what is the domain of the function?

Answer:

[tex]L_c=12.56 \ \text{feet}[/tex]

Step-by-step explanation:

From the question we are told that

Width of circular path [tex]w_c=2 \ \text{feet}[/tex]

Inner Diameter [tex]d_{in}=550 \ \text{feet}[/tex]

Outer diameter [tex]d_{out}=550+2\times2[/tex]  (inner diameter +  2 circular path width)

[tex]d_{out}=550+4[/tex]

[tex]d_{out}=554 \ \text{feet}[/tex]

Generally the equation for inner circumference of the circle  is mathematically given by

[tex]C_1=\pi d_{in}[/tex]

[tex]C_1=3.14\times550[/tex]

[tex]C_1=1727 \ \text{feet}[/tex]

Generally the equation for outer circumference of the circle  is mathematically given by

[tex]C_2=\pi d_{out}[/tex]

[tex]C_2=3.14\times554[/tex]

[tex]C_2=1739.56 \ \text{feet}[/tex]

Generally the difference in length of the two circumference  is mathematically given by

[tex]L_c=C_2-C_1[/tex]

[tex]L_c=1739.56-1727[/tex]

[tex]L_c=12.56 \ \text{feet}[/tex]

Lines I and P can be considered parallel if they have the same slope, and ABC and CEF can be considered similar if they have the same size, but not necessarily the same shape.

Angle is a two-dimensional figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. An angle is measured in degrees, which are represented by the symbol °. The size of an angle is determined by the amount of rotation between the two rays, with the vertex being the point of rotation. Angles can be described as acute, obtuse, right, reflex, straight and full.

A) The slope of line I is equal to the slope of line P. - True. If two lines have the same slope, they are parallel.

B) ABC is congruent to CEF - False. Congruent shapes have the same size and same shape. ABC and CEF are not necessarily the same size or shape.

C) Lines I and P are parallel - True. If two lines have the same slope, they are parallel.

D) ABC is similar to CEF - True. Similar shapes have the same size, but not necessarily the same shape.

E) Sin (A) = Sin (C) - False. The sine of an angle is only equal to the sine of another angle if they are the same angle.

F) Sin (B) = cos (F) - False. The sine of an angle is not equal to the cosine of another angle.

In conclusion, lines I and P can be considered parallel if they have the same slope, and ABC and CEF can be considered similar if they have the same size, but not necessarily the same shape. However, the sine of an angle is only equal to the sine of another angle if they are the same angle, and the sine of an angle is not equal to the cosine of another angle.

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Answer:

Raul is 15 years old.

Step-by-step explanation:

The number of years from the start of the Great Depression to Nixon's election is six years less than three times Raul's age: 3r-6

If then Nixon's first election happened 39 years after the Great Depression, then: 3r-6=39

3r-6=39    Add six to both sides so the 6 on the left side gets canceled out (positive and negative cancel each other out) so the equation will now look like this: 3r=45

Then divide 3 on both sides (multiplication and division also cancel each other out), then the equation looks like this: r=15

And so, Raul is 15 years old.

The angle ∠FNL in the given trapezium shows that ∠FNL is 122°

The opposite angles of a trapezium are not necessarily equal, unlike in a parallelogram.

However, the opposite angles of a trapezium are supplementary, which means that the sum of one pair of opposite angles equals 180 degrees.

In other words, if we label the angles of a trapezium as F, D, N, and L (with F and L being opposite angles, and D and N being opposite angles), then we have:

∠F + ∠L = 180 degrees

∠D + ∠L = 180 degrees

Thus, ∠FDL + ∠FNL = 180

4x - 14 + 9x - 40 = 180

13x - 54 = 180

13x = 234

x = 18

∠FNL = 9x - 40

∠FNL = 9(18) - 40

∠FNL = 122°

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The quadratic equation is:

y = (149/1,800)*(x + 1)² + 2

Remember that if the parabola has a vertex (h, k) and a leading coefficient a can be written as:

y = a*(x - h)² + k

Here we know that the vertex is (-1, 2), then we will get the following equation:

y = a*(x + 1)² + 2

And we know it passes through (-14, - 153/8), then we will get:

