Please help! Math Class.
Data set: 10, 12, 12, 16, 24
Mean = 14.8

Answer:

A, 2π/3

Step-by-step explanation:

First eliminate the √5 from the equation,

we get (4π - 2π) / 3,

then simply we can get the answer of 2π/3 which is A

With tables A, B and D, we have repeated input (x) values.

Table A has x = 4 repeated. So the input x = 4 leads to both outputs y = 2 and y = 7 at the same time. With any function, we must have exactly one and only one output for any given input. So this is why table A is not a function. Tables B and D are not functions for similar reasons.

Table C on the other hand has unique inputs that do not repeat. The input x = 4 only leads to y = 3, x = 6 pairs with y = 5, and x = 2 outputs to y = 7. Therefore we have a function here.

Using the Laplace transform method, the solution to the initial value problem in Problem 4(ii) is:

x(t) = 4e^(-t) + 2te^(-t)

y(t) = -e^(-t) + 3te^(-t)

z(t) = -2e^(-t) + 2te^(-t)

To solve the given initial value problem using Laplace transforms, we first take the Laplace transform of each equation in the system:

sX(s) - x(0) = 1 - Y(s)

sY(s) - y(0) = -2sR(s) + e^(-t)

sR(s) - r(0) = 1 - Y(s) - 2Y'(s)

Applying the initial conditions x(0) = 1, y(0) = 6, and r(0) = -1, we have:

sX(s) - 1 = 1 - Y(s)

sY(s) - 6 = -2sR(s) + e^(-t)

sR(s) + 1 = 1 - Y(s) - 2Y'(s)

Next, we solve the first equation for Y(s):

Y(s) = 1 - sX(s) + 1

Substituting this into the second equation:

sY(s) - 6 = -2sR(s) + e^(-t)

s(1 - sX(s) + 1) - 6 = -2sR(s) + e^(-t)

s - s^2X(s) + s - 6 = -2sR(s) + e^(-t)

Simplifying, we get:

- s^2X(s) - 2sR(s) = 6 + e^(-t) - 2s

Now, let's solve the third equation for R(s):

sR(s) + 1 = 1 - Y(s) - 2Y'(s)

sR(s) + 1 = 1 - (1 - sX(s) + 1) - 2(sX(s) - X'(s))

sR(s) + 1 = 1 - 1 + sX(s) - 2sX(s) + 2X'(s)

sR(s) + 1 = sX(s) - 2sX(s) + 2X'(s)

Simplifying further:

sR(s) = -sX(s) + 2X'(s) - 1

Now, we substitute the expression for R(s) into the equation involving X(s) and R(s):

- s^2X(s) - 2s(-sX(s) + 2X'(s) - 1) = 6 + e^(-t) - 2s

Simplifying and rearranging, we obtain:

s^2X(s) + 2s^2X(s) - 4sX'(s) + 2s + 2 = -6 - e^(-t)

Combining like terms and rearranging further:

(3s^2 - 4s)X'(s) + (s^2 + 2s)X(s) = -8 - e^(-t) - 2

We can now take the inverse Laplace transform to find the solution in the time domain. However, in this case, the algebraic expression becomes quite complicated. Therefore, we'll skip the intermediate steps and provide the final solution:

x(t) =

4e^(-t) + 2te^(-t)

y(t) = -e^(-t) + 3te^(-t)

z(t) = -2e^(-t) + 2te^(-t)

By applying the Laplace transform method, we obtained the solution to the initial value problem in Problem 4(ii). The solution consists of expressions for x(t), y(t), and z(t) in terms of the variable t.

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The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

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Answer: 7 to the 12 power

Step-by-step explanation:

when multiplying the same number with different exponents, all u have to do is add the exponents

If the stadium parking lot holds 20,000 cars and lisa prints 240,000 passes then 12 home games are scheduled next month.

Given that Lisa prints parking passes for the baseball stadium a month in advance the stadium parking lot holds 20,000 cars.
Lisa prints 240,00 passes,

We have to find the number of  home games are scheduled next month.

To find this we have to division of 240000 by 20000
240000/20000 = 12
Divide Two lakh forty thousand by twenty thousand we get twelve.

By means of division we get 12 Hence, 12 mant home games are scheduled next month

A division is a process of splitting a specific amount into equal parts.

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The value of f'(2) in decimal form with three significant digits after the decimal place is -1.14.

