What are the INEQUALITIES of these?

To model with mathematics is to test ideas using math and computer programs to simulate an object or action.

In order to understand a real-life problem, modelling entails developing a set of mathematical equations that accurately reflects a situation.

The model frequently needs to be modified because it does not adequately capture the situation.

By knowing how the system functions, which variables are significant in the system, and how they relate to one another, one can utilise a mathematical model to better understand a real-life situation. Moreover, models can be used to forecast and predict what a system will do in the future or for various parameter values. Finally, a model can be used to estimate variables that are challenging to precisely evaluate.

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Answer:

cos^2 θ/2 = (cos θ + 1)/2.

Step-by-step explanation:

We can use the identity cos 2θ = 2cos^2 θ - 1 to derive an identity for cos^2 θ/2:

cos 2(θ/2) = cos θ

Replacing θ/2 with x:

cos 2x = cos 2(x/2)

Using the double angle formula for cosine:

cos 2x = 2cos^2 x - 1

Substituting θ/2 for x:

cos θ = 2cos^2 (θ/2) - 1

Rearranging this formula, we can solve for cos^2 θ/2:

2cos^2 (θ/2) = cos θ + 1

cos^2 (θ/2) = (cos θ + 1)/2

Therefore, cos^2 θ/2 = (cos θ + 1)/2.

Given : A  = 24 sq feet

A = 0.5 base x height

base = x , height = x+2

A = 0.5 x(x+2)  = 24 sq feet

1) 0.5 x(x+2) = 24 (A)

2) x^2 + 2x - 48 = 0 (D)

To check the rest un-wrap the bracket:

x^2 + (x+2)^2 = 24

x^2 + x^2 + 4 + 4x = 24

2x^2 + 4x - 20 = 0

x^2 + 2x - 10= 0 (NO)

Likewise:

x^2 + (x+2)^2 = 100

x^2 + x^2  +4 + 4x = 100

2x^2 + 4x + 4 = 100

2x^2 + 4x - 96 = 0

3) x^2 + 2x - 48 = 0 (F)

To sum up: that's what apply:

1) 0.5 x(x+2) = 24 (A)

2) x^2 + 2x - 48 = 0 (D)

3) x^2 + 2x - 48 = 0 (F)

Determing how many x intercepts the graph has, as those are the points when y = 0.

The required population of Algeland 16 years from now will be approximately 524937236.

In essence, percentages are fractions with a 100 as the remainder. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on an examination (75/100).

To find the population of Algeland after 16 years, we can use the formula:

[tex]$P = P_0 \times (1 + r)^n$[/tex]

where P is the population after 16 years, [tex]$P_0$[/tex]is the initial population, r is the annual growth rate, and n is the number of years.

Given that the population of Algeland increases by 33% each year, we can express the annual growth rater as:

[tex]$r = 33% = 0.33$[/tex]% = 0.33

We are also given that the current population [tex]$P_0$[/tex] is 5,476,223.

Thus, the population of Algeland after 16 years can be calculated as:

[tex]$P = 5,476,223 \times (1 + 0.33)^{16}$[/tex]

Simplifying this expression, we get:

P = 524937236

Therefore, the population of Algeland 16 years from now will be approximately 524937236.

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Answer:

974.4

Step-by-step explanation:

Answer:

974.4

Step-by-step explanation:

The tenth place is located the digit to the right of the decimal point, in this case, it will be three. When rounding, if it is four or below you keep it, or if it is five or above, you round up to the nearest ten.

974.362 - 6 is above 5, so you will make the three a four.

974.4

The pοssible decimals that satisfy the given cοnditiοns are:5.20, 5.22, 5.24, 5.26, 5.28, 5.60, 5.62, 5.64, 5.66, 5.68, 7.20, 7.22, 7.24, 7.26, 7.28, 7.60, 7.62, 7.64, 7.66, 7.68

Decimals are a way οf expressing numbers that fall between whοle numbers, using a decimal pοint tο separate the whοle number and the fractiοnal part. Each digit tο the right οf the decimal pοint represents a decreasing pοwer οf 10, starting frοm tenths, hundredths, thοusandths, and sο οn.

Since the digit in the tenths place is οdd, it can οnly be 5 οr 7. Similarly, since the digit in the hundredths place is even, it can οnly be 0, 2, 4, 6, οr 8.

Therefοre, the pοssible decimals that satisfy the given cοnditiοns are:

5.20

5.22

5.24

5.26

5.28

5.60

5.62

5.64

5.66

5.68

7.20

7.22

7.24

7.26

7.28

7.60

7.62

7.64

7.66

7.68

Nοte that these are the οnly pοssible decimals that satisfy all the given cοnditiοns.

