use f(x)=1/2x and f^-1(x)=2x

The missing lengths  in the triangles are h = 3/2√2 and b = 4√3

Triangle a and b

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

A special right triangle

For a right triangle with an angle of 45 degrees

The measure of the leg is

h = Hypotenuse/√2

So, we have

h = 3/√2

Evaluate

h = 3/2√2

For the other triangle, we have

sin(60) = b/6

So, we have

b = 6/sin(60)

Evaluate

b = 4√3

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Answer:

hehehheheyeu7777777yggg

Answer: 3/8

Step-by-step explanation:

A graph of the relationship between the amount of yellow paint and the amount of red paint per gallon is shown below.

Yes, the relationship between the amount of yellow paint and the amount of red paint per gallon is proportional.

An equation that describes the relationship is y = 5x/3.

The constant of proportionality is 5/3.

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 5/3 = 10/6 = 15/9 = 20/12

Constant of proportionality, k = 5/3.

Therefore, the required equation is given by:

y = kx

y = 5/3(x)

y = 5x/3

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Calculate the side length of the enlarged picture

Answer:

Hence, final picture will have a side length of 1.02 foot

Step-by-step explanation:

Side length of square photo, s = 0.17

Original dimension = (0.17 by 0.17)

Enlarged photo = double the original dimension:

2 * (0.17 * 0.17)

(0.34 * 0.34)

Second enlargement = Tripling the new dimension:

3 * (0.34 * 0.34)

(1.02 * 1.02)

Hence, final enlarged dimension = (1.02 * 1.02)

Hence, final picture will have a side length of 1.02 foot

Different logs measure different physical properties of the formation that are related to porosity, and the relationship between the log measurement and porosity can be expressed through equations.

The different logs used to obtain porosity and their principles of measurement, quantities measured, and relation to porosity.
There are three main types of logs used to obtain porosity: neutron logs, density logs, and sonic logs.
Neutron logs: These logs measure the hydrogen content in a formation, which is directly related to porosity. The tool emits neutrons that interact with hydrogen atoms, and the resulting gamma rays are measured. The count rate decreases with increasing porosity. The neutron log can be expressed as:
Porosity = (neutron log reading - matrix reading) / (fluid reading - matrix reading)
Density logs: Density logs measure the bulk density of a formation, which can be related to porosity. The tool emits gamma rays that interact with the formation, and the scattered gamma rays are measured. The bulk density decreases with increasing porosity. The density log can be expressed as:
Porosity = (matrix density - bulk density) / (matrix density - fluid density)
Sonic logs: Sonic logs measure the travel time of sound waves through a formation, which can be related to porosity. The tool sends an acoustic wave and measures the time it takes to travel a specific distance. The travel time increases with increasing porosity. The sonic log can be expressed using Wyllie's time-average equation:
Porosity = (sonic log reading - matrix reading) / (fluid reading - matrix reading)
In summary, neutron logs measure hydrogen content, density logs measure bulk density, and sonic logs measure travel time of sound waves. These measurements can be used to calculate porosity using the respective equations provided.

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The auto parts store would have operated approximately 153,423 stores in 2010 if the number of stores followed a linear pattern.

To solve this problem, we can use the formula for the equation of a line: y = mx + b, where y is the dependent variable (the number of stores), x is the independent variable (the year), m is the slope (the rate at which the number of stores is changing over time), and b is the y-intercept (the initial number of stores in the starting year).

We can use the information given to find the slope:

m = (4120 - 3547) / (2007 - 2004)

m = 573 / 3

m = 191

This means that the number of stores is increasing by an average of 191 each year.

Now we can use the slope and one set of coordinates (year, number of stores) to find the y-intercept:

3547 = 191(2004) + b

b = 3547 - 191(2004)

b = -229387

So the equation for the number of stores as a function of the year is:

y = 191x - 229387

To find out how many stores the auto parts store operated in 2010, we can substitute x = 2010 into the equation:

y = 191(2010) - 229387

y = 382810 - 229387

y = 153423

Therefore, the auto parts store would have operated approximately 153,423 stores in 2010 if the number of stores followed a linear pattern.

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The solutions for the inequality y ≤ 2/7x + 1 exist in quadrants I, III, and IV.

What is the quadrants?

The quadrants are the four regions that result from dividing a Cartesian coordinate plane into four parts using two perpendicular lines, the x-axis and y-axis.

