You jump off the high dive at a swimming pool. Your
height as a function of time is modeled by
h = 16t² + 12t + 30, where t is the time in
seconds after you jump and h is the height in feet.
What is your maximum height, in feet?

Yes, 90 degrees (clockwise) and -270 degrees (counterclockwise) are coterminal angles.

Two angles are coterminal if they share the same terminal side when drawn in standard position. In other words, coterminal angles differ by an integer multiple of 360 degrees.

To see if 90 degrees and -270 degrees are coterminal, we can add 360 degrees to the smaller angle (-270 degrees) and see if we get the other angle:

-270 + 360 = 90

Since we obtain 90 degrees after adding 360 degrees to -270 degrees, these two angles are coterminal. They share the same terminal side in standard position, even though their rotations have different directions (clockwise and counterclockwise).

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The true statements are:

A. The graph of function f(x) = -√(√(√x)) will look like the graph of f(x)=√x but will reflect it about the x-axis and shrink it vertically by a factor of 1/2.

D. f(x) = √x has the same domain but a different range as f(x) = -√x.

A graph is a visual representation of a mathematical relationship or data. It consists of points or vertices connected by edges or lines to show the relationship between them.

A function is a mathematical concept that relates an input value to an output value, such that for each input, there is exactly one output. It can be represented as a set of ordered pairs, a graph, or an equation.

According to the given information:

A. The statement A is true. The graph of function f(x) = -√(√(√x)) is a transformation of the function f(x) = √x. The negative sign outside the square roots will reflect the graph of f(x) = √x about the x-axis, and the multiple square roots will shrink the graph vertically by a factor of 1/2.

B. The statement B is false. The graph of function f(x) = -√(√x) is also a transformation of the function f(x) = √x, but it will only reflect the graph about the x-axis. It will not shrink the graph vertically.

C. The statement C is false. The graph of function |f(x)| = √(√(√x)) is not a transformation of f(x) = √x. The absolute value bars will make the graph symmetric about the y-axis, but it will not shrink it horizontally.

D. The statement is true. The graph of function f(x) = √x and f(x) = sqrt(x) are equivalent, and have the same domain (all non-negative real numbers) but different ranges. The range of f(x) = √x is [0, infinity) while the range of f(x) = sqrt(x) is (0, infinity).

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Answer: 252cm^2

Step-by-step explanation:

Find height of parallelogram using the triangle.

[tex]a^2+b^2=c^2\\(9)^2+b^2=(15)^2\\b^2=114\\b=12[/tex]

Now that we have the height, we can fnd the area of the parallelogram using A=bh.

A = (12)(21)

A =252cm^2

The speed of boat is 5/6 meter per second and height of boat is 50[tex]\sqrt{3}[/tex] meter.

An angle is a shape created by two rays or lines that meet at the same terminal. The Latin word "angulus" (which means "corner") is where the term "angle" first appeared. The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean. The sign "" is used to denote angles. The Greek letter,,, etc. can be used to represent the angle between the two beams.

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

After solving the figure:

The speed of boat is 5/6 meter per second and height of boat is 50[tex]\sqrt{3}[/tex] meter.

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The speed of the boat from point C to point B is approximately 10.82 meters per second.

What is speed ?

Speed is a measure of how fast an object is moving. It is the rate at which an object covers distance.

We can use trigonometry to solve for h and the speed of the boat. Let's start with h:

From the right triangle CLB, we have:

tan 30° = h / CB

where CB is the distance between points C and B, which is given as 50 meters. Solving for h, we get:

h = CB * tan 30° = 50 * tan 30° ≈ 28.87 meters

So the height of the lighthouse is approximately 28.87 meters.

