Solutions to Systems of Linear Inequalities in Two Variables

Based on the expanded the expression (2 - 3x)², the student who got the answer 4 – 12 x + 9x² is the first student.

In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two (2).

In Mathematics, the standard form of a quadratic function is given by ax² + bx + c = 0.

By applying the following binomial expression to the given quadratic function, we have:

(a - b)² = a² - 2ab + b²

(2 - 3x)² = 4 - 2(2)(3x) + 3x²

4 - 2(2)(3x) + 3x² = 4 - 12x + 9x².

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Answer:

50.25

C= 2πA= 2·π·200.96 ≈50.25274

Answer: 50.25

C=2πA=2·π·200.96≈50.25274

Step-by-step explanation:

what do you not understand here ?

you got the formula, the numbers for the formula.

since you should use 3 for pi, this is a very simple calculation :

3×15² = 3×225 = 675 ft²

that's it.

The number of students were in the class is 26

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

Let's call the total number of students "n".

Then:

n - 5 students liked either blue or green or both,

12 students liked both blue and green,

17 - 12 = 5 students  liked only blue,

16 - 12 = 4 students liked only green.

So:

n - 5 = 5 + 4 + 12

n = 26

There were 26 students in the class.

Therefore, The number of students were in the class is 26

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The discount amount is $29. The sale price of the scooter is $116.

What is the percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. The symbol "%" represents it.

Given that, the market price of a scooter is $145.

The discount on the scooter is 20%.

The discount amount is $145×20%

                                        = 145 × (20/100)

                                        = 145 × (1/5)

                                         = 29

The sale price is Marke price - discount

= $(145 - 29)

=$116

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Answer:

8400

Step-by-step explanation:

The smallest whole number that is divisible by both 112 and 525 is their LCM.

112 = 2 × 2 × 2 × 2 × 7

525 = 3 × 5 × 5 × 7

Therefore, LCM = 2 × 2 × 2 × 2 × 3 × 5 × 5 × 7 = 8400

So it is 8400.

Hope it helps.

If you have any query, feel free to ask.

Step-by-step explanation:

To find the longest time that Ian has to wait to fill the tank, we need to find the total time it takes to fill the tank from its current level of 20 gallons to its maximum level of 125 gallons.

First, we need to find the amount of water that needs to be added to the tank by subtracting the current water level from the maximum water level:

125 gallons - 20 gallons = 105 gallons

Next, we need to divide the amount of water that needs to be added by the rate at which Ian is filling the tank to find the time it will take:

105 gallons / 8 gallons per minute = 13.125 minutes

So the longest time that Ian has to wait to fill the tank is 13.125 minutes.

The required change in pressure to maintain the flow rate in a pipe with a reducing diameter is ρ * v² / 16.

To maintain a constant flow rate in a pipe with changing diameter, the velocity of the fluid must remain constant. This is known as the principle of continuity, which states that the product of the velocity and the cross-sectional area of a pipe must remain constant.

Given that the diameter of the pipe is reduced from 8 inches to 4 inches, the cross-sectional area of the pipe is also reduced by a factor of 4. Hence, to maintain the same flow rate, the velocity of the fluid must increase by a factor of 4.

Since the fluid is incompressible and Newtonian, the pressure drop can be calculated using the continuity equation and motion equation (Bernoulli's equation).

ΔP = ρ * v²  / 2

where ΔP is the change in pressure, ρ is the density of the fluid, and v is the velocity of the fluid.

Plugging in the values, we get:

ΔP = ρ * (v / 4)² / 2 = ρ * v² / 16

So, the required change in pressure to maintain the flow rate in a pipe with a reducing diameter is ρ * v² / 16.

Complete Question:

'It is required to reduce a pipe diameter of 8 inches to a minimum diameter of 4 inches while maintaining a constant flow rate. Assuming the pipe is circular and the fluid is incompressible and Newtonian, what is the required change in pressure to maintain the flow rate?'

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The correlation between two variables is an important measure that helps us understand the relationship between them. In Scenario 3-2, if the heart disease death rate is expressed as deaths per 1,000 people instead of as deaths per 100,000 people, it would not change the correlation (r) between wine consumption and heart disease death rate.

The correlation coefficient (r) measures the strength and direction of the relationship between two variables. If the heart disease death rate is expressed as deaths per 1,000 people instead of as deaths per 100,000 people, it would change the units in which the death rate is expressed, but it would not change the underlying relationship between wine consumption and heart disease death rate.