The inequality y ≤ 2/7x + 1 represents a line on the x-y plane. The solutions for the inequality are the points on the plane that lie below or on the line. In a standard Cartesian coordinate system with x-axis and y-axis, the x-axis separates the plane into two parts: the upper half-plane (quadrant I) and the lower half-plane (quadrants III and IV). The y-axis separates the plane into two more parts: the right half-plane (quadrants I and IV) and the left half-plane (quadrants II and III).

So the solutions for the inequality y ≤ 2/7x + 1 lie in the region of the x-y plane that is in the lower half-plane (quadrants III and IV) and the right half-plane (quadrant I). Therefore, the solutions exist in quadrants I, III, and IV.

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Answer:

AS:  I, III, and IV

Step-by-step explanation:

Q's; In which quadrants do solutions for the inequality y is less than or equal to two thirds times x minus 4 exist?

AS:  I, III, and IV

 Look at the graph for a better understanding :P

Answer:

  0.82

Step-by-step explanation:

You want the probability of A or B given the frequencies shown in the diagram.

The probability of either event is the ratio of the number of times it occurs to the total number of trials. The total number of trials is shown as ...

  num trials = 23 + 18 + 9 = 50

Then the probability of interest is ...

  P(A or B) = P(A) + P(B) . . . . . . . . . . . . . given in the diagram

  P(A or B) = 23/50 +18/50 = 41/50

  P(A or B) = 0.82

Answer:

The slope is -2

Step-by-step explanation:

(-2, 8) and (1, 2)

Slope formula:

m= (y2-y1)/(x2-x1)

Work:

m= (2 - 8)/(1 + 2)

m= (-6)/3

m = -2

Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.

2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.

3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.

4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.

5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.

6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.

Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

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The given expression's quotient is \(-\frac{m^{12}n^6}{2}\).

Exponential expressions are simply a shorthand way of writing powers. The exponent indicates how many times that base has been used as a factor to multiply. So, in the case of 32, it is 2x2x2x2x2x2 = \(2^5\), where 2 is the "base" and 5 is the "exponent." This expression is translated as "two to the fifth power." In general, an=axaxax...xa(n times), where 'a' is the base and 'n' is the exponent, will be read as "a to the nth power."

Given that the exponential expression is \(\frac{2m^9n^4}{-4m^{-3}n^{-2}}\)

The given expression's quotient is

\(=\frac{2m^9n^4}{-4m^{-3}n^{-2}}\\\\\frac{1}{a^x}=a^{-x}\\\\=\frac{m^9n^4m^{3}n^{2}}{-2}\\\\=\frac{m^{9+3}n^{4+2}}{-2}\\\\=\frac{m^{12}n^6}{-2}\\\\=-\frac{m^{12}n^6}{2}\)

As a result, the given expression's quotient is\(-\frac{m^{12}n^6}{2}\).

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The sum of the numbers from 1 to 14 can be expressed in sigma notation as follows: \[ \sum_{n=1}^{14} n \]

Here's a breakdown of the notation:

- The symbol Σ represents the summation operator.

- The variable n is the index of summation and starts from 1.

- The lower limit of summation is 1, indicated below the Σ symbol.

- The upper limit of summation is 14, indicated above the Σ symbol.

- The term being summed is n, which represents each number in the sequence from 1 to 14.

When the sigma notation is evaluated, it represents the sum of all the terms from 1 to 14:

\[ 1 + 2 + 3 + \cdots + 14 = \sum_{n=1}^{14} n \]

Therefore, the sum of the numbers from 1 to 14 can be expressed in sigma notation as Σ(n, 1, 14).

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Answer:

True

Step-by-step explanation:

Using the vertical line test you can see that it is indeed a function.

The car takes approximately 9.97 seconds to accelerate from a speed of 30 mph to 34 mph.

To calculate the time required for the car to accelerate from 30 mph to 34 mph, we first need to convert the speeds to meters per second (m/s).
30 mph is equal to approximately 13.41 m/s, and 34 mph is equal to approximately 15.18 m/s.
Using the equation of motion s = ut + 0.5at^2, where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time, we can rearrange the equation to solve for time. Rearranging, we have t = (v - u) / a, where v is the final velocity.
Substituting the values, we get t = (15.18 m/s - 13.41 m/s) / 0.59 m/s^2. Simplifying the equation, we find t ≈ 9.97 seconds.
Therefore, it takes approximately 9.97 seconds for the car to accelerate from a speed of 30 mph to 34 mph.

