=−14

x+7−7=−14−7

x=−21

An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.

The inequality   |x|<2  represents the distance between x and 0 that is less than 2 Whereas the inequality  |x|>2 represents the distance between x and 0 that is greater than 2.

You can write an absolute value inequality as a compound inequality.

$$\left | x \right |<2\: or

−2<x<2

This holds true for all absolute value inequalities.

|ax+ b| < c, where c>0

=−c < ax+ b < c

|ax+ b|> c, where c>0

=ax+ b <−corax+ b>c

You can replace > above with ≥ and < with ≤.

When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.

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An absolute value equation is an equation that contains an absolute value expression. An inequality is a mathematical statement that compares algebraic expressions using greater than (>), less than (<), and other inequality symbols.

The absolute number of a number a is written as  |a|

And represents the distance between a and 0 on a number line.

An absolute value equation is an equation that contains an absolute value expression. The equation IxI = a

Has two solutions x = a and x = -a because both numbers are at the distance a from 0.

To solve an absolute value equation as

x+7|=14

You begin by making it into two separate equations and then solving them separately.

x+7=14

x+7−7=14−7

x=7

or

x+7=−14

x+7−7=−14−7

x=−21

An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.

The inequality   |x|<2  represents the distance between x and 0 that is less than 2 Whereas the inequality  |x|>2 represents the distance between x and 0 that is greater than 2.

You can write an absolute value inequality as a compound inequality.

[tex]$$\left | x \right | < 2\[/tex]: or

−2<x<2

This holds true for all absolute value inequalities.

[tex]|ax+ b| < c, where c > 0\\=−c < ax+ b < c\\|ax+ b| > c, where c > 0\\=ax+ b < −corax+ b > c[/tex]

You can replace > above with ≥ and < with ≤.

When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.

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The area of the circle is  1256.64 square inches.

All points on a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

One of the most fundamental curvilinear geometric forms, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its basis in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.

The diameter of the cylindrical barrel is 20 in

So the diameter of the circular base is 20 in = 10 inches in radius.

Area of the circle = [tex]\pi\ r^{2}[/tex] =  π*20*20 = 1256.64 square inches.

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Answer:

3/2

Step-by-step explanation:

3/2 is in the simplest form; it can't be decreased any more.

Answer:

He got 32 candy, he give each person , 3,50. or give only tree each person. and he live 8 candy.

Answer:

2,570 meters

Step-by-step explanation:

110% of what number is 2827

1.1x = 2827  Divide both sides by 1.1

[tex]\frac{1.1x}{1.1}[/tex] = [tex]\frac{2827}{1.1}[/tex]

x = 2570

Wind direction [Mode] is South west

The [Mean] temperature is  

The  [Bimodal] pavement is  Dry Wet

From the question the first question is to determine the wind direction

Generally from the wind direction would be the data with the highest frequency on the wind column i.e the mode of the data, this because this variable(wind direction ) is a nominal level type of level of measurement where the value assigned to the variable are for classification of the data (i.e telling what the data is all about )

So

The mode is Southwest

This means that the wind direction is Southwest

From the question second question is to determine the temperature

Generally given that their are are no outlier that will skew the data we can obtain the temperature by calculating the mean for the temperature column

This is mathematically represented as

T = 89+86+....+93+93/8

T = 91

From the question, the first question is to determine the  pavement

Generally from the pavement would be the data with the highest frequency on the pavement i.e the mode of the data, this because this variable(pavement ) is a nominal level type of level of measurement where the value assigned to the variable are for classification of the data (i.e telling what the data is all about )

From the table we see that the pavement that the pavement column is bimodal

So the mode is Dry Wet

This mean that the pavement is Dry Wet

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The next operation that should be done when evaluating this expression 9-12+-2+3(-3) is A. 3(-3)=-9

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

In this case, it should be noted that the expression given is written as 9-12+-2+3(-3). In PEDMAS, the first operation is parentheses. Therefore, the number on parentheses will be solved first.

In this case, the number in parentheses will be 3(-3). Therefore, the correct option is A.

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Answer: uhm...

Step-by-step explanation:

2...?

A given set of expressions are known as equivalent expression if and only if the result after evaluating those expression is the same number.

Example,

3 + 2 = 5

4 + 1 =  5

5 + 0 = 5

These three are equivalent as because the sum of all of them is same , i.e., 5.

An equivalent expression is an expression which consists of variables, coefficients, constants, and mathematical functions such as addition, subtraction, multiplication, and division.

In general, if two objects are identical, they are then called as identical.

These expressions are also known as duplicates of each other though they look different but they are same.

