this is due today help

Answer:

To get f⁻¹(x), write f(x) = y = x^(1/3)/3, exchange x and y, so x = y^(1/3)/3, then y = (3x)³, this is just the f⁻¹(x) = (3x)³.

Step-by-step explanation:

The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.

The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.

Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).

The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.

The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.

The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).

Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

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Answer:

the answer is 2\(\frac{1}{4}\)

Step-by-step explanation:

(3/4) + (3/4) + (3/4) = 2.25 --> \(2\frac{1}{4}\)

Answer:

\(\frac{dV}{dt}\)  = 1017.87 in³/min

\(\frac{dV}{dt}\) = 17203.35 in³/min

Step-by-step explanation:

given data

radius r of a sphere is increasing at a rate = 3 inches per minute

\(\frac{dr}{dt}\)  = 3

solution

we know volume of sphere is V = \(\frac{4}{3} \pi r^3\)

so \(\frac{dV}{dt} = \frac{4}{3} \pi r^2 \frac{dr}{dt}\)  

and when r = 9

so rate of change of the volume will be

rate of change of the volume \(\frac{dV}{dt} = \frac{4}{3} \pi (9)^2 (3)\)

\(\frac{dV}{dt}\)  = 1017.87 in³/min

and

when r = 37 inches

so rate of change of the volume will be

rate of change of the volume \(\frac{dV}{dt} = \frac{4}{3} \pi (37)^2 (3)\)

\(\frac{dV}{dt}\) = 17203.35 in³/min  

Answer:

  x = 1

Step-by-step explanation:

You want to know the value of x in the trapezoid with adjacent angles (43x+2)° and 135°.

The two marked angles can be considered "consecutive interior angles" where a transversal crosses parallel lines. As such, they are supplementary.

  (43x +2)° +135° = 180°

  43x = 43 . . . . . . . . . . . . . . divide by °, subtract 137

  x = 1 . . . . . . . . . . . . . . . divide by 43

The value of x is 1.

__

Additional comment

Given that the figure is a trapezoid, we have to assume that the top and bottom horizontal lines are the parallel bases.

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Answer:

1000

Step-by-step explanation:

Round the 6 in 600, this is 1 significant figure.6 rounds up to 10 making 1000

The number can be 601, 602, 603, ....... 699

Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit.

If the number is round down to 600 then it's depend on round off

If the round off should be at hundred place, then number can be

601,602,  ..................649.

If we round off the above number then it will be 600 which has 1 significant figure.

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Answer:

ill edit my comment later but is there a graph? its not enough info

Step-by-step explanation:

not enough info i think

The volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis is 51π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = 2π ∫ [a, b] x * h(x) dx

Where:

- V is the volume of the solid

- π represents the mathematical constant pi

- [a, b] is the interval over which we are integrating

- x is the variable representing the x-axis

- h(x) is the height of the cylindrical shell at a given x-value

In this case, we need to solve for x in terms of y to express the equation in terms of y.

Rearranging the given equation:

x = 5 ± √(1 - y)

Since we are only interested in the region in the first quadrant, we take the positive square root:

x = 5 + √(1 - y)

Now we can rewrite the volume formula with respect to y:

V = 2π ∫ [c, d] x * h(y) dy

Where:

- [c, d] is the interval of y-values that correspond to the region in the first quadrant

To determine the interval [c, d], we set the equation equal to zero and solve for y:

1 - (x - 5)² = 0

Expanding and rearranging the equation:

(x - 5)² = 1

x - 5 = ±√1

x = 5 ± 1

Since we are only interested in the region in the first quadrant, we take the value x = 6:

x = 6

Now we can evaluate the integral to find the volume:

V = 2π ∫ [0, 1] x * h(y) dy

Where h(y) represents the height of the cylindrical shell at a given y-value.

Integrating the expression:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * h(y) dy

To find h(y), we need to determine the distance between the y-axis and the curve at a given y-value. Since the curve is symmetric, h(y) is simply the x-coordinate at that point:

h(y) = 5 + √(1 - y)

Substituting this expression back into the integral:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

Now, we can evaluate this integral to find the volume

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

To simplify the integral, let's expand the expression:

V = 2π ∫ [0, 1] (25 + 10√(1 - y) + 1 - y) dy

V = 2π ∫ [0, 1] (26 + 10√(1 - y) - y) dy

Now, let's integrate term by term:

\(V = 2\pi [26y + 10/3 * (1 - y)^\frac{3}{2} - 1/2 * y^2]\)] evaluated from 0 to 1

V = \(2\pi [(26 + 10/3 * (1 - 1)^\frac{3}{2} - 1/2 * 1^2) - (26 * 0 + 10/3 * (1 - 0)^\frac{3}{2} - 1/2 * 0^2)]\)

V = 2π [(26 + 0 - 1/2) - (0 + 10/3 - 0)]

V = 2π (25.5)

V = 51π cubic units

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Given statement solution is :- It  would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

To find the cost of installing tile in the dining room and carpet in the bedroom, we need to calculate the areas of both rooms first.