-153/8 = a*(14 + 1)² + 2

-153/8 = a*225 + 2

a = (153/8 - 2)/225 =

a = 149/1,800

The quadratic is:

y = (149/1,800)*(x + 1)² + 2

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The pressure exerted (in N/m²) by the box on the shelf given that the bottom of the box has an area of 0.30 m² and weighs 60 N, is 200 N/m²

Pressure is defined a force per unit area. Mathematically, it is written as

Pressure (P) = force (F) / area (A)

P = F / A

With the above formular, we can obtain the pressure exerted by the box as follow:

Pressure exerted (P) = Weight of box (W) / Area of box (A)

Pressure exerted = 60 / 0.30

Pressure exerted = 200 N/m²

Thus, we can conclude that the pressure exerted is 200 N/m²

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Complete question:

The area of the bottom of a tiffin box is 0.30 sq. m and weight is 60 N, Calculate the pressure exerted by the box on the shelf in N/sq. m *​

Answer:

the method of exact differential equations:

We need to check if this differential equation is exact. To do that, we check if the partial derivative of the first term with respect to y is equal to the partial derivative of the second term with respect to x:

∂/∂y(x(x-y)) = x(-1) = -x

∂/∂x(y^2) = 0

Since these partial derivatives are not equal, the differential equation is not exact. We can try to make it exact by multiplying the entire equation by a suitable integrating factor.

Let's find the integrating factor (IF) by taking the partial derivative of the IF with respect to y and equating it to the partial derivative of the second term with respect to x:

∂/∂y(IF) = -y^2/(x(x-y)^2)

∂/∂x(y^2) = 0

From the first equation, we can see that an integrating factor of IF = x(x-y)^2 should make the equation exact. Multiplying the entire equation by this integrating factor, we get:

x(x-y)^2dy + y^2x(x-y)dx = 0

Now, we just need to find a function φ(x,y) such that:

∂φ/∂x = x(x-y)^2dy

∂φ/∂y = y^2x(x-y)dx

Integrating the first equation with respect to x, we get:

φ(x,y) = ∫x(x-y)^2dy + f(x)

φ(x,y) = -1/3(x-y)^3x + f(x)

Now, we differentiate this equation with respect to x and equate it to the second equation:

∂φ/∂x = -(x-y)^3 + f'(x)

∂φ/∂y = y^2(x-y)^3

Comparing the two, we can see that f'(x) = 0, which means that f(x) is a constant. We can choose this constant to be zero without loss of generality.

Therefore, the solution to the differential equation is given by:

-1/3(x-y)^3x + C = 0

where C is an arbitrary constant.

The probability that at least 4 accounting majors are on the committee is E. 0.5874.

Probability operates on the principle of dividing the number of expected outcomes by the number of total outcomes. To find the probability that at least 4 accounting majors are on the committee, we can begin by determining the probability of having exactly 4, 5, 6, and 7 accounting majors on the committee. After finding these probabilities, we can then sum up the figures.

First, the total number of ways to choose 8 members from a group of 6+7=13 is:

13! / (8! * 5!) = 1287

Next, we will find the number of ways to choose exactly 4 accounting majors and 4 finance majors is:

6 choose 4 * 7 choose 4 = 15 * 35 = 525

Also, the number of ways to choose exactly 6 accounting majors and 2 finance majors is:

6 choose 6 * 7 choose 2 = 1 * 21 = 21

Finally, the number of ways to choose exactly 7 accounting majors and 1 finance major is:

6 choose 7 * 7 choose 1 = 0 * 7 = 0

Now, we will sum the total number of ways to choose a committee with at least 4 accounting majors as follows:

525 + 210 + 21 + 0 = 756

756 / 1287 = 0.587

Therefore, the probability of selecting a minimum of 4 accounting majors is thus 0.5874.

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Thus, the percentile rank of just an 85 on a test is: 70 percentile for the given test​ scores.

