On the following graph, type the solution that has a multiplicity of (2) or a double root. If there is no double
root, type in 1000

Answer:

228mm^2

Step-by-step explanation:

Answer:

18.19

Step-by-step explanation:

$ = linear f(t)

$16.03 = f(40) = fixed fee + per min fee = x + 40y

$19.72 = f(81) = fixed fee + per min fee = x + 81 y

use above 2 equations to minus the other

you get:

19.72-16.03 = 41y

so y = 0.09

so x = 16.03 - 40*0.09 =12.43

so for 64 mins

cost = 12.43 + 0.09*64 =18.19

You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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A phone company that has started a new plan for young kids that dont send many text messages. Parent can pay a fees of $10 monthly plus $0.05 per text message they send. The equation to represent total cost is y=10+0.05x, $12.5 will be cost per 50 text messages, and 730 text messages kids will send at monthly cost $16.25.

The explaination is given below:

A. The equation to represent the total cost, y, for a given number of text messages, x, is:

y = 10 + 0.05x

B. If a kid ends 50 text messages in one month, the cost will be:

y = 10 + 0.05 * 50 = 10 + 2.5 = 12.5

So it will cost $12.5.

C. To find the number of text messages that a kid ends, we can rearrange the equation to:

x = (y - 10) / 0.05

If the monthly cost was $16.25, then:

x = (16.25 - 10) / 0.05 = 36.5 / 0.05 = 730 text messages

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Answer:

\(47 \frac{11}{12} \)

Step-by-step explanation:

\(10 + (\frac{5}{12} \times 91 )= 10 + (\frac{455}{12} = 37 \frac{11}{12} ) = 47 \frac{11}{12} \)

If the boy is riding a bicycle and gets stuck or got accident by a car, 440ml of IV fluid will be administered.

To avoid further injury, place the victim on the ground very gently and slowly without handling vigorously. In one direction, tilt the sufferer. Dress loosely around the waist, chest, and neck. So that the tongue can fall forward and allow blood and vomit to drain out, tilt your head back and slightly downward. When you come across an accident victim, the first thing you need to determine is whether the victim's body has sustained any physical wounds. Depending on how severe the collision was, you might not be able to see any inside injuries, but you will see a few exterior ones.

In a car accident, spine injuries and head trauma are common. Therefore, be aware that rough handling of the sufferer will result in additional injuries while opting to assist the victim in moving to a safer location on the road. Therefore, request any onlookers to carefully assist in moving the sufferer to a location near the road where it will be safer.

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Check the picture below.

so the volume will simply be the area of the hexagonal face times the height.

\(\textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2\stackrel{\qquad degrees}{\cot\left( \frac{180}{n} \right)}~~ \begin{cases} n=\stackrel{number~of}{sides}\\ s=\stackrel{length~of}{side}\\[-0.5em] \hrulefill\\ n=6\\ s=12 \end{cases}\implies A=\cfrac{1}{4}(6)(12)^2\cot\left( \frac{180}{6} \right) \\\\\\ A=216\cot(30^o)\implies A=216\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the hexagon}}{(216\sqrt{3})}~~\stackrel{height}{(10)}\implies 2160\sqrt{3}~~\approx ~~3741.2~cm^3\)

Answer:

Reflection

Step-by-step explanation:

Figure 1 was reflected accross the y axis :)

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The domain, range, intercepts and symmetry of the graph are;

a) Domain; [-4, 4]

b) Range; [-5, 5]

c) f(-1) = 4

d) x-intercepts; (-3.2, 0), (0, 0), (3.2, 0)

e) y-intercepts; (0, 0)

f) The graph is symmetric about the origin

The y-intercept is the point the graph intersects the y-axis.

The domain is the set of the elements of the input of the function, from the graph, the domain is; -4 ≤ x ≤ 4, which is; [-4, 4]

(b) The range is the set of the possible output value of the function, which consists of the possible y-values of the function.

From the graph, the range is; -5 ≤ y ≤ 5, which is [-5, 5]

(c) The value of the function at x = -1, f(-1), from the graph is 4

f(-1) = 4

(d) The x-intercepts are the points the graph intersects the x-axis

From the graph, the x-intercepts are; x ≈ -3.2, x = 0, and x ≈ 3.2

e) The y-intercept is the point (0, 0)

f) A graph is symmetric with respect to a line if when reflected over the line, the graph is unchanged

Here the graph is symmetric with respect to the origin

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Answer: 3 boxes every 4 minutes, and 0.75 boxed every minute. And  0.75 boxes are filled per minute.

Step-by-step explanation: Hope This Helps!

In the Subgame Perfect Equilibrium of a Stackelberg model, firm 1 chooses a number, and firm 2 chooses a function. Therefore, option (d) is the correct answer.

The Subgame Perfect Equilibrium (SPE) is a solution concept in game theory that analyzes strategic decision-making in sequential games. In a Stackelberg model, firm 1 acts as the leader and sets its output level first, followed by firm 2 as the follower, who observes firm 1's output before making its decision.