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The fraction that is bigger than 2/5 and smaller than 2/3 is 8/15.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Let the fraction be a/b.

2/5 < a/b < 2/3

Now,

a/b

= (2/3 + 2/5) / 2

= (10 + 6) / 30

= 16/30

= 8/15

= 0.533

Thus,

The fraction is 8/15.

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The factors of 2[tex]x^{2}[/tex] + 7x + 3 are ( x + 3) and (2x + 1)

Now, According to the question:

The given function is :

f(x) = [tex]2x^2+7x+3[/tex]

To find the factors of  [tex]2x^2+7x+3[/tex] we need to split the middle term, that is, 7x.

7x = 6x + x

Therefore, 2[tex]x^{2}[/tex] + 7x+ 3 can be written as 2[tex]x^{2}[/tex] + 6x + x + 3 .

On taking '2x' common from first two terms and +1 from next two terms we get

2x (x + 3) +1 (x + 3)

(x + 3) (2x + 1)

Thus, the factors of 2x2 + 7x + 3 are (x+3) and (2x+1)

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The complete question is this:

What are the factors of 2x^2+7x +3?

The Constraints of the inequality are

x ≤ 2y + 500

22500  < √ 35x + 50y

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

The Company A (x) at most 500 more than twice then unit by B(y).

So, x ≤ 2y + 500

Now, the square of Company Profit will be equal to 35x + 50y

Then, the constraints will be

1. x ≤ 2y + 500

2. Company Profit² < 35x + 50y

Company Profit < √ 35x + 50y

22500  < √ 35x + 50y

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In 7th grade math, students learn basic algebra, ratios and proportions, geometry, graphing, probability, equation and statistics.

In 7th grade math, students typically learn basic algebraic principles, including linear equations, variables, and functions. They also learn about ratios, proportions, and percents. Geometry is typically introduced, with topics such as angles, lines, triangles, and circles. Additionally, students may be taught more advanced topics such as graphing, probability, and statistics.In 7th grade math, students learn basic algebra, ratios and proportions, geometry, graphing, probability, and statistics.

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The cone should have its maximum volume. V=1/*3r2h is the formula for calculating the volume V of a cone with height h and radius r.

The cone has a volume of

V=πr2h/3

Therefore, we must calculate the values of r and h in terms of R. R is the diameter of the cone's top-circular circle, and h is the cone's height.

R is the cone's slant height, and it serves as the hypotenuse of a right triangle.

R2 = h2 + r2, or r2 = R2-h2.

So V = (1/3)π

[R2-h2]

h = (π/3)[R2h-h3]

You must take the derivative of the cone's volume, set it to zero, then solve for h to determine the cone's maximum volume.

dV/dh=(π/3)[R2-3h2]

R2-3h2=0 --> h2=R2/3 -> h = R/√3

Now we can determine r:

r2=R2-R2/3 = (2/3)R2

The volume formula with r and h substituted:

V = (π/3)

r2h = (π/3)(2R2/3)

(R/√3)

V(R)=2πR3/(9√3)

The complete question is:

A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and CB. Find the maximum capacity of such a cup (Your answer may depend on R).

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The process of simplify the equation is explained below.

The term equation is known as a mathematical statement that defines the equality between two expressions.

Here we have to define the process of simplifying the equation.

The first and foremost step is to remove parentheses and brackets by multiplying factors.

And then we have to use the exponent rule to remove grouping if the terms contain exponents.

Then we have to combine like terms by adding or subtracting coefficients.

Finally, we have to Combine the constants.

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The equation of the line will be y = -2/3x + 5.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the line passes through points (9, -1) and (6, 1).

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 1 - (-1) / ( 6 - 9 )

Sloe = - 2 / 3

The y-intercept will be calculated as,

y = mx + c

-1 = (-2/3) x 9 + c

c = 5

The equation of the line,

y = mx + c

y = -2/3x + 5

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The value of p is 12.322

In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as: For x > 0 , a > 0, and a ≠1, y= logₐ x if and only if x = a^y Then the function is given by f(x) = logₐ x The base of the logarithm is a. This can be read it as log base a of x.

Given here p=-log(2.1×10¹²)

                  p= - ( log(2.1) +12 log10)

                  p= -(0.322+12)

                  p=12.322

Hence, the value of p is 12.322

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Based on the information given, the number of students from Florida will be; 9000 students.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that At Florida A&M University, the ratio of students from Florida to students not from Florida is about 3 : 1

The Total number of students = 12000

Fraction from Florida = 3/4

Fraction of students not from Florida = 1/4

Therefore, the students from Florida will be:

= 3/4 × 12000

= 9000

Hence, the number of students from Florida is 9000.

