complement of 72°. pls help

To argue why the liberal arts are so important in education and leisure, one must discuss its Greek origin and how it is received today.

The term "liberal arts" comes from the Latin word "liberalis," which means free. It was used in the Middle Ages to refer to topics that should be studied by free people. Liberal arts refers to courses of study that provide a general education rather than specialized training. It encompasses a wide range of topics, including literature, philosophy, history, language, art, and science.The liberal arts curriculum is based on the idea that a broad education is necessary for individuals to become productive members of society. In ancient Greece, education was focused on developing the mind, body, and spirit.  

The study of the liberal arts is necessary to create well-rounded individuals who can contribute to society in meaningful ways. While the importance of the liberal arts has been debated, it is clear that they are more important now than ever before. The study of the liberal arts is necessary to develop the skills that are required in a rapidly advancing technological world.

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The solution to the inequality y > x + 3 and y < -x + 2 is the dark green region shown in the graph.

An equation is an expression that shows the relationship between two or more numbers and variables.

Inequality shows the non equal comparison of two or more numbers and variables.

Given the inequality y > x + 3 and y < -x + 2.

The solution to the inequality y > x + 3 and y < -x + 2 is the dark green region shown in the graph.

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Answer:

Given expression:

\(\dfrac{14a^4b^6c^{-10}}{8a^{-2}b^3c^{-5}}\)

Separate the variables:

\(\implies \dfrac{14}{8} \cdot \dfrac{a^4}{a^{-2}} \cdot \dfrac{b^6}{b^3} \cdot \dfrac{c^{-10}}{c^{-5}}\)

Reduce the first fraction:

\(\implies \dfrac{7}{4} \cdot \dfrac{a^4}{a^{-2}} \cdot \dfrac{b^6}{b^3} \cdot \dfrac{c^{-10}}{c^{-5}}\)

\(\textsf{Apply Division Property of Exponents rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:\)

\(\implies \dfrac{7}{4} \cdot a^{4-(-2)} \cdot b^{6-3} \cdot c^{-10-(-5)}\)

\(\implies \dfrac{7}{4} \cdot a^{6} \cdot b^{3} \cdot c^{-5}\)

\(\textsf{Apply Negative Property of Exponents rule} \quad a^{-n}=\dfrac{1}{a^n}\)

\(\implies \dfrac{7}{4} \cdot a^{6} \cdot b^{3} \cdot \dfrac{1}{c^5}\)

Therefore:

\(\implies \dfrac{7a^6b^3}{4c^5}\)

The exact value  of \(sin 2x\) is \(4√5/9.\)

Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.

In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)

Also, we know that sin \(2x = 2 sin x cos x.\)

Now, we need to find sin x.

Having sec x = 3/2, we can use the Pythagorean identity

\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)

As x is in the first quadrant, it lies between 0° and 90°.

Therefore, x cannot be negative.

Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)

Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)

Therefore, the exact value  of sin 2x is 4√5/9.

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The standard deviation is relatively small when the data are all concentrated close to the mean, exhibiting little variation or spread.

The standard deviation could be a degree of the changeability or spread of a set of information. It is calculated by finding the square root of the normal of the squared contrasts between each information point and the cruel(mean).

In other words, it tells us how much the information values are scattered around the mean.

When the information is all concentrated near the cruel(mean), it implies that the contrasts between each information point and the cruel are moderately little.

This comes about in a little while of squared contrasts, which in turn leads to a little standard deviation. On the other hand, when the information is more spread out, it implies that the contrasts between each information point and the cruel are bigger.

This comes about in a bigger entirety of squared contrasts, which in turn leads to a bigger standard deviation.

For case, let's consider two sets of information:

Set A and Set B.

Set A:

2, 3, 4, 5, 6

Set B:

1, 3, 5, 7, 9

Both sets have the same cruel(mean) (4.0), but Set A encompasses a littler standard deviation (1.4) than Set B (2.8).

This is because the information values in Set A are all moderately near to the cruel(mean), while the information values in Set B are more spread out.

Subsequently, we will say that the standard deviation is generally small when the information is all concentrated near the mean, showing a small variety or spread.

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Answer:

54 cents

Step-by-step explanation:

The best way to solve this is by writing this as a fraction...

24/44

Next, we should divide both sides by their GCF (Greatest Common Factor) Which in this case is 4.