In the Subgame Perfect Equilibrium of this model, firm 1 chooses a number (output level) while firm 2 chooses a function (strategy). This implies that firm 1's decision is made independently as a quantity, and firm 2, observing firm 1's choice, formulates its strategy based on that information.

Therefore, option (d) is the correct answer: Firm 1 chooses a number, and firm 2 chooses a function in the Subgame Perfect Equilibrium of a Stackelberg model.

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You can determine if the inverse of a polynomial function is a function by using the Horizontal Line Test on the inverse.

The Horizontal Line Test is a graphical method that can be used to determine whether a given function is one-to-one, meaning that for each output value, there is at most one input value that maps to it.

If the inverse of a polynomial function is a function, it must pass the Horizontal Line Test, meaning that no horizontal line intersects the graph of the inverse more than once.

In other words, if the inverse of a polynomial function passes the Horizontal Line Test, it is guaranteed to have an inverse, which will be a function itself. If the Horizontal Line Test fails, then the inverse is not a function and does not have an inverse.

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2 hours will pass before they meet.

"Information available from the question"

In the question:

Aaron starts riding a bike at a rate of 3 mi/h on a road toward a store 20 mi away.

Zhang leaves the store when Aaron starts riding his bike, and he rides his bike toward Aaron along the same road at 2 mi/h.

Now, According to the question:

Total distance = 20mi

Aaron starts riding a bike at a rate of  = 3mi/h

Zhang rides his bike toward Aaron along the same road at  = 2mi/h

Let y be the number of hours for them to meet.

The expression is given as

3y + 2y = 20

solving for y, we have

5y = 20

y = 20/5

y = 4hrs

Therefore, 2 hours will pass before they meet.

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Answer:

(4,9)

Step-by-step explanation:

Given

Round 1: (1,3)

Round 2: (2,6)

Round 3: (3,3)

Required

Determine the coordinate of Round 4

Since, Mia score is round 2 and 3 combined;

We have:

Round 4 = 6 + 3

Round 4 = 9

Hence:

The coordinates is (x,y)

Where

x = Round number

y = Score

So, we have: (4,9)

Round 4:

(4, 9)

x = round so 4

y = score of round 2 and 3 combined so 9 (6 + 3)

Answer:

L=18, W=8

Step-by-step explanation:

Given :

Area (A)=144 \(m^2\) =LW

Where, L is length and W is width

According to given question ,

\(W=\frac{1}{3} L-2\)

Now,

A=LW

144=L\((\frac{1}{3} L-2)\)

432=\(L^{2} -6L\)

\(L^{2} -6L-432=0\\L^{2} -18L+24L-432\\(L+24) (L-18)\\L=-24\\and L=18\)

Length can be in negative so L =18

And

\(LW=144\\18W=144\\W=\frac{144}{18} \\W=8\)

Therefore, Length of rectangle is 18 and Width is 8

Answer:

See below

Step-by-step explanation:

a)

P(A or Black) = (73 + 27)/127 = 100/127 =  0.7874015748

b)  

P(Red) = red/total = 39/127 = 0.30708661417

c)

P(Manufacturer B and Red) = (B and red)/total = 10/ 127 = 0.0787401575

d)

P(Manufacturer B or Red) = (B or red)/total = (54 + 29)/127 = 0.65354330708

The Matlab & Simulink model consists of a Clock block to generate a time signal, a Gain block to multiply the time signal by 2, and a Differential Equation block to solve the given differential equation. The Scope block is used to visualize the behavior of the variable x over time.

To construct a Matlab & Simulink model for the given mathematical model, we can use Simulink's Differential Equation block and a Clock and Gain block. Here's a step-by-step guide:

1. Open Simulink in Matlab.

2. Drag and drop a Clock block from the Simulink Library Browser into the model.

3. Drag and drop a Gain block from the Simulink Library Browser into the model.

4. Double-click on the Gain block and set the Gain value to 2.

5. Drag and drop a Differential Equation block from the Simulink Library Browser into the model.

6. Double-click on the Differential Equation block and enter the equation `d²x + 3 + 4*x + 6 = 5*cos(2*t)`.

7. Connect the output of the Clock block to the input of the Gain block, and the output of the Gain block to the input of the Differential Equation block.

8. Connect the output of the Differential Equation block to a Scope block from the Simulink Library Browser.

9. Run the simulation.

The Scope block will show the behavior of the value of x over time according to the given mathematical model.

In conclusion, The Clock block provides the independent variable t, and the Differential Equation block evaluates the given equation to compute the value of x. The simulation shows the dynamic response of x as influenced by the equation and the time signal.

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The total number of boxes that can be loaded onto the trailer is 27.

Here we have to determine the maximum number of boxes.

That can be stored in a locker by the volume of one box.

From the given information volume of the box is Vb and the volume f the locker is Vl.

\(Volume=Length\times width\times height\)

Therefore we get,

\(V_b=4\times3\times2\\V_b=24ft^3\)

The volume of the locker is

\(V_L=12\times6\times 9\\V_L=684ft^3\)

Therefore the number of the maximum boxes are

\(\frac{VL}{V_b} =\frac{648}{24} \\=27\)

Therefore, The total number of boxes can be loaded onto the trailer are 27.