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The largest segment of individuals in the U.S. who experienced a substance use disorder in 2017 were those whose problems involved alcohol.

This is based on the given information that states there were an estimated 19.7 million individuals with a substance use disorder.

Alcohol was the substance most commonly associated with substance use disorders in the U.S. in 2017.

The largest segment by far was those whose problems involved alcohol.

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Answer:

nine

Step-by-step explanation:

Answer:

2.

Step-by-step explanation:

The number is 2.

Multiply 2 by 2 (twice the number) and you'll get 4. Add 5 (five more) and you'll end up with 9.

Answer:

the answer is 1100

Step-by-step explanation:

you will do... 5500*20/100

Answer:

\(sin \theta =\cfrac{7}{8}\)

Step-by-step explanation:

Using the given identity, find the  required value as per following steps:

\((sin x)^2 + (cos x)^2 = 1\)

\((sin x)^2 = 1 - (cos x)^2\)

\(sinx=\sqrt{ 1 - (cos x)^2}\)

\(sin \theta = \sqrt{1-(\cfrac{\sqrt{15}}{8})^2 } = \sqrt{1-\cfrac{15}{64} } =\sqrt{\cfrac{49}{64} }=\cfrac{7}{8}\)

Answer:

\( \red{\sin( \theta) = \frac{7}{8} }\)

Step-by-step explanation:

We know that,

\(\cos( \theta) = \frac{adjacent}{hypotenuse} \\ \cos( \theta) = \frac{ \sqrt{15} }{8} \)

First, let us find the length of the opposite side of the right triangle using Pythagorean theorem.

Let the opposite side of the right triangle be x.

\(\sqrt{15} ^{2} + {x}^{2} = {8}^{2} \\ 15 + {x}^{2} = 64 \\ {x}^{2} = 64 - 15 \\ {x}^{2} = 49 \\ x = \sqrt{49} \\ x = 7\)

And now we can write sin theta as:

\( \sin( \theta) = \frac{opposite}{hyotenuse} \\ \sin( \theta) = \frac{7}{8}\)

Answer:

Sum of Interior Angles = (Number of Sides -2) • 180 degrees

Sum = (12 -2) * 180

Sum of the interior angles = 1,800 degrees

Source:  http://www.1728.org/polygon.htm

Step-by-step explanation:

As a linear combination of 30 and 37, we have:

gcd(30, 37) = -11(30) + 9(37)

To find gcd(30, 37) and express it as a linear combination of 30 and 37, we can use the Euclidean Algorithm.

Step 1: Divide 37 by 30.

37 = 30(1) + 7

Step 2: Divide 30 by 7.

30 = 7(4) + 2

Step 3: Divide 7 by 2.

7 = 2(3) + 1

Step 4: Divide 2 by 1.

2 = 1(2) + 0

Since the remainder is 0, the last nonzero remainder is gcd(30, 37) = 1.

Now, we can work backward to express gcd(30, 37) as a linear combination of 30 and 37.

From Step 3, we have:

1 = 7 - 2(3)

Replacing 7 with the expression from Step 2, we get:

1 = 7 - 2(30 - 7(4))

= 7 - 2(30) + 8(7)

= -2(30) + 9(7)

Replacing 7 with the expression from Step 1, we get:

1 = -2(30) + 9(37 - 30(1))

= -2(30) + 9(37) - 9(30)

= -11(30) + 9(37)

Therefore, gcd(30, 37) = -11(30) + 9(37).

As a linear combination of 30 and 37, we have:

gcd(30, 37) = -11(30) + 9(37)

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Answer:

Yes, because when the side lengths of a triangle are in the ratio 3: 4: 5, then it is a right triangle. These sides are 6: 8: 10, then the triangle is a right one.

Step-by-step explanation:

The line's equation is written as y = (3/7) (x) - 9/7 in slope-intercept form.