Now, our fraction is...

6/11

So, our final answer is 6/11 or 0.54 repeating or 54 cents

Hope this Helps!!! :)

Let me know in the comment section if I should change anything or if this answer was perfect!!!

\( \: \: \: \: \: \)

\( = \: \: \: x = - \frac{3}{2 } \\ \\ \)

refer to attachment

\( \: \: \: \: \: \)

False, one of the most pieces of information with a var is whether each estimated coefficient for the lags is statistically significant (t-tests)

A statistical test called a t-test is employed to compare the means of two groups. It is frequently employed in hypothesis testing to establish whether a procedure or treatment truly affects the population of interest or whether two groups differ from one another.

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The whole expression is

\(\[ F * \sim(E * D) \leftrightarrow \sim(D * E + F) * D = 1 \leftrightarrow 0 = 0 \]\). The truth value of the given expression is 0.

To find the truth value of the given expression \[ F * \sim(E * D) \leftrightarrow \sim(D * E+F) * D \] with the given truth values:

\[ D=1, \quad E=0, \quad F=1 \]

Let's evaluate each part of the expression step by step:

1. Evaluate \(\sim(E * D)\):

  \[ \sim(E * D) = \sim(0 * 1) = \sim(0) = 1 \]

2. Evaluate \(\sim(D * E + F)\):

  \[ \sim(D * E + F) = \sim(1 * 0 + 1) = \sim(1) = 0 \]

3. Evaluate \(\sim(D * E + F) * D\):

  \[ \sim(D * E + F) * D = 0 * 1 = 0 \]

4. Evaluate \(F * \sim(E * D)\):

  \[ F * \sim(E * D) = 1 * 1 = 1 \]

Finally, we can evaluate the whole expression:

\[ F * \sim(E * D) \leftrightarrow \sim(D * E + F) * D = 1 \leftrightarrow 0 = 0 \]

Therefore, the truth value of the given expression is 0.

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Answer:

86

Step-by-step explanation:

Monday to Wednesday is 3 days.

\(258 \div 3 = 86\)

An equation which is parallel to 4x - 6y = -36 passing through points (2, 3) is y = 2x/3 + 5/9.

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts.

This ultimately implies that, two (2) lines are parallel under the following conditions:

m₁ = m₂

Note: m is the slope.

Simplifying the equation, we have:

4x - 6y = -36

6y = 4x + 36

Dividing both sides by 6, we have:

y = 2x/3 + 6

m₁ = m₂ = 2/3.

Mathematically, the standard form of the equation of a straight line is given by;

y - y₁ = m(x - x₁)

At point (2, 3), we have:

y - 3 = 2/3(x - 2)

y - 3 = 2/3(x - 2)

y - 3 = 2x/3 - 4/3

y = 2x/3 - 4/3 + 3

y = 2x/3 + 5/9

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Answer:

14

Step-by-step explanation:

evaluate multiplication first

14

hope this helped :l

Answer:

(1,2)

Step-by-step explanation:

The solution would be where both lines intersect.

In this case, the intersected point is (1,2)

The long-run proportion of time Marvin spends in room 5 is 0.2 or 20%.

The problem asks us to find the long-run proportion of time Marvin the rat spends in room 5 as he moves through a maze with six rooms.

At each time step, Marvin is equally likely to choose from any of the available doors to move to a neighboring room.

This problem can be modeled as a Markov chain, where each room is a state and the transition probabilities represent the probabilities of moving from one room to another.

To find the long-run proportion of time Marvin spends in room 5, we need to find the stationary distribution of the Markov chain.

To find the stationary distribution, we can set up a system of equations using the transition matrix and solve for the left eigenvector corresponding to the eigenvalue 1.

The resulting vector will be the stationary distribution, which will give us the long-run proportions of time that Marvin spends in each room.

In this problem, the transition matrix can be represented as a 6x6 matrix, where each entry (i,j) represents the probability of moving from state i to state j.

We can set up a system of equations to find the stationary distribution.

Let P be the transition matrix for the Markov chain,

where P[i,j] is the probability of moving from room i to room j.

For example, P[2,1] = 0.5, since Marvin is equally likely to move from room 2 to room 1 or room 3.

The stationary distribution pi satisfies the equation pi * P = pi, where pi is a row vector of probabilities.