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In general F^-1(f(x))=f(f^-1(x)) wherein f^-1(x) is the inverse of f(x).

Function is a process or activity that fulfills a specific purpose or set of requirements. It is a building block of programming and can be used to create various types of applications. Functions allow coders to modularize their code and make it easier to debug and maintain. Functions can also be used to process data, perform calculations, and display outputs.

It is a mathematical law which states that if a function f(x) has an inverse function then the composition of the function with its inverse should be equal to the original function. This law is also known as the Involution Law or the Composition Law of Inverse Functions.

The Involution law or the Composition law of inverse functions is a fundamental law of mathematics. This law states that for any function f(x) which has an inverse function, f^-1(x), the composition of the function with its inverse should be equal to the original function. That is, F^-1(f(x))=f(f^-1(x)). This law is important as it helps to understand the relationship between the original function and its inverse. This law is useful in solving various mathematical problems and in understanding various mathematical concepts such as differentiation and integration.

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A polynomial with roots A, B, and C can be written as it follows:

Because every time a complex number is the root of a polynomial, it's conjugated also is, let the roots A, B, and C stands for -2i, +2i, and 3, respectively. So, we can write the polynomial as follows:

Now, we just need to make the calculation needed to reach the expanded form:

The answer to the present question is the following polynomial:

Check the picture below.

Answer:

A

Step-by-step explanation:

because u use RISE/RUN

and the rise is 3 and the run is 1

3/1=3

Answer:

A.

Step-by-step explanation:

To determine the price the student-athlete should charge for each hot dog to break even, we need to consider the total costs she incurs, including the vendor fee, equipment cost, and the cost per hot dog. By dividing the total costs by the anticipated number of hot dogs sold, we can find the price per hot dog that would allow her to break even.

The total costs for the student-athlete include the vendor fee of $3000 and the equipment cost of $4500, which sums up to $7500 for the season. Additionally, she incurs a cost of $0.35 per hot dog sold. With an anticipation of selling 2000 hot dogs, the total cost for the hot dogs would be 2000 x $0.35 = $700.

To break even, the total revenue from selling the hot dogs should cover the total costs. Therefore, the price per hot dog should be set in such a way that the revenue from selling 2000 hot dogs equals $7500. Dividing the total costs ($7500) by the number of hot dogs (2000), we find that the student-athlete should charge $3.75 per hot dog in order to break even. This price per hot dog would allow her to cover all her expenses and reach the break-even point.

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An example of a linear function table is y=3x

A linear function is used to relate an independent variable and a dependent variable by introducing a rate of change(function) of which the independent variable is equated to find the dependent variable. Linear functions are those whose graph is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.

for example:

y=3x hence is the dependent variable as it depends on the change of x and 3 is the rate of change which is a constant and is determined by the division of the values of y/x hence to make a table of y over x of which y is determined by the rate of change the unrelated variable x, 3.

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Answer:

$20.58

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

         20

28     _______

         30

        - 2

         ____

          10

Answer:

b

Step-by-step explanation:

The correct answer is c. 6 ft³.To calculate the volume of the sculpture, we need to find the volume of one pyramid and then multiply it by four.

The volume of a pyramid can be calculated using the formula V = (1/3) * base area * height. In this case, the base area of the pyramid is a square with side length 2 feet, so the area is 2 * 2 = 4 square feet. The height of the pyramid is 6 feet. Plugging these values into the formula, we get V = (1/3) * 4 ft² * 6 ft = 8 ft³ for one pyramid. Since there are four identical pyramids, the total volume of the sculpture is 8 ft³ * 4 = 32 ft³.

However, the question asks for the volume of sculpting material needed, so we need to subtract the volume of the hollow space inside the sculpture if there is any. Without additional information, we assume the sculpture is solid, so the volume of material needed is equal to the volume of the sculpture, which is 32 ft³. Therefore, the correct answer is c. 6 ft³.

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System developers can initiate a formal project as early as the preliminary investigation stage, or later on, as analysis, design, and implementation activities occur. True.

System developers can initiate a formal project as early as the preliminary investigation stage or at any point in the analysis, design, and implementation activities.

The decision to initiate a formal project depends on various factors, including the scope of the project, the availability of resources, the complexity of the system, and the stakeholders' needs and requirements. A formal project may involve a team of developers, analysts, and other experts who work collaboratively to design and implement a system that meets the stakeholders' requirements and objectives.

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True. System developers can initiate a formal project as early as the preliminary investigation stage or later on as

analysis, design, and implementation activities occur.

The initiation stage is when the need for a new system is identified, and preliminary investigations are conducted to

determine the feasibility of the project.

If the project is deemed feasible, the formal project can be initiated at this stage.

However, if the project is initiated later on, the analysis, design, and implementation activities will have already begun.

System developers can initiate a formal project as early as the preliminary investigation stage or later on as

analysis, design, and implementation activities occur. therefore, the given statement is true.

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Answer:

135

Step-by-step explanation:

sum of interior angles of a triangle is 180

so

180-35-10

135