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the given data in the question,

We must first get the slope of the line in order to determine the equation of the line in slope-intercept form. Use the following formula to accomplish this:

slope = (y₂ - y₁) / (x₂ - x₁)

Since we have the points (-7, -3) and (-14, -6) in this instance, our formula is:

slope = (-6 - (-3)) / (-14 - (-7))

Slope = -3 / -7 = 3/7

The equation of the line can now be determined using the point-slope formula:

y - y₁ = m × (x - x₁)

Where (x1, y1) is a line point and m is the slope.

Assuming that m = 3/7 and (x₁, y₁) = (-7, -3), our equation is as follows:

y - (-3) = (3/7) × (x - (-7))

This equation can now be rearranged into slope-intercept form as follows:

y = (3/7) (x) + (3 × (-7) / 7)

y = (3/7) × (x - 9/7)

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The measure of the angle MKO in  ΔMOK when MK is the diameter of the circle is equal to option a. 36 degrees.

From Attached figure.

Since MK is the diameter of the circle,

Triangle formed in the semi circle are right angled triangle.

This implies,

MKO is a right angle triangle.

Measure of angle KMO is 54°.

Calculate the measure of angle MKO as follows,

Measure of angle MKO

= Measure of angle MOK - Measure of angle KMO

Since angle MOK is also a right angle, we have,

Measure of angle MKO

= 90° - 54°

= 36°

Therefore, the measure of angle MKO in the circle is equal to option a. 36 degrees.

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The above question is incomplete , the complete question is;

MK is the diameter of Circle and m ∠KMO=54°. What is m ∠MKO

a. 36

b. 90

c. 12

d. 55​​​​

Attached figure.

The Hungarian algorithm, we can find the optimal assignment that minimizes the overall cost, ensuring all jobs are completed and each worker is assigned to a job.

The transportation model for the allocation problem with r workers and o jobs, we can use the transportation problem framework. We can represent the problem as a cost matrix C, where C[i][j] represents the cost of worker i doing job j.

The objective is to minimize the total cost, considering that each worker must be assigned to exactly one job and each job must be done by exactly one worker.

By applying the transportation problem algorithms, such as the minimum-cost network flow or the Hungarian algorithm, we can find the optimal assignment that minimizes the overall cost, ensuring all jobs are completed and each worker is assigned to a job.

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When these conditions are met, you can use the dependent samples t-test to compare the mean of the difference between the two populations.

Paired samples

Random sampling.

Normal distribution

Independence of pairs.

To use the dependent samples t-test for the mean of the difference of two populations, the following conditions are necessary:
Paired samples:

The data must consist of pairs of observations (e.g., pre- and post-test scores) that are related or dependent on each other.
Random sampling:

The paired samples must be randomly selected from the populations.
Normal distribution:

The distribution of the differences between the paired samples should be approximately normally distributed.

This condition can be evaluated using a normality test, such as the Shapiro-Wilk test, or by visually inspecting a histogram or Q-Q plot of the differences.
Interval or ratio data:

The data should be measured on an interval or ratio scale (e.g., weight, height, test scores), rather than on an ordinal or nominal scale.
Independence of pairs:

The differences within each pair of observations should be independent of the differences in other pairs.

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If these conditions are met, then the dependent samples t-test can be used to test the null hypothesis that the mean difference between the two populations is zero.

The dependent samples t-test is used to compare the means of two related or dependent populations, where the samples are paired or matched. In order to use the dependent samples t-test for the mean of the difference of two populations, the following conditions should be met:

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To be 95% positive that the population proportion is within 0.02 percentage points, we would need to survey at least 2,450 drivers.

To determine the minimum sample size needed to estimate a population proportion with a certain level of confidence and a given margin of error, we use the following formula:

n = [Z² * p * (1-p)] / E²

where:

- n is the sample size

- Z is the Z-score corresponding to the desired level of confidence

- p is the estimated population proportion

- E is the desired margin of error

Assuming we do not have any prior information about the population proportion, we can use a conservative estimate of 0.5 for p, which maximizes the sample size needed. Also, for a 95% confidence level, the Z-score is approximately 1.96.

Plugging in the values, we get:

n = [1.96² * 0.5 * (1-0.5)] / 0.02²

n = 2.45 * 10³

Rounding up to the nearest whole number, we get:

n = 2,450

Therefore, we would need to survey at least 2,450 drivers to be 95% confident that the population proportion is estimated to within 0.02.

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Answer:

7.25

Step-by-step explanation:

58 dollar divided by 8 passes. Each is the same amount, therefore each is 7.25