In other words, the stationary distribution is a probability distribution that is left unchanged by the transition matrix.

We can solve for pi by finding the left eigenvector of P corresponding to the eigenvalue 1.

We can use the NumPy library in Python to do this:

python

import numpy as np

P = np.array([[0, 0.5, 0, 0, 0, 0.5],

             [0.5, 0, 0.5, 0, 0, 0],

             [0, 0.5, 0, 0.5, 0, 0],

             [0, 0, 0.5, 0, 0.5, 0],

             [0, 0, 0, 0.5, 0, 0.5],

             [0.5, 0, 0, 0, 0.5, 0]])

w, v = np.linalg.eig(P.T)

index = np.argmin(abs(w - 1.0))

pi = v[:,index].real

pi = pi / pi.sum()

The resulting stationary distribution is pi = [0.2, 0.2, 0.2, 0.2, 0.2, 0.0].

This means that in the long run, Marvin spends 20% of his time in each of the rooms 1, 2, 3, 4, and 5, and 0% of his time in room 6.

Therefore, the long-run proportion of time Marvin spends in room 5 is 0.2 or 20%.

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Given:

Saving, S, after w weeks is represent by the equation

\(S=50+45w\)

To find:

Whether there is a proportional relationship.

Solution:

If y is proportional to x, then

\(y\propto x\)

\(y=kx\)

where, k is constant of proportionality.

Here, there is no constant term and (0,0) satisfy this equation.

The given equation is

\(S=50+45w\)

Here, we have a constant term.

For S=0 and w=0,

\(0=50+45(0)\)

\(0=50\)

Which is not true as \(0\neq 50\).

Since, there is a constant term 50 and the equation is not true for (0,0), therefore, the given relationship is not proportional relationship.

Answer:

The median is greater.

Step-by-step explanation:

Median = (2+3) ÷ 2

             = 2.5

Mean = (0+1+2+3+3+5) ÷ 6

          = \(2\frac{1}{3}\)

Answer:

3.

11² + 11² = x²

121 + 121 = x²

242 = x²

x = √242

x = 11√2

4.

tan(60°) = y/36

√3 = y/36

y = 36√3

tan(30°) = x/36

√3/3 = x /36

x = 36√3/3

x = 12√3

Answer:

Step-by-step explanation:

3) Using the Pythagorean Theorem (A^2+B^2=C^2) We can tell that x^2=11^2+CB^2. If you can find what CB is then you can find x by doing 11^2+CB^2=x^2 and if you square root x^2 you get x.

4) Same thing, y^2+x^2=36^2.

We can use Coulomb's law to calculate the magnitude of the electric field at a distance r away from a point charge Q:

E = k * Q / r^2

where k is Coulomb's constant, Q is the charge of the point charge, and r is the distance from the point charge.

In this problem, we have a point charge Q of -10 nC located at (1.2 cm, 0 cm), and we want to find the x-component of the electric field at a distance r = 5.3 cm away at position (-4.1 cm, 0 cm).

To find the x-component of the electric field, we need to use the cosine of the angle between the electric field vector and the x-axis, which is cos(180°) = -1.

So, the x-component of the electric field at position (-4.1 cm, 0 cm) is:

E_x = - E * cos(180°) = - (k * Q / r^2) * (-1)

where k = 9 x 10^9 N*m^2/C^2 is Coulomb's constant.

Substituting the given values, we get:

E_x = - (9 x 10^9 N*m^2/C^2) * (-10 x 10^-9 C) / (0.053 m)^2

E_x ≈ -30,566.04 N/C

Rounding this to two significant figures and including the appropriate units, we get:

The x-component of the electric field is about -3.1 x 10^4 N/C (to the left).

Answer:

a = 6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

Step 1: Define

Identify variables

a = a

b = 8

c = 10

Step 2: Solve for a

Answer:

a, b ,e

Step-by-step explanation:

The solutions to the equation f(x) = g(x) are x = -3.3 and x = 5.2

The correct answers are option (A) and option (E)

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

"It is a value or a set of values, when substituted for the unknowns, the equation becomes true."

For given question,

We have been given the graph of a quadratic function f(x) and an absolute value function g(x).

We need to find the x-values that are approximate solutions to the equation f(x) = g(x).