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Answer:

Incorrect

Step-by-step explanation:

In step one, when they multiplied exponents, they added them which is correct

Step two, they divided exponents, which means they should have subtracted. if they subtracted 6/5 and 2/5, it would have been

[tex]( {x}^{ \frac{4}{5} } )^{ \frac{1}{2} } [/tex]

The correct sample space is given in option C.

What exactly is a sample space?

In probability theory, a sample space is the set of all possible outcomes or results of an experiment or random phenomenon. It is denoted by the symbol "S". For example, when rolling a fair six-sided die, the sample space would be {1, 2, 3, 4, 5, 6} because those are the only possible outcomes. The sample space can be finite, countably infinite, or uncountably infinite, depending on the experiment being considered. The concept of a sample space is fundamental to probability theory, as all probabilities of events are defined in terms of the sample space.

Now,

To determine the sample space for spinning the spinner two times, we need to consider all possible outcomes for each spin and then combine them.

For one spin of the spinner, there are three possible outcomes: blue, orange, and red.

For two spins of the spinner, we need to consider all possible combinations of outcomes from the first and second spin. This can be done by creating a table

            1st spin      2nd spin

1       blue                  blue

2       blue                  orange

3            blue                  red

4       orange               blue

5       orange          orange

6      orange           red

7      red                   blue

8      red                   orange

9      red                   red

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Answer:

Step-by-step explanation:

1000m = 1km

So 3000m = 3km

9x^3 + 4x^2 + 5

Explanation:

Let's simplify step-by-step.

6x^2−3−5x^3−(4x^3+2x^2−8)

Distribute the Negative Sign:

=6x^2−3−5x^3+−1(4x^3+2x^2−8)

=6x^2+−3+−5x^3+−1(4x^3)+−1(2x^2)+(−1)(−8)

=6x^2+−3+−5x^3+−4x^3+−2x^2+8

Combine Like Terms:

=6x^2+−3+−5x^3+−4x^3+−2x^2+8

=(−5x^3+−4x^3)+(6x^2+−2x^2)+(−3+8)

=−9x^3+4x^2+5

Using Algebraic equations, The diagram might also show other values or quantities related to the equation, depending on the specific context or purpose of the diagram.

Algebraic equations are mathematical statements that involve one or more variables, as well as constants and mathematical operations such as addition, subtraction, multiplication, and division. An algebraic equation usually has an equals sign (=) that separates the two sides of the equation. The goal of an algebraic equation is to find the value of the variable that makes the equation true.

For example, the equation x + 3 = 7 is an algebraic equation that involves the variable x. The goal is to find the value of x that makes the equation true. In this case, we can solve the equation by subtracting 3 from both sides, which gives us x = 4.

Algebraic equations can be used to model a wide variety of real-world situations, such as the relationship between the price and quantity of goods sold, the growth rate of a population, or the amount of interest earned on an investment. They are a fundamental tool in many branches of mathematics, science, engineering, and economics, and they are also used extensively in computer programming and data analysis.

Without a specific diagram to refer to, it's difficult to provide a specific answer. However, I can provide a general explanation of how a diagram might show that x + 4 has the same value as 17 and how it might indicate the quantity x.

One way a diagram might represent this equation is through the use of a balance or scale. For example, the diagram might show a balance with a weight of 17 on one side and a weight of x + 4 on the other side. If the balance is level, it indicates that the weight of x + 4 is equal to the weight of 17, which means that x + 4 has the same value as 17.

To indicate the quantity x, the diagram might show a box or symbol on the side of the balance representing x + 4. This box might have a label or caption indicating that it represents x + 4. By subtracting 4 from both sides of the equation, we can determine that x is equal to 13, which would be the value of x that the diagram is representing. The diagram might also show other values or quantities related to the equation, depending on the specific context or purpose of the diagram.

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As a result, the particle's velocity changes as time passes. It is -4/a³ m/s at time t = a, -4 m/s at time t = 1, -0.5 m/s at time t = 2, and -0.15 m/s at time t = 3.

A mathematical equation, such as 6 x 4 = 12 x 2, states that two numbers or values are equivalent. a meaningful noun. When several or even more components need to be taken into account simultaneously in order to comprehend or describe the entire situation, an equation is used.

The derivatives of the displacing equation with time as a parameter is the particle's velocity.

v = ds/dt = d/dt (2/t²) = -4/t³

As a result, the particle's velocity at times t = a, t = 1, t = 2, and t = 3 is as follows:

v(a) = -4/a³

v(1) = -4/1³ = -4 m/s

v(2) = -4/2³ = -0.5 m/s

v(3) = -4/3³ = -0.15 m/s

The particle's velocity consequently varies over time. It is -4/a³ m/s at time t = a, -4 m/s at time t = 1, -0.5 m/s at time t = 2, and -0.15 m/s at time t = 3. Due to the fact also that velocity is negative for any and all values of t, the particle is travelling in the reverse way (i.e., to the left).