Now let's find the speed of the boat. We know that the boat travels from point C to point B in 1 minute, which is equivalent to 60 seconds. Let's define the speed of the boat as v, in meters per second. Then we have:

v = CB / t

where t is the time it takes for the boat to travel from point C to point B. We can find t using the distance formula:

[tex]CB = \sqrt{(x_B - x_C)^2 + (y_B - y_C)^2[/tex]

where x and y are the coordinates of each point. From the diagram, we can see that:

[tex]x_C = 0[/tex]

[tex]y_C = 0[/tex]

[tex]x_B = BL * cos \theta[/tex]

[tex]y_B = BL * sin \theta[/tex]

where BL is the distance from point B to the foot of the lighthouse, which is equal to h / tan θ. Therefore:

CB [tex]= \sqrt{((BL * cos \theta)^2 + (BL * sin \theta)^2)[/tex]

     [tex]= \sqrt{(BL^2 * (cos^2 \theta + sin^2 \theta))[/tex]

     [tex]= BL = h / tan \theta[/tex]

Substituting the values we have found, we get:

v = CB / t = (h / tan θ) / 60 ≈ 10.82 meters per second

Therefore, the speed of the boat from point C to point B is approximately 10.82 meters per second.

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The correct equations for x = - 2 and x = 2 are,

⇒ x² - 4 = 0

⇒ 4x² = 16

We have to given that;

Find the equations which are true for x = - 2 and x = 2.

Now, We can simplify as;

⇒ x² - 4 = 0

⇒ x² = 4

⇒ x = ± 2

⇒ x² = - 4

⇒ x = ±2i

⇒ 3x² + 12 = 0

⇒ x² + 4 = 0

⇒ x = ±2i

⇒ 4x² = 16

⇒ x² = 4

⇒ x = ±2

⇒ 2 (x - 2)² = 0

⇒ (x - 2)² = 0

⇒ x = 2, 2

Thus, The correct equations for x = - 2 and x = 2 are,

⇒ x² - 4 = 0

⇒ 4x² = 16

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Answer:

17

Step-by-step explanation:

The midpoint theorem states that “The line segment in a triangle joining the midpoint of any two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

therefore 2(x+5) = 3x-7

distribute

2x+10 = 3x-7

subtract 2x from both sides

2x+10 -2x = 3x-7 -2x

x-7 = 10

add 7 to both sides

x- 7 +7 = 10 + 7

x = 17

Answer:

Step-by-step explanation:

I think you are in 11th grade

we can use the theorem midpoint theorem.

as the mid-point theorem,

2(x+5)=3x-7

2x+10=3x-7

x=17

I really love your profile picture, is it real?

Answer: B and D.

Step-by-step explanation: We can simplify the expression -3.75+ 2(-4x +6.1) - 3.25x as follows:

-3.75+ 2(-4x +6.1) - 3.25x

= -3.75 - 8x + 12.2 - 3.25x (distributing the 2)

= -11.25x + 8.45 (combining like terms)

Now, let's check each expression to see if it is equivalent to -11.25x + 8.45:

A. 7x-2x +8.2

= 5x + 8.2

Not equivalent to -11.25x + 8.45

B. 8.45-8x-3.25x

= 8.45 - 11.25x

Equivalent to -11.25x + 8.45

C. -1.75-7.25x=6.1

This is not an expression, it is an equation. It is not equivalent to -11.25x + 8.45.

D. -11.25x +12.2 - 3.75

= -11.25x + 8.45

Equivalent to -11.25x + 8.45

Therefore, the expressions that are equivalent to -3.75+ 2(-4x +6.1) - 3.25x are B and D.

Answer:

2c + 3d = 24. For c = 4.25 and d = 3.75, we have 2(4.25) + 3(3.75) = 8.5 + 11.25 = 19.75

and

c^2 + d^2 = 24. For c = 4.25 and d = 3.75, we have 4.25^2 + 3.75^2 = 18.0625 + 14.0625 = 32.125

Step-by-step explanation:

There are many possible algebraic expressions involving c and d that are worth 24, but two possibilities are:

2c + 3d = 24. For c = 4.25 and d = 3.75, we have 2(4.25) + 3(3.75) = 8.5 + 11.25 = 19.75, which is not equal to 24. Therefore, this expression is not true for the given values of c and d.

c^2 + d^2 = 24. For c = 4.25 and d = 3.75, we have 4.25^2 + 3.75^2 = 18.0625 + 14.0625 = 32.125, which is not equal to 24. Therefore, this expression is also not true for the given values of c and d.

It is important to note that there are many

The value of x is given as follows:

x = 5.