Given:

Every 2 centimeters on the floor plan represents 1 meter of the house.

Dining Room:

On the floor plan, the dining room is 8 cm by 10 cm.

Converting this to meters, the dimensions of the dining room are 8 cm / 2 = 4 meters by 10 cm / 2 = 5 meters.

The area of the dining room is 4 meters * 5 meters = 20 square meters.

Bedroom:

On the floor plan, the bedroom is 6 cm by 10 cm.

Converting this to meters, the dimensions of the bedroom are 6 cm / 2 = 3 meters by 10 cm / 2 = 5 meters.

The area of the bedroom is 3 meters * 5 meters = 15 square meters.

Now, let's calculate the costs.

Cost of Tile:

The cost of installing tile is $34 per square meter.

The area of the dining room is 20 square meters.

Therefore, the cost of installing tile in the dining room is 20 square meters * $34/square meter = $680.

Cost of Carpet:

The cost of installing carpet is $21 per square meter.

The area of the bedroom is 15 square meters.

Therefore, the cost of installing carpet in the bedroom is 15 square meters * $21/square meter = $315.

Therefore, it would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

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Given statement solution is :- Mathematical models are extremely valuable tools in various fields, including chemistry, biology, and physics. They offer several advantages: Simplification and abstraction, Prediction and simulation, Cost and time efficiency, Insight and understanding.

Mathematical models are extremely valuable tools in various fields, including chemistry, biology, and physics. They offer several advantages:

Simplification and abstraction: Mathematical models allow complex systems or processes to be represented using simplified mathematical equations or algorithms. This simplification helps in understanding the underlying principles and relationships of the system, making it easier to analyze and predict outcomes.

Prediction and simulation: Models enable scientists to make predictions about the behavior of a system under different conditions. They can simulate scenarios that are difficult or impossible to observe in the real world, allowing researchers to explore various hypotheses and make informed decisions.

Cost and time efficiency: Models can be used to explore different scenarios and test hypotheses in a relatively quick and cost-effective manner compared to conducting real-world experiments. They can help guide experimental design by providing insights into the most relevant variables and parameters.

Insight and understanding: Mathematical models often reveal underlying patterns and relationships that may not be immediately apparent from experimental data alone. They provide a framework for organizing and interpreting data, leading to a deeper understanding of the system being studied.

However, mathematical models also have limitations and potential disadvantages:

Simplifying assumptions: Models are based on assumptions and simplifications, which may not fully capture the complexity of the real-world system. If these assumptions are incorrect or oversimplified, the model's predictions may be inaccurate or misleading.

Uncertainty and error: Models are subject to uncertainties and errors stemming from the inherent variability of the system, limitations in data availability or quality, and simplifying assumptions. It is crucial to assess and communicate the uncertainties associated with model predictions.

Validation and verification: Models need to be validated and verified against experimental data to ensure their accuracy and reliability. This process requires rigorous testing and comparison to real-world observations, which can be challenging and time-consuming.

Mathematical models are closely linked to the fields of chemistry, biology, and physics, providing valuable insights and predictions in these disciplines. Here are some examples:

Chemistry: Mathematical models are used to study chemical reactions, reaction kinetics, and molecular dynamics. One example is the use of rate equations to model the kinetics of a chemical reaction, such as the reaction between reactants A and B to form product C.

Biology: Mathematical models play a crucial role in understanding biological systems, such as population dynamics, gene regulation, and the spread of infectious diseases. For instance, epidemiological models like the SIR (Susceptible-Infectious-Recovered) model are used to simulate and predict the spread of diseases within a population.

Physics: Mathematical models are fundamental in physics to describe physical phenomena and predict outcomes. One well-known example is Newton's laws of motion, which can be mathematically modeled to predict the motion of objects under the influence of forces.

Quantum mechanics: Mathematical models, such as Schrödinger's equation, are used to describe the behavior of particles at the quantum level, providing insights into atomic and molecular structures and the behavior of subatomic particles.