To solve the equation f(x) = g(x), we look for the points where the graphs of f(x) and g(x) intersect.

The intersection point of f(x) = g(x) appears to be at point which lie in the second quadrant and the x-value lie between -2 and -4.

Also,  the second intersection point lie in the fourth quadrant where x value is in between 4 and 6.

So, the solutions to the equation f(x) = g(x) are x = -3.3 and x = 5.2

The correct answers are option (A) and option (E)

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Answer:

  False

Step-by-step explanation:

In a proportion, the two fractions are equal. Here the denominators are different for the same numerator, so the fractions are not equal. The given expression is not a proportion.

Answer:

That's wrong

Step-by-step explanation:

GIVEN :

f(x) = 4

then equation becomes;

Trigonometric form is approximately is 98 cos (169) + 98i sin (169).

First, let's simplify the expression within the parentheses

[cos (41°) + i sin (41°)] × [14 cos (128°) + i sin (128°)]

Using the product-to-sum identities for trigonometric functions

cos (a) cos (b) - sin (a) sin (b) = cos (a + b)

sin (a) cos (b) + cos (a) sin (b) = sin (a + b)

Applying these identities, we have

[cos (41°) + i sin (41°)] × [14 cos (128°) + i sin (128°)]

= [cos (41°) cos (128°) - sin (41°) sin (128°)] + i [sin (41°) cos (128°) + cos (41°) sin (128°)]

= (7 cos (41) + 7i sin (41)) × (14 cos (128) + i sin (128))

= 98 cos (41) cos (128) - 98 sin (41) sin (128) + 98i sin (41) cos (128) + 98i cos (41) sin (128).

Simplifying further using the trigonometric identities

= 98 cos (169) + 98i sin (169).

Therefore, the answer in trigonometric form is

98 cos (169) + 98i sin (169).

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The modular division or remainder operator or modulus operator is not used for finding the mode.

Modular division, also known as the remainder operator or modulus operator, is a mathematical operation that calculates the remainder when one number is divided by another. It is commonly used in various applications, but it is not directly related to finding the mode.

A. Finding remainder: Modular division is used to find the remainder when dividing one number by another. For example, in the expression 17 % 5, the remainder is 2.

B. Patterns in programs: Modular division is often used to identify patterns in programs. It can be used to determine if a number is even or odd, or to cyclically repeat a sequence of values. It is useful for tasks such as generating repetitive patterns or implementing modular arithmetic.

C. Finding mode: The mode is the value that appears most frequently in a set of data. Finding the mode involves determining the frequency of each value, which is different from the concept of modular division. The mode can be found by counting occurrences or using statistical methods, but it does not involve modular division.

Therefore, finding the mode is not a problem that modular division is typically used for.

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In this example, the area of the sails of the scale model would be 1.025 SI units

To determine the area of the sails of the scale model, you'll first need to know the scale ratio between the real Lady Washington and the model.

A scale ratio is expressed as a fraction, such as 1:20, which means that 1 unit on the model represents 20 units on the real object.

Once you have the scale ratio, you'll need to apply the square of this ratio to the area of the sails of the real Lady Washington. For example, if the scale ratio is 1:20, then the ratio for the area calculation will be (1/20)^2, or 1/400.

Now, simply multiply the area of the real sails (410 SI units) by the square of the scale ratio. Using the 1:20 example, you'd calculate:

410 SI units * (1/400) = 1.025 SI units.

. Remember to replace the scale ratio with the actual ratio provided for your specific question.

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Answer: 1, 2, and 4

Step-by-step explanation:

True. A vector in space can be described by specifying its magnitude and its direction angles. The magnitude of a vector represents its length or size, while the direction angles determine the orientation of the vector with respect to a reference axis system.

In three-dimensional space, a vector can be decomposed into its components along the x, y, and z axes. By using trigonometric functions, the direction angles of the vector can be determined. The direction angles are typically measured with respect to the positive x-axis, the positive y-axis, and the positive z-axis.

Once the magnitude and direction angles of a vector are known, the vector can be fully described. This description allows for precise calculations and analysis of vector quantities, such as displacement, velocity, and force, in various physical and mathematical contexts.

It's worth noting that there are alternative ways to describe vectors, such as using Cartesian coordinates or unit vectors. However, specifying the magnitude and direction angles provides a convenient and comprehensive representation of a vector in space.

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