A percentile in statistics refers to a score's position in relation to other scores in a given set. Although percentile has no one fixed meaning, it is frequently described as the proportion of numbers within a collection of data scores that are lower than a particular value.

Percentile shows the proportion of persons who fall below a given value. When we declare that a score of 365 out of 400 represents the 90% percentile on an exam, it means that 90% of test-takers received scores that were lower than or equal to 365.

Give: Seven of the ten test results are inside the 85th percentile.

The percentage of those who received less than or equal to 85 is just as follows: 7/10 = 0.7.

percentile rank:

0.7*100 = 70

Thus, the percentile rank of just an 85 on a test is: 70 percentile for the given test​ scores.

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Answer: Please provide further information for help so I can assist you.

Answer:

19, 993

Step-by-step explanation:

35, 617

15, 624

19, 993

Answer:

Step-by-step explanation:

20,047 using simple subtraction

The statement that is NOT one of the axioms of Euclidean geometry is D. If two planes intersect, their intersection is a point.

Euclidean geometry is a branch of mathematics that deals with the study of two-dimensional and three-dimensional figures using a set of axioms or postulates.

The axioms of Euclidean geometry are a set of five statements that are used as the foundation for all of the theorems and proofs in Euclidean geometry.

The first two axioms are relatively straightforward and intuitive, while the third axiom involves the use of circles to construct geometric figures. The fourth axiom establishes the concept of a right angle, which is a 90-degree angle, while the fifth axiom deals with the concept of parallel lines and their relationship to intersecting lines.

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Answer: >

Step-by-step explanation:

The exponential function that describes the amount in the account after time t is:

A(t) = 17509*e^(0.066t).

The balance after 10 years is $39,499.57

The doubling time is approximately 10.48 years.

a) The formula for continuously compounded interest is given by:

A = P*e^(rt)

where A is the amount after time t, P is the principal, r is the annual interest rate (as a decimal), and e is the mathematical constant approximately equal to 2.71828.

In this case, P = $17,509, r = 0.066 (6.6% expressed as a decimal), and t is the time in years. So the exponential function that describes the amount in the account after time t is:

A(t) = 17509*e^(0.066t)

b) To find the balance after 1 year, we plug in t=1:

A(1) = 17509e^(0.0661) ≈ $18,693.68

To find the balance after 2 years, we plug in t=2:

A(2) = 17509e^(0.0662) ≈ $19,971.60

To find the balance after 5 years, we plug in t=5:

A(5) = 17509e^(0.0665) ≈ $25,150.24

To find the balance after 10 years, we plug in t=10:

A(10) = 17509e^(0.06610) ≈ $39,499.57

c) The doubling time is the time it takes for the investment to double in value. We can solve for the doubling time by setting A(t) = 2P and solving for t:

2P = P*e^(rt)

2 = e^(rt)

ln(2) = rt

t = ln(2)/r

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

t = ln(2)/0.066 ≈ 10.48 years

So the doubling time is approximately 10.48 years.

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In linear equation, 1161.8 lb is the total weight of the liquid in the tank, to the nearest full pound.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                         Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

d = 12 ft

r = 12 ft/2 = 6 ft

volume of sphere = (4/3)πr³

volume of hemisphere = (1/2)(4/3)πr³

volume = (2/3)π(6 ft³) =  12.56 ft³

weight = volume × density

weight = 12.56 ft³ × 92.5 lb/ft³

weight = 1161.8 lb

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Answer:

101 = k + 33

101 - 33 = k + 33 - 33

68 = k

this is your required answer

Equation in the standard slope-intercept form: y = 2X + 2

The slope intercept form of an equation is represented as follows:

y = mx + c

where, m = slope, c = y-intercept

We want to rewrite the equation X = (y - 2) ÷ 2 in slope-intercept form, which is in the form y = mx + b, where m is the slope and b is the y-intercept.

First, let's isolate y on one side of the equation by multiplying both sides by 2:

2X = y - 2

Next, let's add 2 to both sides:

2X + 2 = y

Finally, let's switch the sides to get the equation in the standard slope-intercept form:

y = 2X + 2

So the slope of the line is 2 and the y-intercept is 2.