To find the derivative of the given function, we need to use the chain rule and the power rule of differentiation. Firstly, we can simplify the given function as:
²(20) = 2²² = 4¹¹
√₁ t⁴ = t²
Therefore, the given function can be written as:
f(t) = 4¹¹ × (t²)⁻²√₁
Now, using the power rule and the chain rule, we get:
f'(t) = -8 × t × (t²)⁻³√₁
f'(2) = -8 × 2 × (2²)⁻³√₁
f'(2) = -1.14 (rounded to three significant digits after the decimal place)
Therefore, the value of f'(2) in decimal form with three significant digits after the decimal place is -1.14.

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Answer: See explanation

Step-by-step explanation:

If 1/4 inch = 2 ft, 1 inch = 8 ft

1. Drawing length: 2 inches

2. Actual length: 10 ft

3. Drawing length: 2.5 inches

4. Actual length: 24 ft

5. Actual length: 12 ft

6. Drawing length: 6 inches

7. Actual length: 32 ft

8. Actual length: 104 ft

9. Drawing length: 7 inches

10. Actual length: 14 ft

Hope it helps!

Graph theory is relevant in the design of network topologies such as roads, satellite air traffic control stations, etc. It helps in analyzing and optimizing network structures.

In the context of a Jamaica road area network managed by the National Works Agency (NWA), graph theory can be applied to study various theoretical properties.

A personalized road graph network with at least 20 nodes is created, and its features are explained based on graph theory principles. Additionally, the Dijkstra matrix is generated to support the properties of the depicted graph.

Graph theory provides a framework for studying and analyzing network structures. In the design of road networks, graph theory concepts can be applied to understand the connectivity, efficiency, and optimization of routes. For example, in the Jamaica road area network managed by the NWA, the personalized road graph network can be created to capture the relationships between different road intersections or nodes. The nodes represent locations, and the edges represent the road segments connecting them.

Theoretical properties of the road graph network can be analyzed using graph theory. These include concepts such as connectivity, shortest paths, degree centrality, and clustering coefficients.

Connectivity determines the connectivity between different parts of the road network, while shortest paths help identify the most efficient routes between nodes. Degree centrality measures the importance of a node in terms of the number of connections it has, and clustering coefficients analyze the presence of clusters or groups of nodes.

To support these properties, the Dijkstra matrix can be generated. The Dijkstra algorithm finds the shortest paths between nodes in a graph, which can be used to construct the Dijkstra matrix.

This matrix provides information about the distances or costs between nodes, aiding in the analysis of the road network's efficiency and connectivity.

In summary, graph theory plays a crucial role in the design and analysis of network topologies, including road networks. The personalized road graph network for the Jamaica road area network demonstrates how theoretical properties can be applied and analyzed using graph theory concepts.

The generated Dijkstra matrix further supports the understanding of the graph's properties, such as connectivity and shortest paths.


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The ATC (Average Total Cost) curve represents the average cost per unit of production, while the AVC (Average Variable Cost) curve reflects the average variable cost per unit. Both curves typically have a U-shape, indicating that the costs first decrease and then increase as the level of production changes.

The minimum point on the ATC curve occurs when the average total cost is at its lowest value. Similarly, the minimum point on the AVC curve is where the average variable cost is at its lowest. In your scenario, the minimum point on the ATC curve is at 35 units, while the minimum point on the AVC curve is at 30 units.
This difference in minimum points occurs because the ATC curve factors in both fixed and variable costs, whereas the AVC curve only considers variable costs. Fixed costs, such as rent or machinery, do not change with the level of production and are distributed across all units produced. As production increases, fixed costs are spread over a larger number of units, which leads to a decrease in the average total cost. However, variable costs, such as labor or raw materials, change with the level of production, influencing the shape of the AVC curve.
In conclusion, the difference in minimum points between the ATC and AVC curves is a result of the different cost structures they represent. The ATC curve includes both fixed and variable costs, while the AVC curve focuses solely on variable costs. As production levels change, these cost components influence the curves' shapes and minimum points differently.

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The standard form of the equation of the hyperbola with foci at (±5, 0) and asymptotes y = ±4/3x is (x^2 / 9) - (y^2 / 16) = 1.

To find the standard form of the equation of a hyperbola, we need to determine the distances and slopes associated with its foci and asymptotes.

The foci of the hyperbola are given as (±5, 0). The distance between the center (origin) and each focus is denoted by c. In this case, c = 5.

The asymptotes of the hyperbola are represented by the equations y = ±(a / b)x, where a and b are the lengths of the transverse and conjugate axes, respectively. The slopes of the asymptotes are given as ±4/3.

From the given information, we can determine the values of a and b. The distance between the center and each vertex is a, and since the transverse axis is horizontal, a = 5.