Fluid dynamics: Mathematical models, such as the Navier-Stokes equations, are employed to study the behavior of fluids, including airflow, water flow, and weather patterns.

These examples demonstrate the wide range of applications for mathematical models in understanding, predicting, and simulating various phenomena in the fields of chemistry, biology, and physics.

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You have the following inequality:

z/4 ≤ 12

To solve the previous inequality you proceed as follow:

z/4 ≤ 12 multiply both sides by 4

z ≤ 48

Hence, the solution is z ≤ 48

when you want to graph a solution of the form "z lower or equal than", you draw a black point, that means the solution are all number lower than 48, including 48.

The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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Answer:

\((a)\ f^{-1}(-15) = -6\)

\((b)\ f^{-1}(4) + f(9)=0\)

Step-by-step explanation:

Given

The attached table

\((a)\ f^{-1}(-15)\)

This represents an inverse function.

So, we look into x row for its value.

i.e.

\(f^{-1}(-15) = -6\)

\((b)\ f^{-1}(4) + f(9)\)

Just like (a)

\(f^{-1}(4) = -11\) ---- by looking into the x rows

\(f(9) = 11\)

So:

\(f^{-1}(4) + f(9)=-11 + 11\)

\(f^{-1}(4) + f(9)=0\)

Answer:

5/3

Step-by-step explanation:

use the rise/run tactic

Answer:

approx 41.6%

Step-by-step explanation:

Answer:

41.7%

Step-by-step explanation:

First, you will divide 20 by 48.

\(20/48=0.4167\)

Secondly, you would multiply by 100%

\(0.4167* 100= 41.67%\)%

If you round to the nearest whole number it would give you \(42\)%. If it is rounded to the nearest tenth it would be \(41.7%\)%

Answer:

y¹⁰

Step-by-step explanation:

Let’s say y=2.

This means 2 to the power of 4 is 16.

Then, we do 16 times 2, because it says y4 times 6.

16 times 2 is 32.

Now we find what 2 to the power of 5 is.

That is also 32.

Finally, we do 32 times 32 which is 1,024.

As you can see, we used 2, aka y 10 times. This is because y4 has 4 y’s, and y5 has  5 y’s. Then, there is one extra y in the middle.

Therefore, 4 + 5 + 1 is equal to 10.
This can be written as y10.

hope this helped!

Answer:

m = -3 ; c = 1

Step-by-step explanation:

y = -3x + 1

y = mx + c

m = -3

c = 1

Answer: (5 , 1)

Step-by-Step explanation:

hihi your problem is a system of question y = x-4 and  y = -x+6 okay so  graph them both normally and then find the point where they intersect which is gonna be a coordinate point, and that's your solution !!

y = x-4
the y intersect is going to be 4
the slope is a positive 1 , going up to the right, through the positive quadrant, line is facing to the right

y = -x+6
the y intersect is going to be -6
the slope is going to be a -1 , following up the opposite way the line is going to face the left

once you graph them both you'll see the point of intersection, the solution
make sure you drew your lines very clearly !!!!

the solution is  x = 5 and y = 1 which is also (5 , 1)

hopefully this was helpful !

Answer:

65

Step-by-step explanation:

Answer:

like 149

Step-by-step explanation:

big brain

Combining the homogeneous and the particular solutions, and applying the initial conditions, the solution to the given IVP is:

\(x(t) = -\cos{(2t)} + \frac{1}{2}\sin{(2t)}\)

The IVP is given by:

\(x^{\prime\prime} + 4x = -2\sin{(2t)} + 8\cos{(2t)}\)

First, we find the homogeneous solution, which depends on the roots of the characteristic equation, given by:

\(r^2 + 4 = 0\)

\(r^2 = -4\)

\(r = \pm \sqrt{-4}\)

\(r = \pm 2i\)

Thus:

\(x_h(t) = a\cos{(2t)} + b\sin{(2t)}\)

Then, according to the source(left-side of the equality), the particular solution has the following format:

\(x_p(t) = A\cos{(2t)} + B\sin{(2t)}\)

Applying the derivatives:

\(x_p^{\prime}(t) = -2A\sin{(2t)} + 2B\cos{(2t)}\)

\(x_p^{\prime\prime}(t) = -4A\cos{(2t)} - 4B\sin{(2t)}\)

Replacing into the IVP:

\(x^{\prime\prime} + 4x = -2\sin{(2t)} + 8\cos{(2t)}\)

\(-4A\cos{(2t)} - 4B\sin{(2t)} + 4A\cos{(2t)} + 4B\sin{(2t)} = -2\sin{(2t)} + 8\cos{(2t)}\)

\(0A\cos{(2t)} + 0B\sin{(2t)} = -2\sin{(2t)} + 8\cos{(2t)}\)

Thus, the particular solution is \(x_p(t) = 0\).