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Answer:

Step-by-step explanation:

make them all the same denominator so

the least common denominator for all of them is  24:

1/3 x 8/8=8/24

5/6x4/4=20/24

3/8x3/3=9/24

so from least to greatest it is:

1/3, 3/8, 5/6

From the given answer choices, the equation that shows work being calculated with the correct unit is C. 113J = (17.4N) x (6.51m)

In physics, work is defined as the amount of energy transferred by a force when it causes an object to move over a certain distance. Work is a scalar quantity and is expressed in units of joules (J) or foot-pounds (ft-lbs).

Mathematically, work (W) is given by the product of the force (F) applied on an object and the displacement (d) of the object in the direction of the force, as expressed in the formula:

W = F * d * cos(theta)

where theta is the angle between the force vector and the displacement vector.

Thus, the correct units which are Joules, metres and Newton are used.

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Answer:

The range of the stock prices is from $10.82 to $33.17. To find the upper quartile, we need to find the value of the stock price that is greater than 75% of the data.

The distance between the minimum value and the maximum value is:

$33.17 - $10.82 = $22.35

To find the upper quartile, we need to find the value that is three-quarters of the distance above the minimum value:

$10.82 + 0.75($22.35) = $26.69

Therefore, the upper quartile of the stock price is $26.69.

To find the value above which the stock price is higher 25% of the time, we need to find the value that is 75% of the distance above the minimum value:

$10.82 + 0.25($22.35) = $15.62

Therefore, 25% of the time, the stock price is above $15.62.

To find the upper quartile, we need to first find the median of the stock prices, which is the value that divides the distribution into two equal parts. The midpoint of the distribution is:

Midpoint = (10.82 + 33.17) / 2 = 22.995

Now, we can find the upper quartile, which is the median of the upper half of the distribution. The upper half of the distribution ranges from the midpoint to the highest value of 33.17. Therefore, we calculate the median of this range as follows:

Upper quartile = (22.995 + 33.17) / 2 = 28.0825

So, the upper quartile of the stock prices is $28.08.

To find the value above which the stock is priced 25% of the time, we need to find the 75th percentile of the distribution. Since the distribution is uniform, we can use the formula for the percentile as follows:

Percentile rank = (percentile / 100) = (value - minimum) / (maximum - minimum)

Solving for the value, we get:

value = minimum + percentile rank x (maximum - minimum)

For the 75th percentile, we have:

value = 10.82 + 0.75 x (33.17 - 10.82) = 28.49

Therefore, the stock is priced above $28.49 on 25% of all days.

The 18th term of the sequence is -140

It is important to note that the formula for the nth term of an arithmetic sequence is expressed with the equation;

an = a + (n - 1) d

Such that the parameters are enumerated as;

From the information given, we have;

The sequence is;

-21, -14, -7, 0, 7, ...

Then, the common difference = -14 - (-21) = -14 + 21 = -7

Substitute the value

a18 = -21 + (18 - 1) -7

expand the bracket

a18 =-21 + (17)-7

a18 = - 21 - 119

a18 = - 140

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The function m(t) shifts the time frame by 1hr later the original function d(t).

The function s can be written in terms of d as follows:

s (r) = d ×  [tex](r+7)^{-1}[/tex]

The core concept of calculus in mathematics is a function. The relations are certain kinds of the functions. In mathematics, a function is a rule that produces a different result for every input x. In mathematics, a function is represented by a mapping or transformation. Letters like f, g, and h are widely used to indicate these operations.

In this situation, d (5) = 0.25 means that Tyler is 0.25 minutes away from his home at 7:05am. This is because Tyler's distance from his house at time t after 7am is provided by the function d (t).

Tyler's school starts at 9 a.m. with a 120-minute delay. As a result, if d (5) = 0.25, Tyler has walked for 5 minutes, and his distance function s (r) calculates his distance starting at 7 minutes after 7 a.m. with a 120-minute start delay. The matching point, then, indicates Tyler's separation from his home at 7 minutes after 9 a.m. If he started walking at 7 am and took 5 minutes.