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Answer:

v=πr²h

divide both sides by πh

v/πh=r²

r²=v/πh

square root both sides

r=√v/√πh

I hope this helps

The probability that a randomly selected customer will have to wait between 32 minutes and 37 minutes is 59.81%

How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability. Look up all the related responses.

The likelihood that an event will happen is quantified by probability. An event's likelihood is determined by how frequently it will occur over the long run. Probabilities are all digits that fall between 0 and 1, inclusive—that is, all digits that fall between 0 and 1.

Let the equation of Z score be:

z = (raw score - mean) / standard deviation

Given mean of 36 minutes and a standard deviation of 3 minutes.

If x = 32:

z = (32 - 36)/3 = -1.33

and x = 37:

z = (37 - 36)/3 = 0.33

P(-1.33 < z < 0.33) = P(z < 0.33) - P(z < -1.33)

= 0.6179 - 0.0198

= 0.5981

A consumer selected at random has a 59.81% chance of having to wait between 32 and 37 minutes.

The complete question is:

At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 36 minutes and a standard deviation of 3 minutes. What is the probability that a randomly selected customer will have to wait between 32 minutes and 37 minutes, to the nearest thousandth?

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the answer to your question is 36

Answer:

Step-by-step explanation: i'd say jus divide

Answer:

[tex] \sf \: h(-3) = 13[/tex]

Step-by-step explanation:

Given information,

→ h(a) = a² + 4

The value of h(a) when a is -3,

→ h(a) = a² + 4

→ h(-3) = (-3)² + 4

→ h(-3) = 9 + 4

→ [ h(-3) = 13 ]

Hence, required answer is 13.

Answer:

5.5

Step-by-step explanation:

7*8=56

42-8=34

56-34=22

22/4=5.5

Answer:

120 cm.

Step-by-step explanation:

The perimeter of a rectangle is found by adding up the length of all four sides. In this case, the length is 36 cm and the breadth is 24 cm. Therefore, the perimeter of the rectangular table-top is

2 (length + breadth) = 2 (36 + 24) = 2 × 60 = 120 cm.

No, I'm not agree with Noah. Because the equation 1. 20(d+5)=42 is a mathematical equation and can be false depending on the value of the variable d.

The equation 1. 20(d+5)=42 is a mathematical equation that contains a variable d. The equation states that when you multiply 20 with (d+5) the result should be 42.

The equation is true if there is a value of d that makes the equation true. For example, if d=1, then 20(1+5)=20(6)=120 which is not equal to 42, so this value of d does not make the equation true.

On the other hand, if d=-7, then 20(-7+5)=20(-2)= -40 which is equal to 42, so this value of d makes the equation true.

Therefore, the equation can be true or false depending on the value of the variable d. In general, without knowing the specific context or situation in which the equation is being used, it is impossible to determine if the equation accurately represents a situation or not.

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(a) The concentration of our solution in the tank initially is 0.060 kg/L. (b) the amount of salt in the tank after 2. 5 hours is 44.45 kg. (c) The concentration of salt in the solution in the tank as time approaches infinity is 0.030 kg/L.

Divide the solute's gram weight by the total weight of the solution, then multiply the result by 100 to get the mass/mass percent of the solution. The amount of solute (measured in grams) per milliliter of solution is known as the mass/volume percent.

(A) Tank contains 60 kg of salt and 1000 L of water. So the concentration of solution in the tank initially = 60/1000 kg/l

The concentration of solution in the tank initially = 0.060 kg/L

(B) Let y(t) denote the amount of salt in the tank at any time t.

Rate In

A solution of concentration 0.03 kg of salt per liter enters a tank at the rate 9 L/min.

[tex]R_{i}[/tex]  =(concentration of salt in inflow)(input rate of solution)

= (0.03kg/L)*(9L/min)

= 0.27kg/min

Rate Out

The solution is mixed and drains from the tank at the same rate.

Concentration, C(t) = Amount/Volume = y(t)/1000

[tex]R_{out}[/tex] =(concentration of salt in outflow)(output rate of solution)

= {y(t)/1000}kg/L*9L/min

= 0.009y(t) kg/min

Therefore, the differential equation for the amount of Salt in the Tank  at any time t:

dy/dt = 0.27 - 0.009y(t)

So the amount of salt in the tank after 2. 5 hours (2.5*60 min = 150 min) is  44.45 kg.

(c) The concentration of salt in the solution in the tank as time approaches infinity

As t -> -∞, e^-∞ = 0

so, the concentration of salt in the solution in the tank as time approaches infinity is 0.030 kg/L.

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