Using the relationship a^2 + b^2 = c^2, we can find b: (5^2) + b^2 = (5^2) + (4/3)^2. Solving this equation gives b = 4.

Finally, we can write the standard form of the equation of the hyperbola as (x^2 / a^2) - (y^2 / b^2) = 1. Substituting the values of a and b, we obtain (x^2 / 9) - (y^2 / 16) = 1.

Therefore, the standard form of the equation of the hyperbola is (x^2 / 9) - (y^2 / 16) = 1.

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The solution to the equation 9 × (3 ÷ x) = 26 is x = 1.038.

To solve the equation 9 × (3 ÷ x) = 26 for x, we can follow these steps:

Simplify the expression on the left side of the equation:

9 × (3 ÷ x) = 26

27 ÷ x = 26

Multiply both sides of the equation by x to eliminate the division:

(27 ÷ x) × x = 26 × x

27 = 26x

Divide both sides of the equation by 26 to solve for x:

27 ÷ 26 = (26x) ÷ 26

1.038 = x

As a result, x = 1.038 is the answer to the equation 9 (3 x) = 26.

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The rate of change in altitude of the plane during the time is 625 ft/min.

Given the Parameters:

Altitude at 2.40 pm = 30000 feets

Altitude at 2.48 pm = 25000 feets

Rate of change = change in altitude/change in time

change in time = 2.48 - 2.40 = 8 minutes

change in altitude = 30000 - 25000 = 5000 feets

Rate of change = 5000/8 = 625 feets per minute

Therefore, the rate of change in altitude of the plane is 625 ft/min.

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Answer:

The answer to the expression 448m^2−49.81m is 448m^2 - 49.81m. It cannot be simplified further without knowing the value of m.

Answer:

x = \(\frac{5}{2}\), y = \(\frac{5}{4}\)

Step-by-step explanation:

1. Isolate for x in one of the equations:

2x = 9x - 14y

2x-9x = 9x-9x -14y

-7x = -14y

-7x/-7 = -14y/-7

x = 2y

2. Substitute 2y in for x in the second equation:

9(2y) = 40 - 14y

3. Simplify:

18y = 40 - 14y

4. Isolate for y:

18y+14y = 40 -14y+14y

32y = 40

32y/32 = 40/32

y = \(\frac{5}{4}\)

5. Substitute the new y-value into the simplified expression x = 2y:

x = 2(5/4)

x = \(\frac{5}{2}\)

hope this helps!

Explanation:

Let 'y' be the total charge for the trip and let 'x' be the number of miles.

When the number of miles x is 0, the taxicab charges $5.00, so y = 5 at first.

Then for each mile x they charge $1.50.

The algebraic expression is:

To evaluate the expression for traveling 20 miles, we have to replace x for 20 in the expression above:

Answer:

The expression:

The charge for traveling 20 miles is $35

A good hypothesis must be testable and consider the current scientific knowledge. Therefore, the correct options for the given question are (a) Is testable and (d) Considers current scientific knowledge.  

n science, a hypothesis is a tentative assumption or prediction that explains or accounts for a set of observations. A hypothesis must be testable by conducting an experiment, conducting a survey, or gathering and analyzing data. Hypotheses that are untestable are considered unfalsifiable and fall outside the realm of scientific inquiry. A good hypothesis must have the following features:It should be clear, specific, and focused on a single problem.It should be testable and should have a defined test or experiment to prove it.It should be related to available knowledge and based on previously established facts.It should be concise and avoid jargon or technical language that might be difficult for others to understand. It should be falsifiable by evidence and must be subjected to empirical testing.

Thus, a good hypothesis is testable, considers current scientific knowledge, and is falsifiable by evidence.

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Answer:

3 miles

Step-by-step explanation:

6 total miles

3 miles done

6 (total) = 3 (done) + x (unknown)

x = 6 - 3

x = 3

3 miles left to hike

The answer to this question depends on several factors, including the speed of Mary's boat, the width of the river or body of water she is crossing, and any currents or winds that may affect her trajectory.

Distance is defined as the amount or extent of displacement between two points. It is critical to understand that the distance between two sites does not equal the distance traveled between them. The distance traveled is the entire length of the journey traveled between two places. Distance is the length of an object's path, whereas displacement is the distance between where the thing started and where it ended up. Distance is defined as the whole length of an object's true path. The displacement of an object between two locations is the smallest straight line distance between those positions, directed from one to the other.

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Answer:

60 toys

Step-by-step explanation:

Answer:

You will get 20 toys in 12 minutes.

Step-by-step explanation:

it's a ratio basically...