In other words, regardless of the units in which the death rate is expressed, the correlation between wine consumption and heart disease death rate would remain the same. This is because the correlation measures the relationship between two variables, not the units in which they are expressed. It is important to note that expressing the death rate in different units may make it easier or more difficult to understand the relationship between two variables, but it does not change the underlying correlation.

In conclusion, the correlation (r) between wine consumption and heart disease death rate would not change if the death rate were expressed as deaths per 1,000 people instead of as deaths per 100,000 people.

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Answer:none of the above

Step-by-step explanation:

The maximum Z is 1800 and the value of X₁ and X₂ at the optimal solution : X₁ = 5 and X₂ = 3.

The constraints for the linear programming problem:

30X₁ + 70X₂ ≤ 210

20X₁ + 10X₂ ≤ 100

X₁, X₂ ≥ 0

First we draw the graph for equations 30X₁ + 70X₂ = 210 and 20X₁ + 10X₂ = 100

Consider equation 30X₁ + 70X₂ = 210

For X₁ = 0,

70X₂ = 210

X₂ = 3

For  X₂ = 0,

30X₁ = 210

X₁ = 7

This means, the line 30X₁ + 70X₂ = 210 passes through (0, 3) and (7, 0) as shown in the following graph.

So, 30X₁ + 70X₂ ≤ 210  includes the region below the line.

Consider equation 20X₁ + 10X₂ = 100

For X₁ = 0,

10X₂ = 100

X₂ = 10

For  X₂ = 0,

20X₁ = 100

X₁ = 5

This means, the line 20X₁ + 10X₂ = 100 passes through points (0, 10) and (5, 0) as shown in the following graph.

so, an inequality 20X₁ + 10X₂ ≤ 100 includes the region below the line.

From the figure, (0, 3) and (5,0) are feasible corner points.

Thus the optimal solution is:  X₁ = 5 and X₂ = 3

For X₁ = 5 and X₂ = 3,

Z = 300X₁ + 100X₂

Z = 300(5) + 100(3)

Z = 1500 + 300

Z = 1800

Therefore, the maximum value of Z is 1800

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Answer: D

Step-by-step explanation:

The class section with the larger standard deviation will be the one with the larger variance.

The standard deviation is a measure of how much variation exists in a set of data. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. To calculate the standard deviation for Joseph and Nichole's class sections, we need to first calculate the variance for each class. To do this, we need to subtract the mean of each class from each data point, square the result, and then average the squared differences. The larger the variance, the larger the standard deviation will be. Therefore, the class section with the larger standard deviation will be the one with the larger variance.

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Answer:

None

Step-by-step explanation:

[tex]1-\frac{7}{12}-\frac{1}{6}-\frac{1}{4}=1-\frac{7}{12}-\frac{2}{12}-\frac{3}{12}=1-\frac{12}{12}=0[/tex]

Answer:

Step-by-step explanation:

an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?

According to the problem statement the actual boat is 96 inches long.

Boat in math is a geometric shape that is formed when two perpendicular lines intersect at two points, forming two pairs of equal-length sides that cross each other in the middle. It looks like the bottom of a boat with two sides meeting at the center. In mathematics, the boat shape is often used to represent an equation or a function. It is also used to illustrate the concept of a mathematical set, or group of related objects. The boat shape can also be used to graphically represent relationships between two or more variables.

The actual boat is 96 inches long. The scale factor of 24:1 means that for every 1 inch on the model, there are 24 inches on the actual boat. Therefore, for the 4 inch model boat, there are 4 × 24 = 96 inches on the actual boat.

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A two-dimensional reducing bend has a linear velocity profile at section  The flow is uniform at sections  The fluid is incompressible and the flow is steady.

As given in the  problem statement,flow is in compressible and flow is internal flow

Re=5*10^5

Using equation

V=Re/density*diameter of pipe

Maximum velocity=98.98 m/s

why are the Navier-stokes equations difficult to solve?

Being nonlinear makes the Navier-Stokes equation challenging to solve. Although it's frequently used, this word has a specific meaning in this context. A linear equation can have multiple simple solutions, all of which combined can yield a complex answer.

The Navier-Stokes equations lack an additional equation to determine the pressure levels at various locations. A partial differential equation used to model the flow of incompressible fluids is the Navier-Stokes equation in fluid mechanics.

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On solving the provided question we can say that this figure is a quadrilateral and area will be = A = 38.5199475951548 units

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

x = √(a2 + b2 - 2ab cos X) = √(3.62 + 5.12 - 2*3.6*5.1 cos 108°) = 7.09345501384537

Then, we can get the area of the second triangle either by solving for one of the angles using the cosine law and using 1/2 ab sin C or use Abel's law.