The function s can be written in terms of d as follows:

s (r) = d ×  [tex](r+7)^{-1}[/tex]

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a) the journey took 11 hours and 50 minutes.

b)the average speed of the bus was 70.95 km/hour.

c) the cost of fuel for the journey was K240.08.

Distance is the measure of how far apart two objects or points are from each other. It is a scalar quantity, which means it only has magnitude and no direction. Distance is usually measured in units such as meters (m), kilometers (km), feet (ft), miles (mi), or any other appropriate unit of length.

a) convert the times to a 24-hour format to perform the calculation.

07:00 in 24-hour format is 07:00, and 18:50 in 24-hour format is 18:50.

The journey duration is:

18:50 - 07:00 = 11 hours and 50 minutes

Therefore, the journey took 11 hours and 50 minutes.

b) The average speed of the bus can be found by dividing the distance traveled by the time taken:

Average speed = Distance ÷ Time

= 840 km ÷ 11.83 hours (converted from 11 hours and 50 minutes)

= 70.95 km/hour

Therefore, the average speed of the bus was 70.95 km/hour.

c) The fuel consumption rate is 1 liter per 20 km. Therefore, the bus consumed 840 km / 20 = 42 liters of diesel fuel for the journey.

The cost of fuel can be calculated by multiplying the fuel quantity by the cost per liter:

Cost of fuel = Fuel quantity x Cost per liter

= 42 liters x K5.74/liter

= K240.08 (rounded to two decimal places)

Therefore, the cost of fuel for the journey was K240.08.

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The inverse of the linear function, f(x), f(x) = (2x - 3)/5 is f⁻¹(x) = (5·x + 3)/2. The correct option is option A

A. f⁻¹(x) = (5·x + 3)/2

The inverse of a function is a function that reverses the effect the original function.

The original function is; f(x) = (2·x - 3)/5

The inverse of f(x) can therefore be found by making x the subject of the equation as follows;

f(x) = (2·x - 3)/5

5 × f(x) = (2·x - 3)

5 × f(x) + 3 = 2·x

2·x = 5 × f(x) + 3

x = (5 × f(x) + 3)/2

Plugging in x = f⁻¹(x) and f(x) = x, in the above equation, we get;

f⁻¹(x) = (5 × x + 3)/2

The correct option that is an inverse of f(x) is therefore, option A

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The simplified expression for x+2x-8+3x+1-2x is 4x - 4.

Expression is a term used to describe a wide variety of communication methods such as verbal, nonverbal, written, and artistic. It is the way we communicate our thoughts, feelings, and ideas to others. It is an important part of our lives, from the simplest forms of communication like body language to more complex forms like written literature. Expression is a powerful tool for self-expression, communication, and connection.

The expression x+2x-8+3x+1-2x can be simplified by combining like terms.

First, the x-terms can be combined, resulting in 4x:
x + 2x + 3x - 2x = 4x

Next, the remaining constants can be combined, resulting in -4:
4x - 8 + 1 = -4

Finally, the resulting expression can be written as 4x - 4.

Therefore, the simplified expression for x+2x-8+3x+1-2x is 4x - 4.

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Answer:

the definition of adjacent mathematically means two angles if they have a common side and a common vertex.

Step-by-step explanation:

a would b adjacent to d. c would be adjacent to d.

Answer:√x

Step-by-step explanation:

I am assuming the equation says [tex]f^{-1}(x)=x^{2}[/tex]

What you do is put x instead of [tex]f^{-1}(x)[/tex] and y² instead of x²

So x = y²

Rearrange for y

y = √x

Replace y with f(x)

f(x) = √x

Answer:

3/20

Step-by-step explanation:

To find the product of 2/8 and 3/5, we simply multiply the numerators and the denominators:

(2/8) x (3/5) = (2 x 3) / (8 x 5) = 6/40

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:

6/40 = (6 ÷ 2) / (40 ÷ 2) = 3/20

Therefore, the product of 2/8 and 3/5 is 3/20.