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Answer:

2 = 5

Step-by-step explanation:

4 + (-2) = 5

After opening the parenthesis, the + will turn into a -

4 - 2 = 5

Not sure if there was any other part to this question, so I just answered what was given

Answer:

18π or

Step-by-step explanation:

To find the area of a semicircle, use the formula of the area of a semicircle.

Area = [tex]\frac{1}{2}[/tex] π r^2

Radius = 6

Area = [tex]\frac{1}{2}[/tex] π 6^2

Area = [tex]\frac{1}{2}[/tex] (36π)
Area = 18π (in terms of π)

Area = 56.52 (in terms of 3.14)

Answer:

B) 15 days

Step-by-step explanation:

Total Work = (Number of men) x (Hours worked per day) x (Number of days)

Using this formula, we can find the total amount of work to be done in the scenario given in the question:

Total Work = (20 men) x (6 hours per day) x (10 days) = 1200 hours

(a) To find out how many hours a day the remaining 16 men should work to finish the work in 10 days, we need to subtract the work that was not done due to the absence of the 4 men:

Remaining Work = Total Work - Work not done by 4 men

Remaining Work = 1200 - (4 men) x (6 hours per day) x (10 days)

Remaining Work = 840 hours

To finish the remaining work in 10 days, the 16 men would need to work:

Hours per day = Remaining Work / (Number of men) x (Number of days)

Hours per day = 840 / (16 men) x (10 days)

Hours per day = 5.25 hours

Therefore, the 16 men would need to work 5.25 hours per day to finish the work in 10 days.

(b) To find out how many hours a day the remaining 16 men should work to finish the work in 15 days, we need to calculate the total amount of work that needs to be done each day:

Daily Work = Total Work / Number of days

Daily Work = 1200 / 15

Daily Work = 80 hours

To finish the daily work of 80 hours, the 16 men would need to work:

Hours per day = Daily Work / Number of men

Hours per day = 80 / 16

Hours per day = 5 hours

Therefore, the 16 men would need to work 5 hours per day to finish the work in 15 days.

Step-by-step explanation:

subs8biiisowm9bbbs9 to

Answer: 94%

Step-by-step explanation: there are 16 .4's in 6.4 and if he missed by .4 then he got 15/16 which equals 94%

We will be able to put out $36598.19. The solution has been obtained by using the concept of present value of annuity.

The present value of an annuity is the current value of its anticipated future payments at a given rate of return, or discount rate. With higher discount rates, the annuity's present value falls.

We are given that $400,000 are saved for retirement. The account earns  6% interest.

Using present value of annuity,

⇒Present value of annuity due = P + P [tex][\frac{1-(1+r)^{-(n-1)} }{r}][/tex]

⇒400,000 = P + P [tex][\frac{1-(1+0.06)^{-(15-1)} }{0.06}][/tex]

⇒400,000 = P [1 + 9.295]

⇒P = 400,000/10.9295

⇒P = $36598.19 (approx.)

Hence, we will be able to put out $36598.19.

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Answer:

It is not possible to form a right triangle with the lengths 4, 8, and 10 because the longest side of the triangle must be shorter than the sum of the other two sides. This is known as the Pythagorean Theorem, which states that in a right triangle, the square of the longest side (the hypotenuse) is equal to the sum of the squares of the other two sides. Since 8² + 10² = 164, and 10 is greater than the sum of 4 + 8, it is not possible to form a right triangle with those three lengths.

In this case, assuming that 10 is the hypotenuse, we have:

10² = 4² + 8²

100 = 16 + 64

This equation is not true, as 100 is not equal to 80. Therefore, we cannot form a right triangle

Answer:

We can use inequality B to determine the number of sessions Sam needs to conduct. The reason is that he already has $50 and he wants to have enough money, so he needs to earn the remaining amount through tutoring. Thus, we can write the inequality as:

15s + 50 ≥ 125

where s is the number of tutoring sessions he needs to conduct. We can simplify and solve for s as follows:

15s ≥ 75

s ≥ 5

Therefore, Sam needs to conduct at least 5 tutoring sessions to have enough money to buy the video game.

The area of the larger triangle is 72cm²

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle. Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed by a point where the three sides are joined end to end. The triangle's three angles add up to a total of 180 degrees.

The large triangular figure below is composed of triangles with a base and height of 4 cm.