Abel's law for variety.

p=(8,5 + 10.2+ 7.09345501384537)/2

A =√((p(p-a)(p-b)p-c) = 29.7892487755653

A = 8.73069881958951 + 29.7892487755653 = 38.5199475951548

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The compound interest is ₹46,148.68 and the total amount after 4 years and 6 months is ₹1,46,148.68.

The formula to calculate compound interest is:

A = P * (1 + r/n)^(nt)

Where:

A is the total amount after t years

P is the principal amount

r is the interest rate per annum

n is the number of times the interest is compounded per year

t is the number of years

In this case:

P = ₹1,00,000

r = 10% per annum = 0.10

n = 1 (since the interest is compounded annually)

t = 4 years and 6 months = 4.5 years

A = ₹1,00,000 * (1 + 0.10/1)^(1 * 4.5) = ₹1,00,000 * 1.461486788

A = ₹1,46,148.68

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The total number of newspapers sold each day is: 200 + 2 + 16 + 128 + 22 = 368.

To find the total number of newspapers sold each day, we need to find the sum of the daily sales of each variety:

English language newspapers: 25 * 8 = 200

French language newspapers: 1 * 2 = 2

Korean language newspapers: 16 * 1 = 16

Japanese language newspapers: 16 * 8 = 128

Russian language newspapers: 22 * 1 = 22

Addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

In mathematics, addition is the process of joining two or more integers. The numbers being added are known as addends, and the result or final response obtained after the procedure is known as the total.

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Answer:

4c+20

Step-by-step explanation:

The probability that an outcome of 5 appears before an outcome of 7 is 1.

The probability of getting a 5 or a 7 in one roll of two fair dice is 6/36 = 1/6. The probability of getting a 5 before a 7 is equal to the sum of the infinite geometric series with the first term being 1/6 and common ratio 5/6:

1/6 + (5/6) * (1/6) + (5/6)² * (1/6) + ... = 1/6 / (1 - (5/6)) = 1/6 / (1/6) = 1.

So, the answer is 1.

The method used here is called the Geometric Series formula. It is used to calculate the sum of an infinite geometric series, which is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed constant called the common ratio. The formula for the sum of an infinite geometric series is:

S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio.

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The solution of the complex numbers are

a. 3+j(5j/2+3j) = j * (3 + 8i)

b. (4+2j)([tex]3e^{j.2\pi/4}[/tex])+1/3+2j+5[tex]e^{j0.5}[/tex] = 12j² + 12j³ + 1/3 + 2j + 5 * cos(0.5) + 5 * j * sin(0.5)

Complex arithmetic involves working with complex numbers, which are numbers that have both real and imaginary parts.

a. 3+j(5j/2+3j)

To perform this operation, we first need to simplify the expression inside the parentheses: 5j/2 + 3j. We can simplify this expression by adding the two imaginary parts together:

5j/2 + 3j = (5 + 3)j = 8j

Next, we substitute this result back into the original equation:

3 + j(8j) = 3 + j(8 * j) = 3 + j * 8i

Now we can simplify this expression by multiplying the real part 3 with j, and adding it to the real part of the expression:

3 + j * 8i = 3j + j * 8i = j * (3 + 8i)

So the final result is: j * (3 + 8i)

Next, let's look at the second part of the problem:

b. (4+2j)([tex]3e^{j.2\pi/4}[/tex])+1/3+2j+5e^j0.5

We can simplify this expression by using the properties of complex numbers and exponential functions:

(4 + 2j) * ([tex]3e^{j.2\pi/4}[/tex]) = (4 + 2j) * (3 * (cos(2π/4) + j * sin(2π/4)))

= (4 + 2j) * (3 * (cos(π/2) + j * sin(π/2)))

= (4 + 2j) * (3 * j)

= (4 + 2j) * 3j

= 12j² + 6j³ * 2j

= 12j² + 12j³

Next, we substitute this result back into the original equation:

12j² + 12j³ + 1/3 + 2j + [tex]5e^{j0.5}[/tex]

Next, we simplify the remaining terms:

=> 3 + 2j + [tex]5e^{j0.5}[/tex] = 1/3 + 2j + 5 * (cos(0.5) + j * sin(0.5))

=>  1/3 + 2j + 5 * cos(0.5) + 5 * j * sin(0.5)

So the final result is: 12j² + 12j³ + 1/3 + 2j + 5 * cos(0.5) + 5 * j * sin(0.5)

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The area of the given circle is 36π square meters.