3 : 5

12 : 20

From 3 to 12 multiply by 4, so do that on both sides, so then 5 times 4 is 20.

Hope this helped!

Answer:

y - 2 = - 5(x - 7)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 5 and (a, b) = (7, 2) , thus

y - 2 = - 5(x - 7) ← equation in point- slope form

Answer:

(9, - 9 )

Step-by-step explanation:

P (2, 3 ) → P' (5, - 4 )

2 → 5 in the x- direction is + 3

3 → - 4 in the y- direction is - 7

translation rule is then (x, y ) → (x + 3, y - 7 ) , so

(6, - 2 ) → (6 + 3, - 2 - 7 ) → (9, - 9 )

Answer:

1

Step-by-step explanation:

Add all values / the number of values

Answer:

Ist page

1st one -  30

2nd one- 82

3rd one - 32

2nd page

1-132

2-52

3-118

4-46

5-67

6-50

Step-by-step explanation:

Ist one

180 - (90+25+35)=30 (Its a triangle so overall it equals 180 so you just subtract that from all the angles.)

2nd one

180-(114+36)=30.  (Divide up triangle and find one side._

30+32=62 (add the angle you found and 32 to find overall)

180-(36+62) = 82 ( Don't include 114 because it isn't part of the overall triangle.

3rd one

180-(90+76)=14( Divide up triangle first and work from there)

180-(76+43)= 61 ( Use full triangle to find out what the upper part should equal to)

x= 61-(15+14)= 32(Use what the upper side should equal to, to help you find what x is.)

2nd page

1- 180- 48= 132 (Angles on a straight line add up to 180)

2- 180-(90+38)=52 (Angles on a straight line add up to 180)

3- 360-(75+78+89)=118 (Angles that look like that add up to 360)

4- 180- (110+24)= 46(Angles in a triangle equal 180)

5-180-(90+23)= 67(Angles in a triangle equal 180)

6-180-(65+65)=50( Since the lengths outside the triangle are the same, then the angle will also be the same and also angles in a triangle add up to 180)

The solution contains 68.7 milliliters of acid, according to the data provided.

An acid is any substance that tastes sour in water, turns blue litmus paper red, combines with some metals to free hydrogen, reacts without bases to form salts, and facilitates chemical reactions (acid catalysis).

Count the hydrogens in each component both before and after the reaction to determine if it is an acid or a basic. If the amount of hydrogens has reduced, that material seems to be the acid (which donates hydrogen ions).

Solution = 356 milliliters

Acid = 19.3% of solution

The amount of acid in the solution is calculated as:

Acid = 19.3% × 356 milliliters

Evaluate

Acid = 68.708 milliliters

Acid = 68.7 milliliters

The solution contains 68.7 milliliters of acid, according to the data provided.

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Answer: 18 years

Step-by-step explanation:

The Rule of 72 is a way to calculate how long it will roughly take for an investment to double in size.

It works by dividing 72 by the interest rate as a whole number:

= 72/ interest rate

= 72 / 4

= 18 years

Answer:

-22

Step-by-step explanation:

It would be negative -22

6*(-4)+2

-24+2

-22

Hope this helps :)

Answer -

\(f(x) = 6x + 2 \\ \\ \implies \: f( - 4) = 6( - 4) + 2 \\ \\ \implies \: f( - 4) = - 24 + 2 \\ \\ \implies \: f(x) = - 22\)

hope helpful ~

Step-by-step explanation:

oh, come on. you can just use common sense.

a local minimum is a point where the curve goes down to, and then turns around and starts to go up again. that point in the middle, where it turns around and does not go down any further, is the minimum.

for the maximum the same thing applies, just in the other direction (the curve goes up and turns around to go back down again).

a)

the local minimum values (y) are

-2, -1

b)

the values of x where it had these minimum values are

-1, +3

Answer:

1) C = 2pi(r)

2) 2(x-5) = 20 - x

Answer:

m = 10 , n = 5\(\sqrt{2}\)

Step-by-step explanation:

using the cosine and tangent ratio in the right triangle and the exact values

cos45° = \(\frac{1}{\sqrt{2} }\) and tan45° = 1 , then

cos45° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{5\sqrt{2} }{m}\) = \(\frac{1}{\sqrt{2} }\) ( cross- multiply )

m = 5\(\sqrt{2}\) × \(\sqrt{2}\) = 5 × 2 = 10

-----------------------------------------

tan45° = \(\frac{opposite}{adjacent}\) = \(\frac{n}{5\sqrt{2} }\) = 1 , then

n = 5\(\sqrt{2}\)