The midsegment of a triangle is the line segment that connects the midpoint of two sides of the triangle. The Triangle Midsegment Theorem states that the midsegment of a triangle is parallel to the third side of the triangle, and its length is equal to half the length of the third side.

Thus the equation relating the lengths in this problem is given as follows:

3x + 11 = 2(x + 8)

3x + 11 = 2x + 16

x = 5.

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Check the picture below.

btw that picture above is misleading, whenever is 3 longer than 7?  and 2 longer than 7? =)

so let's just get the area of the trapezoidal face and multiply that by the depth of 7.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=2\\ b=4\\ h=3 \end{cases}\implies A=\cfrac{3(2+4)}{2}\implies A=9 \\\\[-0.35em] ~\dotfill\\\\ (9)(7)\implies \text{\LARGE 56}\qquad \impliedby volume[/tex]

The linear approximation of [tex]f(x) = x^2 at x = 3.5 is f(3.5)[/tex]  ≈ 9.5.

To write a linear approximation (equation of the tangent) and use it to approximate the value of a function, we can follow these steps:

Choose a point on the function where you want to approximate the value.

Let's call this point (a, f(a)).

Find the slope of the tangent line at that point using the derivative of the function at that point.

The slope of the tangent line is equal to the derivative of the function at that point, which is denoted by f'(a).

Write the equation of the tangent line using the point-slope form, which is given by: y - f(a) = f'(a)(x - a)

Use this equation to approximate the value of the function at a nearby point.

Plug in the value of x that is close to a into the equation and solve for y. The resulting y-value will be an approximation of the value of the function at the nearby point.

For example, suppose we want to approximate the value of [tex]f(x) = x^2 at x = 3.[/tex]

We can follow these steps:

Choose the point (3, f(3)) = (3, 9) on the function.

Find the slope of the tangent line at x = 3 using the derivative: f'(x) = 2x, so f'(3) = 6.

Write the equation of the tangent line using the point-slope form: y - 9 = 6(x - 3), which simplifies to y = 6x - 9.

Use this equation to approximate the value of f(x) at x = 3.5: f(3.5) ≈ 6(3.5) - 9 = 9.5.

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Therefore, the can of beans that is the best deal is option b, which has the lowest price per unit volume.

Volume is a measure of the amount of space occupied by an object or a substance. It is often measured in cubic units such as cubic centimeters, cubic inches, or cubic meters. The formula for finding the volume of different objects may vary based on their shape and size, but it typically involves measuring the length, width, and height of the object and multiplying them together.

Here,

To determine which can of beans is the better deal, we need to compare their volumes and prices per unit volume.

The volume of the small can of beans is:

V₁ = πr₁²h₁

= π*(1)²*(3)

= 3π

The price per unit volume of the small can is:

P₁ = $1.49 / 3π

≈ $0.157 per cubic inch

For the other cans of beans, we can calculate their volumes and prices per unit volume:

a. V₂ = πr₂²h₂

= π*(3)²*(9)

= 81π

P₂ = $39.95 / 81π

≈ $0.155 per cubic inch

b. V₃ = πr₃²h₃

= π*(2)²*(3)

= 12π

P₃ = $5.96 / 12π

≈ $0.132 per cubic inch

c. V₄ = πr₄²h₄

= π*(3)²*(3)

=27π

P₄ = $13.41 / 27π

≈ $0.165 per cubic inch

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The sides of the triangle are;

c = 5√2

b = 3√3

A right triangle is a triangle that has a right angle that measures 90 degrees. The hypotenuse, which is the side that faces the right angle, is the longest side. The right triangle's other two sides are referred to as its legs.

1) Cos 45 = 5/c

√2/2 = 5/c

c√2 = 10

c = 10/√2

c = 5√2

2) Tan 30 = b/3

√3/3 = b/3

3√3= 3b

b = 3√3/3

b = 3√3

We have used to concept of the special angles to solve the problem above.

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Answer:

10 oranges

Step-by-step explanation:

We Know

A grocery store sells a bag of 6 oranges for $4.80

4.80 / 6 = $0.80 for one orange

If Austin spent $8.00 on oranges, how many did he buy?

We Take

8 / 0.80 = 10 oranges

So, he bought 10 oranges.

The surface area will be equal to 1,017.9 square feet.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.