What is the area of a circle?

The region encircled by a circle is known as the area of a circle in geometry. The area of a circle is π multiplied by the square of the radius r. Here, the Greek letter π stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.

Given,

 Diameter of the circle = 12 metres

Radius of the circle = Diameter/2 =12/2 = 6 metres

Area of circle = πr² = π ×6² = 36 π square meters

Therefore the area of the given circle is 36π square meters.

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20 miles/hours best express the speed of Joey's golf cart.

speed = time + distance

That is, speed = time + distance. To put it another way, distance divided by speed equals time.

You can figure out the third input if you know the first two.

For example, if a car drives 120 miles in two hours,

Then the speed is 120/2 = 60 miles per hour.

As per the data given,

We have,

So, the value of the speed of Joey's golf cart can be expressed as a unit rate by dividing the total distance he covers by the time it takes him to cover that distance.

So, the value of the unit rate will be

=40 miles/2 hours = 20 miles/hour.

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Answer:

2 green

Step-by-step explanation:

The ratio of blue to green is 4 to 1  <===== there is 1/4th asmany green as blue.... so if there are 8 blue, there are only   2 green

The required complete table regarding the distance traveled has been shown.

From the given condition, let y be the distance left and x be the time,
According to the question an equation model is given as,

Distance traveled = 5x
Distance remaining to travel = y = 5000 - 250x

Now,
Put x = 5
Distance traveled = 250x
                           = 250(5) = 1250

Distance remaining to travel = y
y = 5000 - 1250
y = 3750 ft

Similarly,
At
x = 20
Distance traveled = 5000

X = 10
Distance remaining = 2500

Thus, the required complete table has been shown.

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The values of x and y are the same with x = 3√2 and y = 3√2 derived using the trigonometric ratio of sine and cosine of the angle 45°.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

sin 45° = √2/2 and cos 45° = √2/2

considering the right triangle;

sin 45° = x/6 {opposite/hypotenuse}

√2/2 = x/6

x = 6 × √2/2

x = 3√2

cos 45° = y/6 {adjacent/hypotenuse}

√2/2 = y/6

y = 6 × √2/2

y = 3√2

Therefore, the values of x and y are the same with x = 3√2 and y = 3√2 derived using the trigonometric ratio of sine and cosine of the angle 45.

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Person A's optimal choices are x1 = x2 and person B's optimal choices are x1 = x22. Also Demand(x1,x2) = 2x1 + x1 + x22 represents the market demand for x1 and x2.

In order to find the optimal choices of person A and person B, we need to find the values of x1 and x2 that maximize their respective utility functions.

For person A, their utility function is ua = min{x1,x2}, which means their satisfaction is equal to the minimum value of x1 and x2. The optimal choice for x1 and x2 would be the values that make x1 = x2, because if one value is higher, the minimum will always be the lower value. Hence, person A's optimal choices are x1 = x2.

For person B, their utility function is ub = min{x1,x22}, which means their satisfaction is equal to the minimum value of x1 and x22. The optimal choice for x1 and x2 would be the values that make x1 = x22, because if x1 is higher, x22 will be even higher and the minimum will always be x1. Hence, person B's optimal choices are x1 = x22.

To find the market demand, we need to find the aggregate demand of both person A and person B. The aggregate demand is the sum of the individual demands. The demand for x1 and x2 can be found by adding the individual demands.

Person A's demand for x1 and x2 is the same, x1 = x2, hence the total demand for x1 and x2 is 2x1.

Person B's demand for x1 and x2 is x1 = x22, hence the total demand for x1 and x2 is x1 + x22.

The aggregate demand for x1 and x2 is the sum of both individual demands:

Demand(x1,x2) = 2x1 + x1 + x22

This represents the market demand for x1 and x2.

Therefore, Person A's optimal choices are x1 = x2 and person B's optimal choices are x1 = x22. Also Demand(x1,x2) = 2x1 + x1 + x22 represents the market demand for x1 and x2.

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The value of x in the equation is x = -1 and x = -4.67

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

3x^2 + 13x + 4 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 3, b = 13, c = 4

So, we have

x = (-13 ± √(13² - 4 * 3 * 4)) / 2 * 3

x = (-17 ± √(169 +- 48)) /6

x = (-17 ± 11) /6

Expand

x = (-17 + 11)/6 and x = (-17 - 11)/6

Evaluate

x = -1 and x = -4.67

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