The complete solution is:

\(x(t) = x_h(t) + x_p(t)\)

\(x(t) = x_h(t)\)

\(x(t) = A\cos{(2t)} + B\sin{(2t)}\)

Applying the initial conditions:

\(x(0) = -1 \rightarrow A + 0B = -1 \rightarrow A = -1\)

\(x^{\prime}(0) = 1 \rightarrow 2B = 1 \rightarrow B = \frac{1}{2}\)

Thus, the solution is:

\(x(t) = -\cos{(2t)} + \frac{1}{2}\sin{(2t)}\)

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The variance of Z is 1.67

What is a variance?

A data set's variance is a measure of dispersion that accounts for the spread of each data point. Along with the standard deviation, which is just the square root of the variance, it is the measure of dispersion that is most frequently employed.

To calculate the variance,

First, we need to calculate the mean.

So, the Mean of Z = \(\frac{4+5+6+7}{4}\) = 5.5

Then,

the variance of Z = \(\frac{(4-5.5)^{2} + (5-5.5)^{2}+(6-5.5)^{2}+(7-5.5)^{2} }{3}\) = 1.67

Hence, the variance of Z is 1.67

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First we are going to use the sin trigonometric function to find x,

Now, we do the analogous procedure for the angle of 30 degrees

Answer: you can maybe show them being trapped in the bathroom them come in with a sharp knife and splash or put ketchup on the part you stabbbed them

Step-by-step explanation:

The comparisons that are true are 11. -5 < 0 12. 9 > -8 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51  19. 17 < 23  20. 18 > -36 and that is not true are 13. -7 = -7 (not true) 18. -32 > 4 (not true)

To make each statement true, write < or >. We need to compare two values for each statement to determine whether it is true or false.

To indicate that the first value is less than the second value, write <.

Alternatively, to indicate that the first value is greater than the second value, write >.

Below are the comparisons: 11. -5 < 0 12. 9 > -8 13. -7 > -7 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 18. -32 > 4 19. 17 > 23 20. 18 > -36

To determine the direction of inequality, we need to compare the values.

We used inequality signs such as > (greater than) or < (less than) to indicate which value is larger or smaller than the other.

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The correct question would be as

Write > or < to make each statement true.

11. -5 0

12. 9 -8

13. -7 7

14. 55 -75

15. -32 -24

16. 89 73

17. -58 -51

18. -32 4

19. 17 23

20. 18 -36​

They will be when they pass each other at 44 4/9 mins.

This is a classic question on Speed, time, & distance.

1. When time traveled in each segment is constant, then average speed is simple mean of speeds.

2. When distance traveled in each segment is constant, then average speed is reciprocal of simple mean of reciprocal of speeds. It is basically called Harmonic mean.

So this question falls in the category of 2.

=> So, average speed = Reciprocal of mean of reciprocals of 40 & 50.

=> Average speed = Reciprocal of mean of 1/40 & 1/50.

=> Average speed = Reciprocal of (1/40 + 1/50)/2

= Reciprocal of (5+4)/400

= 44 4/9 mins

Hence, they will be when they pass each other at 44 4/9 mins.

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Answer:

a = 3/28

Step-by-step explanation:

To start solving for a variable, you need to isolate it.

-4/3b = 4a

-4/3 divided by 4 equals -4/12 or -1/3

a = -1/3b

To completely solve for a we need to plug it back in and solve for b.

b = (4(-1/3b)) - 3/4

b = -4/3b - 3/4

7/3b = -3/4

b = -9/28

Finally, we can plug b back in to the previous equation we got for a to solve for a.

a = -1/3(-9/28)

a = 3/28

Furthermore, we can check if this is correct by plugging in 3/28 for a into the original problem and see if we get what we got for b (-9/28)

The percentage increase China's population from 1970 to 1995 is: 56.25%.

Percentage increase = (Final Value - Original Value)/Original value × 100.

Given the following:

Original value = 0.8 billion

Final Value = 1.25 billion

Final Value - Original Value = 1.25 - 0.8

Final Value - Original Value = 0.45

Percentage increase = 0.45/0.8 × 100 = 56.25%.

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Step-by-step explanation:

Given that the ratio of zebras are 5 and giraffes are 2

We add them giving is 7

So: giraffe=2/7 × 21 = 6

Zebra 5/7 × 21 = 15