Given that:-

The surface area of the cylinder will be calculated as:-

SA = 2 πrl

SA = 2 π x 9 x 18

SA = 1,017.9 square feet

Therefore surface area will be equal to 1,017.9 square feet.

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The surface area of the given cylinder is 486π m² or 1526m².

From the figure, given height of the cylinder (h) = 18m

Given radius of the cylinder (r) = 9m

To find out the surface area of the cylinder the formula s = 2πr² + 2πrh

By substituting the given radius and height of the cylinder in the above equation we get the required surface area value.

s = 2πr² + 2πrh

s = (2 x π x (9)²) + (2 x π x 9 x 18)

s = (2 x π x 81) + (324π)

s = 162π + 324π

s = 486π m²

s = 486 x 3.14......           (since, π = 3.14....)

s = 1526m²

From the above explanation, we can conclude that the surface area of the given cylinder is equal to 486π m² or 1526m².

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Answer: Either 58 or 85

Step-by-step explanation:

5 + 8 = 13
8 + 5 = 13

5 x 8 = 40

8 x 5 = 40

Answer:

x = 7.5

Step-by-step explanation:

3(x + 4.5) = 36

Distributive property

3x + 13.5 = 36

Isolate the x, Subtract 13.5 from both sides

3x = 22.5

Divide both sides by 3

x = 7.5

The surface area of the prism is 78 square units, which corresponds to option A.

You provided three dimensions: 5 units, 3 units, and 3 units. I assume these are the dimensions of a rectangular prism.

Let's label the dimensions: length (l) = 5 units, width (w) = 3 units, and height (h) = 3 units.

There are two bases, and their areas are equal:

Base Area = l * w = 5 * 3 = 15 square units

There are also three pairs of lateral faces. The areas of the lateral faces are:

Two faces with dimensions l and h: 2 * (l * h) = 2 * (5 * 3) = 30 square units

Two faces with dimensions w and h: 2 * (w * h) = 2 * (3 * 3) = 18 square units

Now, add the areas of all the faces together:

Surface Area = Base Area * 2 + Lateral Area = 15 * 2 + 30 + 18 = 30 + 30 + 18 = 78 square units

So, the surface area of the prism is 78 square units, which corresponds to option A.

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When working with mu, sample size requirement is an important consideration. Mu, also known as the population mean, represents the average value of a variable across the entire population.

In order to estimate mu with a reasonable degree of accuracy, it is necessary to take a representative sample from the population.

The sample size required to accurately estimate mu will depend on a variety of factors, including the variability of the population, the desired level of precision, and the level of confidence required.
One of the most important factors influencing sample size requirements is the variability of the population.

The population is highly variable, larger sample sizes are required to obtain accurate estimates of mu.

This is because a larger sample size reduces the impact of random sampling error, allowing the true population to mean to be estimated with greater accuracy.

Similarly, when a high level of precision is required, larger sample sizes are necessary to ensure that the estimate of mu is sufficiently precise.
Another important consideration when determining sample size requirements is the desired level of confidence.

In order to estimate mu with a certain level of confidence, it is necessary to choose a sample size that provides the required level of precision.

If a researcher wants to estimate mu with 95% confidence, they may choose a sample size that provides an estimate with a margin of error of 5%.
When working with mu, sample size requirement is a critical factor in obtaining accurate estimates of the population mean.

The sample size required will depend on the variability of the population, the desired level of precision, and the level of confidence required.

By carefully considering these factors, researchers can select an appropriate sample size to ensure that their estimates of mu are reliable and meaningful.

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Answer:

∠A=∠P, AC = PR

Step-by-step explanation:

Because triangles ABC and PQR are congruent their corresponding angles and sides are congruent.

So

∠A=∠P

∠B=∠Q

∠C=∠R

Also

Side AB = Side PQ

Side BC = Side QR

Side AC = Side PR

Answer: 18 square feet im pretty sure

Step-by-step explanation:

Answer:  B)  216

Step-by-step explanation:

The cost to charge an electric car's home battery charger is $3.355 (to the nearest penny).

The cost to charge an electric car's home battery charger can be calculated using the following equation:

Cost = (kW x hours x rate)

Where kW stands for kilowatts, hrs stands for hours and rate stands for the rate per kilowatt-hour.