The area of small triangle is 1/2 base × height = 1/2 × 4 × 4 = 8cm²

There are 9 small triangles in the large one so the area will be 9 × 8 =72cm²

Hence the area of the larger triangle is 72cm².

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The inverse of the given functions are f⁻¹(x) = 3/4(x + 7) and f⁻¹(x) = x^2 + 10x + 25

The inverse of a function is a new function that undoes the effects of the original function.

In other words, if we have a function f(x) that maps x to y, then the inverse of f(x), denoted by f^-1(y), maps y back to x.

Given that:

f(x) = 4/3x - 7

Write as an equation

y = 4/3x - 7

Interchange the variables

x = 4/3y - 7

Solve for y

y = 3/4(x + 7)

Replace y with f⁻¹(x) to show the final answer.

f⁻¹(x) = 3/4(x + 7)

Also, the inverse of the function f(x) = √x -5 is computed as follows:

Interchange the variables and solve for y;

x = √y -5

y = x^2 + 10x +25

Replace y with f⁻¹(x) to show the final answer.

f⁻¹(x) = x^2 + 10x + 25

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The domain and range and the type of relation should be determined as follows;

In Mathematics, a function is generally used for uniquely mapping an independent value (domain or input variable) to a dependent value (range or output variable).

Based on relations 3 and 4, we can logically deduce that they do not represent a function because their independent value (domain) has more than one dependent value (range).

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As a result, the usual professional basketball player makes 125000 times more than the typical American worker.

Mathematicians use the unitary method to tackle proportionality-related issues. Finding the value of one unit of a quantity and then using that value to determine the value of another quantity is what this process entails. The unitary technique, for instance, can be used to calculate how far a car will travel on 5 gallons of gas if it travels 40 miles on 2 gallons. We start by determining the price of one unit of gasoline: 2 gallons of fuel equals 20 miles per gallon, while 1 gallon of gasoline travels 40 miles. The distance the car will drive on 5 gallons of gasoline can then be calculated using this value:

given

The query does not include information on the typical wage of a professional basketball player. Let's say the average wage for a professional basketball player in the NBA is $5x106 per year.

We divide the salary of the basketball player by the salary of the worker to determine how many times higher the typical professional basketball player's salary is than the average American worker's salary:

$5x10^6 / $4x10^4 = $125000 / $1 = 125000

As a result, the usual professional basketball player makes 125000 times more than the typical American worker.

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Answer:

The given complex number is (-2.5 + i4.2).

To express it in exponential form, we need to find the modulus (r) and argument (θ) of the complex number.

The modulus is given by:

|r| = √((-2.5)^2 + (4.2)^2) = √(6.25 + 17.64) = √23.89 ≈ 4.888

The argument is given by:

θ = tan⁻¹(4.2/(-2.5)) = tan⁻¹(-1.68) ≈ -1.03 radians

Therefore, the exponential form of the complex number is:

(-2.5 + i4.2) = 4.888e^(-i1.03)

Answer: 36 cubes

Step-by-step explanation:

Length x Width x Height

18 x 6 x 9 = 972

3 x 3 x 3 = 27

972 / 27 = 36

The ball may rise height a maximum of [tex]119[/tex] feet.

Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base but something above it. Anything that can be measured vertically, whether it is high or low, is referred to as having height.

As the ball hits the quadratic function's vertex, it has grown to its highest point. The position (b, c), wherein b is the vertex's x-coordinate, is where a quadratic function of the type is said to have its vertex.

As the quadratic function in this instance is, the point serves as the vertex (5, 119). The ball therefore reaches its highest point after 5 seconds.

[tex]h=-16(5-5)^{2}+119[/tex]

[tex]h=119[/tex]

Therefore, the maximum height of the ball is [tex]119[/tex] feet.

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Answer: To find the equation of a line parallel to 12x + 8y = -40, we need to first rearrange the equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

12x + 8y = -40

8y = -12x - 40

y = -1.5x - 5

So, the slope of the line is -1.5.

Since the line we want is parallel to this line, it will have the same slope, which is -1.5. Now we can use the point-slope form of a line to find the equation:

y - y1 = m(x - x1)

where (x1, y1) is the point through which the line passes, and m is the slope.

Substituting (6,-3) and -1.5 for x1, y1, and m respectively, we get:

y - (-3) = -1.5(x - 6)

y + 3 = -1.5x + 9

y = -1.5x + 6

So the equation of the line parallel to 12x + 8y = -40 through the point (6,-3) is y = -1.5x + 6.

Step-by-step explanation:

Answer:

Base = 5inches

Step-by-step explanation:

2(x+2) + x
2x+4+x
3x+4=19
3x=15
x=5

Answer:x5

Step-by-step explanation: