Below are two inequalities and the graphs of their lines without the shading. By
imagining where the shading should be, identify which point would satisfy BOTH
inequalities.
y<-5/6x+2
y>1/3x+3

The length of the radius, diameter, and circumference are 78.5 and 31.4.

Supposing that a considered circle has its radius of 'r' units.

Then, its area and circumference is given as:

[tex]Area = \pi r^2 \: \rm unit^2 Circumference = 2\pi r \: \rm units[/tex]

Radius of a circle is half of its diameter.

Given;

Let the diameter be 10cm

Radius=d/2

=10/2=5

Diameter=10

Circumference=2pi*r

=2*3.14*5=31.4

Area= pi*r^2*

=3.14*5*5=78.5

Therefore, the area and circumference will be 78.5 and 31.4.

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A graph of the inequality "y is less than negative one fourth times x minus 3" is: D. The graph shows a dashed line passing through the point negative 12 comma 0 and 0 comma negative 3, with shading below the line.

In order to determine the ordered pair that is included in the solution to this linear inequality, we would first of all translate the word problem into an algebraic equation as follows;

y is less than negative one-fourth times x minus 3 ⇒ y < -x/4 - 3.

Next, we would use an online graphing calculator to graphically solve the linear inequality. Therefore, the required solution for the given linear inequality is the shaded area below the dashed line, which is given by the ordered pairs (−12, 0) and (0, -3).

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Answer:

it’s D dotted line with shading below

Step-by-step explanation:

i got it on my quiz

Answer:

Step-by-step explanation:

110 x 0.20 = 22

your total is 132

The vehicle in motion produces 44000 joules of kinetic energy.

Kinetic energy is a type of power that a moving object or particle possesses.

An item accumulates kinetic energy doing work, which involves the transfer of energy, is done on it by exerting a net force.

Given, The formula for kinetic energy is, K = (1/2)mv².

The vehicle has a mass of 2200 kilograms and a velocity of 20 m/s.

So, Replacing the values in the formula will yield the result.

K = (1/2)mv².

K = 1100×400.

K = (1/2)×2200×(20)².

K = 44000 joules.

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the events A and B as follows: A = { x | x < 72.5] and B = { x | x > 52.5].

From the question given above, the following data were obtained:

Angle θ = 71°

Hypothenus = 25

Adjacent = x

Thus, we can obtain the x component of the vector by using the cosine ratio as illustrated below:

Cos θ = Adjacent /Hypothenus

Cos 71 = x/25

Cross multiply for events

x = 25 × Cos 71

x = 25 × 0.3256

x = 8.1

Therefore, the x component of the vector is 8.1

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The function A(x) = x(400 - x) gives the area (in square feet) of the fenced-in region as a function of the length of the side of the rectangle perpendicular to the building (x).

The area of a rectangular field enclosed by 400 feet of fence can be calculated using the formula Area = Length x Width. Since one side of the field is against a building, fencing is not required on that side. Thus, the length of the rectangle perpendicular to the building (x) is one of the sides of the rectangle. The other side is calculated by subtracting x from 400 feet. The area (in square feet) of the fenced-in region is then given by the function A(x) = x(400 - x).

To illustrate, if the length of the rectangle perpendicular to the building (x) is 200 feet, then the width is calculated by subtracting 200 from 400, giving a width of 200 feet. The area of the fenced-in region is then given by A(x) = 200 x (400 - 200) = 200 x 200 = 40,000 square feet.

Therefore, the function A(x) = x(400 - x) gives the area (in square feet) of the fenced-in region as a function of the length of the side of the rectangle perpendicular to the building (x).

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The cost of an electronic music device after 8 years is, $59.83

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

We have to given that;

The value of an electronic music device decreases by 11% each year.

And, The device was purchased for $125.

We know that;

The formula as the value of the machine depreciates every year by 11%,

⇒ A = P (1 - r)ⁿ

Here, P = $125

r = 11% = 0.11

n = 8 years

Substitute all the values, we get;

⇒ A = P (1 - r)ⁿ

⇒ A = 125 (1 - 0.11)⁸

⇒ A = 125 (0.89)⁸

⇒ A = 125 × 0.3936

⇒ A = $59.83

Thus, The cost of an electronic music device after 8 years is, $59.83

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The probability mass function (PMF) of N can be determined by finding the probability that N = k, for each k = 1, 2, 3, ....

Let p_k = P(N = k) be the probability that the first bid that is better than the initial bid X_0 is the kth bid. We can calculate p_k as follows:

p_k = P(X_k > X_0, X_1 < X_0, X_2 < X_0, ..., X_{k-1} < X_0) = P(X_k > X_0 | X_1 < X_0, X_2 < X_0, ..., X_{k-1} < X_0) * P(X_1 < X_0, X_2 < X_0, ..., X_{k-1} < X_0)

Since X_0, X_1, ... are independent and identically distributed, we have:

p_k = P(X_k > X_0) * (P(X_1 < X_0))^{k-1}

To find the mean E[N], we need to calculate the expected value of N. The expected value of N is given by:

E[N] = 1 * p_1 + 2 * p_2 + 3 * p_3 + ... = ∑_{k=1}^∞ k * p_k

Since p_k = P(X_k > X_0) * (P(X_1 < X_0))^{k-1}, we can write E[N] as:

E[N] = ∑_{k=1}^∞ k * P(X_k > X_0) * (P(X_1 < X_0))^{k-1}

To find E[N], we need to know the distribution of X_0, X_1, .... Unfortunately, without further information on the distribution of X_0, X_1, ..., it is not possible to determine the PMF of N or the mean E[N].

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To solve for 1/x(x-3) = 2/(x-3) + 3/x, we can simplify and rearrange the terms on the right side:

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

Multiplying both sides by x(x-3):

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

Expanding the right side:

1 = 2x + 3x^2 - 9x/x

Cancelling x from the right side:

1 = 2x + 3x^2 - 9

Dividing both sides by x^2:

1/x^2 = 2/x + 3 - 9/x^2

Rearranging the terms:

1/x^2 - 9/x^2 = 2/x + 3

Isolating the x terms:

-8/x^2 = 2/x + 3

Multiplying both sides by x^2:

-8 = 2x + 3x^2

Expanding the right side:

-8 = 2x + 3x^2

Rearranging the terms:

3x^2 + 2x + 8 = 0

This is a quadratic equation and can be solved using the quadratic formula or factoring. The solutions are the values of x that make the equation equal to zero.

There are 1049 children went to movie.

Two or more expressions with an Equal sign is called as Equation.

Let the number of children are x and number of adults were y.

Tickets are $5.50 for children and $7 for adults.

1250 are the total number of people attended the movie.

x+y=1250

5.50x+7y=7979

x=1250-y

Now plug in x value in the second equation.

5.5(1250-y)+7y=7979

6875-5.5y=7979

Subtract 6875 on both sides

-5.5y=7979-6875

-5.5y=1104

y=-200.7

Now plug in y value

x+(-200.7)=1250

x=1049

Hence, there are 1049 children went to movie.

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Then the 3 integer even numbers are:

-24, -22, -20

We know that the sum of 3 consecutive even numbers is -78, that can be written as:

x + (x + 2) + (x + 4) = -78

Now we can solve that equation for x:

3x + 6 = -78

3x = -78 - 6 = -72

x = -72/3 = -24

The next even integer is:

-24 + 2 = -22

-24 + 4 = -20

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The three consecutive integer even numbers are -24, -22, -20

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

The sum of three consecutive even integers is -78

Represent the smallest integer with x

So, we haee the following equation:

x + (x + 2) + (x + 4) = -78

Evaluate the like terms

3x + 6 = -78

So, we have

3x = -72

Divide both sides by 3

x = -72/3 = -24

This means that the next integers are

-24 + 2 = -22

-24 + 4 = -20

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Answer:

The answer should be should be 51.45°

Answer:

Step-by-step explanation:

Number 10⁻² is 100 times as great as 10⁻⁴.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Numbers are 10⁻² and 10⁻⁴.

Let number 10⁻² is x times great as 10⁻⁴.

Hence, We can formulate;

⇒ 10⁻² = x × 10⁻⁴

⇒ x = 10⁻² / 10⁻⁴

⇒ x = 10⁻²⁺⁴

⇒ x = 10²

⇒ x = 100

Thus, Number 10⁻² is 100 times as great as 10⁻⁴.

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(a) The reliability of this system is 0.42

(b) The reliability of this system is 0.8376

As per the given data that the probabilities that components A, B, C, and D function properly are 0.6, 0.7, 0.8, and 0.9 respectively.

Let the name of the components itself denote the event that the corresponding component works properly.

So P(A) = 0.6,  P(B) = 0.7, P(C) = 0.8, P(D) = 0.9.

We have to find the reliability of the given structure of the combination of the above-said components.

The diagrammatic representation(attached at the end of solution(a)) of the system is as follows.

The above system consists of components A and B connected in the sequel. So the reliability of the system is the probability that both A and B function properly.

This probability is given by P(A ∩ B) = P(A)P(B) as the events are independent. Substitute the probabilities in the above formula.

P(A ∩ B) = (0.6)(0.7)

P(A ∩ B) = 0.42

The diagrammatic representation(attached at the end of solution(b)) of the system is as follows.

In the above system, the components A and B and components C and D are connected the in the sequel. The entire system is connected in parallel with A, B and C, D. The reliability of this system is given by the probability.

P(A ∩ B) ∪ P(C ∩ D) = P(A ∩ B) + P(C ∩ D) - P(A ∩ B) ∩ P(C ∩ D)

= P(A)P(B) + P(C)P(D) - P(A)P(B)P(C)P(D)

= (0.6)(0.7) + (0.8)(0.9) - (0.6)(0.7)(0.8)(0.9)

= 0.42 + 0.72 - 0.3024

= 1.14 - 0.3024

= 0.8376

Therefore answer is 0.8376

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Answer:

Therefore you will be able to get 6 * 3 different pizzas = 18 pizza combinations.

Answer: 12

Step-by-step explanation:

The fraction in simplest form is, 5/12.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

All the fractions are,

⇒ 2/10, 5/12, 3/6, 4/8

Now, We know that;

The fraction is in simplest form if the GCD of denominator and numerator is 1.

So, By all the fractions;

⇒ 5/12

Clearly, GCD of 5 and 12 are 1.

Hence, The fraction in simplest form is, 5/12.

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The equation that represents the relationship between the distance of Tamara and Marcia is y = x-4

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

let x represent the kilometers covered by Tamara and y by the kilometers covered by Marcia.

x+y = k

x = k/2

x = Y+2

Y+2 = K/2

2Y+4 = K

x+ y = 2y+4

collect like terms

2y -y = x-4

y = x-4

therefore the linear equation they represents the relationship between the distances each girl has run is y = x-4

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The equation of the function is f(x) = 4x + 11

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

f(-2)=3, and f(4)=5

A linear function is represented as

y = mx + c

So, we have

-2m + c = 3

4m + c = 5

When solved, we have

2m = 8

This gives

m = 4

So, we have

c = 3 + 2m

c = 3 + 8 = 11

So, the function is

f(x) = 4x + 11

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The values of the function are

a) f(-1)+ f(2) = 32

b)  f(-1) - f(2) = -30.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f( x ) = 3x² + 7x + 5

a) f(-1)+ f(2)

=  3(-1)² + 7(-1) + 5 +  3(2)² + 7(2) + 5

= 3 -7 + 5 +12 + 14 + 5

= 32

So, the value of f(-1)+ f(2)= 32

b)  f(-1) - f(2)

=  3(-1)² + 7(-1) + 5 -{  3(2)² + 7(2) + 5}

= 3 -7 + 5 -{12 + 14 + 5}

=-30

So, the value of  f(-1) - f(2)= -30.

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A convex octagon can be split into a set of triangles by connecting its vertices in a way that each vertex is connected to its neighboring vertices.

There are several ways to split a convex octagon into triangles, but a common approach is to use the ear clipping algorithm, which involves finding triangles that have their vertices on the octagon's perimeter and have no other vertices inside the triangle.

For example, if the vertices of the octagon are given by v1, v2, v3, v4, v5, v6, v7, and v8, then we can split the octagon into the following triangles:

(v1, v2, v3), (v3, v4, v5), (v5, v6, v7), (v7, v8, v1), (v2, v3, v5), (v4, v5, v7),

(v6, v7, v1), and (v8, v1, v3).

Each of these triangles has three vertices that are connected to form a closed polygon, and together they form the entire convex octagon. By splitting the octagon into smaller triangles, it is easier to perform computations, such as finding the area or the normal vectors of the octagon's surface.

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Answer: 39 in^2

Step-by-step explanation: To find the area of this polygon, we can break it down into two triangles and one rectangle. The following formulas are to solve for the area of each polygon:

Area of a Triangle: A = b x h / 2

Area of a Rectangle: A = l x w

We can plug in the values by what we are given. The triangle to the top has a base of 6 in and a height of 5 in. We can multiply these to get 30 in but cut it in half to get 15 in. The second triangle has a base of 3 in and a height of 4 in, so when we multiply, we get 12 in / 2 to get 6 in. The rectangle's length is 6 in and the width is 3 in. So, 6 x 3 is 18. Add all these values together, and you get 39 in^2.

Let me know if this is right! :)

a) The length of the third side of the triangle is; 6n - 9

b) The lengths of the three sides of the triangle when n = 5 are;

8, 7 and 22.

c) The lengths of the three sides of the triangle when n = 7 are;

12, 13 and 33.

The perimeter of a triangle is defined as the total length of the boundary of the triangle.

The parameters are;

Perimeter of triangle = 7n - 19

Length of side 1 = 2n - 2

Length of side 2 = 3n - 8

a) Thus;

Length of third side = 7n - 19 - (2n - 2 + 3n - 8)

= 7n - 19 - n + 10

= 6n - 9

b) When n = 5, the lengths of the three sides are;

Length of side 1 = 2(5) - 2 = 8

Length of side 2 = 3(5) - 8 = 7

Length of third side = 6(5) - 9 = 22

c) When n = 7, the lengths of the three sides are;

Length of side 1 = 2(7) - 2 = 12

Length of side 2 = 3(7) - 8 = 13

Length of third side = 6(7) - 9 = 33

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The amount he should invest today is $279,229.23.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

A = $460,000

r = 4.59%

t = 11 years

Semi-annually.

So,

n = 2

Now,

A = P [tex](1 + r/n)^{nt}[/tex]

460,000 = P [tex](1 + 0.0459/2)^{22}[/tex]

P = 460,000 / [tex]0.02295^{22}[/tex]

P = $279,229.23

Thus,

He should invest $279,229.23 today.

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The expression ⅘ x 50 represents the multiplication of a fraction and a whole number, and the answer is 40.

The expression "⅘ x 50" is a mathematical equation that represents a multiplication operation. The symbol "x" represents the multiplication operator. In this expression, the first number, ⅘, represents a fraction, while the second number, 50, represents a whole number.

When solving the expression, we first simplify the fraction ⅘ by dividing the numerator (4) by the denominator (5). This results in a decimal value of 0.8. Then, we multiply the decimal by 50 to obtain the final answer. 0.8 x 50 = 40.

So, the expression "⅘ x 50" equals to 40. This means that if we have 4 out of 5 equal parts of a whole, and the whole is equal to 50 units, then each part is equal to 40 units

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Answer:

699.626 kilopascals after 4 minutes

Step-by-step explanation:

We can use the formula for simple interest to calculate the tire pressure after 4 minutes. Let's call the initial pressure "P", the rate of loss "r", and the time elapsed "t".

P = P * (1 - r)^t

Where r is the rate of loss in decimal form and t is the number of minutes elapsed.

Substituting the given values, we have:

P = 1,060 * (1 - 0.10)^4

P = 1,060 * (0.9)^4

P = 1,060 * 0.6561

P = 699.626 kPa

Therefore, the tire pressure will be 699.626 kilopascals after 4 minutes.

Answer: z=4

Step-by-step explanation:

5(z+6) - 10 = 10z

The first step is to distribute the 5 to the inside of the parenthesis. So,

5*z = 5z , 5*6 = 30 .

Now the equation has become 5z+30-10=10z. Next, the like terms can be reduced. So,

30-10= 20

The equation is: 5z+20=10z, 5z will be subtracted on both sides, canceling one side out.

5z-5z=0 , 10z-5z=5z

: 20=5z

The last step is to isolate the variable by dividing 5 on both sides.

5/5 = 0 , 20/5 = 4

Therefore, z=4

1) The independent variable is ''Day'' shown in x - axis.

2) Days shows on x - axis are incorrectly arranged.

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

We have to given that;

The graph is shown in graph.

On the graph;

Day is shown in x - axis.

And, Earnings shown in y - axis.

Now, We know that;

The independent variable is shown in x - axis.

Hence, The independent variable is Day.

And, One wrong thing in graph is,

Days shows on x - axis are incorrectly arranged.

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The general solution is an equation that describes all possible solutions of the system. Finally, we can use the general solution to find the specific solutions to the system.

1. [tex]\frac{dy}{dt} = t - y, \frac{dx}{dt} = y - t$a.[/tex]

b. [tex]$y^2 - 2ty + x = c$[/tex]

2.[tex]$\frac{dy}{dt} = y - t^2, \frac{dx}{dt} = t^2 - x$a.[/tex]

b. [tex]$y^2 - 2tx + x^2 - t^2 = c$[/tex]

3. [tex]$\frac{dy}{dt} = ty - x, \frac{dx}{dt} = y - tx$[/tex]

a.

b. [tex]$y^2 - 2tx + x^2 = c$[/tex]

4.[tex]$\frac{dy}{dt} = xy, \frac{dx}{dt} = x$[/tex]

a.

b. [tex]$y = cxe^{x^2/2}$[/tex]

In each of the four problems, we are given a system of equations. To solve the system, we first need to draw a direction field and sketch a few trajectories. This gives us a visual representation of the system, which helps us understand it better. Next, we need to find the general solution of the system. To do this, we need to solve the system of equations algebraically. The general solution is an equation that describes all possible solutions of the system. Finally, we can use the general solution to find the specific solutions to the system.

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