In this case, we have: kW = 6.1, hrs = 11 and rate = $0.05

Therefore, Cost = (6.1 x 11 x 0.05) = $3.355

Therefore, it will cost $3.35(to the nearest penny) to charge the car's battery.

To calculate this cost, we first multiply the kW (6.1) by the hours (11) to get the total kWh used (67.1). We then multiply this number by the rate ($0.05) to get the total cost of charging the battery ($3.355). This cost is to the nearest penny as we rounded up to the nearest cent when multiplying the kWh by the rate.

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Complete Question:

An  electric car's home battery charger uses 6.1 kilowatts for 11 hours. If electricity costs $0.05 per kilowatt-hour, how much (in dollars, to the nearest penny) does it cost to charge the car's battery? Use  exact numbers; do not estimate.

The probability that the arrival time between vehicles is 12 seconds or less is approximately 0.573.

Given that the time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 14 seconds.

We know that the exponential probability distribution function is given by

f(x) = λ e^(-λx)

Where λ is the rate parameter of the distribution and is equal to 1/mean in this case. So, λ = 1/14.

Now, we need to find the probability that the arrival time between vehicles is 12 seconds or less. Mathematically, we can express this as:

P(X ≤ 12) = [tex]\int\limits^{12}_0[/tex] λ e^(-λx) dx

Integrating this expression, we get:

P(X ≤ 12) = [-e^(-λx)]_[0,12] = -e^(-λ12) + e^(-λ0)

Since e^(-λ×0) is equal to 1, we have:

P(X ≤ 12) = 1 - e^(-λ×12)

Substituting the value of λ, we get:

P(X ≤ 12) = 1 - e^(-12/14)

P(X ≤ 12) ≈ 0.573

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The given question is incomplete, the complete question is:

The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 14 seconds . What is the probability that the arrival time between vehicles is 12 seconds or less?

Answer:

1. Mean : 85.6

2. Median : 90

3. Mode : 95

4. Range : 35

Step-by-step explanation:

1. For Mean, you add up all the terms and divide the resulting sum by the number of terms. In this case there were 9 terms that added up to 770, and when you divided that result by 9, the answer was 85.555 repeating. Since the question asks to round to the nearest tenth 85.6 represents the correct mean or average of the class.

2. To find the median, line up all the numbers in order from least to greatest. Like so :

60,75,75,90,90,95,95,95,95

In order to find the median, find the middle term. Since there are 9 terms, the middle term will be the fifth one. In this case, the answer was 90.

3. Mode represents the number that appears the most in a data set. Look at the 9 terms and find the one that appears the most. In this case it is 90.

4. Lastly, to find the range, subtract the lowest value in the data set from the highest one. 95 is the highest and 60 is the lowest. Do [tex]95-60[/tex] and you will get an answer of 35.

Hope this helps!

Answer:

Mean: 85.6

Median: 90

Mode: 95

Range: 35

Step-by-step explanation:

Mean: Add up all the value and divide by the number of values you have.

75 + 95 + 90 + 95 + 60 + 95 + 75 + 95 + 90 = 770

770 / 9 = 85.6

Median: Rearrange in increasing order + look at middle number

60, 75, 75, 90, 90, 95, 95, 95, 95

Mode: Number that shows up the most.

95 shows up 4 times.

Range: Maximum - Minimum.

95 - 60 = 35.

Answer:

To the nearest hundredth of a percent, an interest rate of 6.68% would be required for Deondra to end up with $82,000 after 5 years of compounding interest.

Step-by-step explanation:

We can use the formula for compound interest to solve this problem:

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

where:

A = the final amount (in this case, $82,000)

P = the principal (the initial investment, in this case, $64,000)

r = the interest rate (what we're trying to find)

n = the number of times the interest is compounded per year (in this case, 4, since it's compounded quarterly)

t = the number of years (in this case, 5)

Plugging in the values we know and solving for r, we get:

$82,000 = $64,000(1 + r/4)^(4*5)

$82,000/$64,000 = (1 + r/4)^20

1.28125 = (1 + r/4)^20

Taking the 20th root of both sides, we get:

(1.28125)^(1/20) = 1 + r/4

0.0167 = r/4

r = 0.0668 (rounded to four decimal places)

Therefore, to the nearest hundredth of a percent, an interest rate of 6.68% would be required for Deondra to end up with $82,000 after 5 years of compounding interest.

the area of given figure made from two part Parallelogram and Triangle is 288sq cm

A parallelogram is a four-sided shape with opposite sides that are parallel and equal in length. The opposite angles of a parallelogram are also equal in measure. Parallelograms can have various orientations, but their opposite sides will always be parallel.

A triangle, on the other hand, is a three-sided shape with three angles and three vertices. The sum of the angles in a triangle is always 180 degrees. Triangles can come in various shapes and sizes, such as equilateral (all sides and angles are equal), isosceles (two sides and two angles are equal), and scalene (all sides and angles are different).

given that

1st part:

Base=6cm

height=8cm

Area=1×Base×Height/2

Area=(1×6×8)cm²/2

Area=24cm²

it have two part so, Area=2×24=48sq cm

2nd part:

if we assume Parallelogram

Area=Base×Height

Area=15cm×8cm

Area=120 sq unit

it have two part so,2×120sq cm

240sq unit

total area of given figure is 48 sq cm+240sq cm=288 sq unit.

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The total revenue between the two companies is $3,200

To find the Nash Equilibrium, we need to look for a situation where neither firm has an incentive to change their strategy. This occurs when both firms are charging a price of $8 per month and each has 200 customers, resulting in total revenue of $3,200.

At this price and quantity, neither firm can increase their revenue by changing their strategy. If Netflix were to increase its price above $8, some of its customers would switch to Flixbuster, and Netflix's revenue would decrease. Similarly, if Flixbuster were to decrease its price below $8, it would gain customers from Netflix, but its revenue would still decrease.

Therefore, the Nash Equilibrium in this scenario is a price of $8 and 200 customers for each firm, resulting in total revenue of $3,200 between the two companies.

In mathematical terms, the Nash Equilibrium is a solution to the following system of equations:

Qn = 300 - P

Qf = 300 - P

TRn = P(Qn)

TRf = P(Qf)

where Qn and Qf are the quantities demanded by Netflix and Flixbuster, respectively, P is the price, and TRn and TRf are the total revenues earned by Netflix and Flixbuster, respectively. Solving this system of equations, we get P = 8 and Qn = Qf = 200, which results in total revenue of $3,200.

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Complete Question:

The following table shows a small community's demand for monthly subscriptions to a streaming movie service. Assume that only two firms (Nextflix and Flixbuster) sell in this market, that each firm offers the same quality of service and movie selection, and that each firm's marginal cost is constant and equal to 0 (zero) due to excess capacity.

Price/Month    Number of Total (P) Customers (Q)        Revenue/Month(TR)

$10                                                     0                                                         $0

9                                                      100                                                     900

8                                                      200                                                1,600

7                                                      300                                               2,100

If the two companies are behaving in each best interest, and the market is able to reach a Nash Equilibrium. What is the total revenue between the two companies?

The piecewise function when represented on the graph based on each domain is added as an attachment

Given that

So, we have the following piecewlse function that represents the scenario

f(x) = 12 when 0 < x ≤ 2

     = 19 when 2 < x < 6

     = 25 when 6 ≤ x ≤ 14

Next, we plot the function on the graph based on each domain

See attachment for the graph

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The answer for the given equation is 5x-4.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Some algebraic expressions use the same variables raised to the same exponents for like terms in the equation. Similar phrases remain constant. We initially formulate an expression as the sum of its terms in order to locate the terms and the similar terms in it.

An algebraic expression is considered to be in its simplest form when it doesn't contain any brackets or like terms. We employ the distributive property to add or subtract coefficients that are linked to variables.

according to question,

= -(x+4)+6x

= -x-4+6x

=5x-4

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The time required to ring up the customer with 11 items is; 20 seconds

A linear equation is defined as an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

We are given the linear equation:

t = p + 9

Where;

p is the variable that represents the number of items being purchased

t reprensts the time required to ring up the customer.

Thus:

When p = 11 items, we have:

t = 11 + 9

t = 20 seconds

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