What is the midpoint of the vertical line segment graphed below?
10
(2,4)
X
-10
10
(2,-9)
-10

There are 4 incongruent primitive roots and 6 has order 12 and it is a primitive root.

There are 12 elements of the group     \(U_{13}\)   , namely all the positive integers less than 13, as these are relatively prime to 13. Now, if there are primitive roots, there are     \(\phi (\phi (n))\)    of them. So we must compute     \(\phi (12) = \phi (4\times 3) = \phi (4) \phi (3) = 2\times 2 = 4\)   . There are 4 incongruent primitive roots.

To find them, take the powers each element in turn:

1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1  (2 has order 12, it is a primitive root)

Of course, the higher powers of 2 cannot be.

Proceeding this way, we get next get that 6, 7, and 11 are also primitive roots.

For example, the powers of 6 give: 6, 10, 8, 9, 2, 12, 7, 3, 5, 4, 11, 1. We see 6 has order 12 and it is a primitive root. So 2, 6, 7, 11.

Therefore, There are 4 incongruent primitive roots and 6 has order 12 and it is a primitive root.

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Answer:

\(\frac{27y^6}{8x^{12}}\)

Step-by-step explanation:

1) Use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3x^{-5+2}{y^3}}{2z^0yx}) ^3\)

2) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3\times\frac{1}{x^3} y^3}{2x^0yx} )^3\)

3) Use Rule of Zero: \(x^0=1\).

\((\frac{\frac{3y^3}{x^3} }{2\times1\times yx} )^3\)

4) use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3y^3}{2x^{3+1}y} )^3\)

5) Use Quotient Rule: \(\frac{x^a}{x^b} =x^{a-b}\).

\((\frac{3y^{3-1}x^{-4}}{2} )^3\)

6) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3y^2\times\frac{1}{x^4} }{2} )^3\)

7) Use Division Distributive Property: \((\frac{x}{y} )^a=\frac{x^a}{y^a}\).

\(\frac{(3y^2)^3}{2x^4}\)

8) Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{(3^3(y^2)^3}{(2x^4)^3}\)

9) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{(2x^4)^3}\)

10)  Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{26y^6}{(2^3)(x^4)^3}\)

11) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{8x^12}\)

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Answer:

\(\displaystyle \frac{27y^{6}}{8x^{12}}\)

Step-by-step explanation:

\(\displaystyle \biggr(\frac{3x^{-5}y^3x^2}{2z^0yx}\biggr)^3\\\\=\biggr(\frac{3x^{-5}y^2x}{2}\biggr)^3\\\\=\frac{(3x^{-5}y^2x)^3}{2^3}\\\\=\frac{3^3x^{-5*3}y^{2*3}x^3}{8}\\\\=\frac{27x^{-15}y^{6}x^3}{8}\\\\=\frac{27y^{6}x^3}{8x^{15}}\\\\=\frac{27y^{6}}{8x^{12}}\)

Notes:

1) Make sure when raising a variable with an exponent to an exponent that the exponents get multiplied

2) Variables with negative exponents in the numerator become positive and go in the denominator (like with \(x^{-15}\))

3) When raising a fraction to an exponent, it applies to BOTH the numerator and denominator

Hope this helped!

Expression that has the same addend twice, such as 3 + 3 = 6 or 8 + 8 = 16

What do you mean by One-to-One Correspondence?

the capability of relating one object to another. For each number spoken aloud, the learner should be able to count or move one object while saying "1,2,3,4". She has not learned one-to-one correspondence if she accidentally counts an object twice or skips one of the things while counting. Before starting Giggle Facts, students must be able to match one object to each number counted.

Remind your kids that a double fact is a mathematical expression that has the same addend twice, such as 3 + 3 = 6 or 8 + 8 = 16. Give children the chance to practise combining groups of the same number using manipulatives or other classroom supplies.

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Answer:

A double expression

Step-by-step explanation:

Answer:

-16r^2 - 10r

Step-by-step explanation:

all you got to do is distribute

The amount of money earned by Kiki earned $614 in three days.

The amount paid by any company or industry to the employees after deductions of the several taxes is the salary.

Given that:

Per day salary of Kiki = $150

Commission = 8% of sales

Worth of sold items = $350+$500+$1200 = $2050

Amount of commission = 0.08 x 2050 = $164

Total amount earned in three days = Base salary per day * Number of days + Commission

Total amount earned = 150*3 + 164

Total amount earned = 450 + 164 = $614

Hence, Kiki earned $614 in three days.

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Answer:

Step-by-step explanation:

There are 3 possibilities for the graph as shown in the figure.

(a) having zero intersection

(b) having one intersection point (touching point)

(c) having two intersection points.

So, the greatest possible number of intersections for these graphs is 2 as shown in figure (c).

Answer:

c

Step-by-step explanation:

Answer:

Slope intercept form is -1/7x + 7

!Hope this helps!

Step-by-step explanation:

Answer:

1.75

Step-by-step explanation:

Answer:

\( \frac{1}{2} \times x = \frac{1}{2} \times 7 \\ \\ \frac{x}{2} = \frac{7}{2} \\ \\ 2x = 2 \times 7 \\ 2x = 14 \\ \\ x = \frac{14}{2} \\ \\ x = 7\)

hope I helped you^_^

The measure of the missing angle(a) in the isosceles triangle(two sides and angle equal) is 70 degrees.

An Isosceles triangle is a triangle that has two of it sides equal to each other and two of it angles equal to each other.

The base angle of an isosceles triangle are equal. Therefore, let's find angle a in the triangle.

55 + 55 + a = 180

Recall the sum of angle in a triangle is 180 degrees.

110 + a = 180

subtract 110 from both sides

110 - 110 + a = 180 - 110

a = 70 degrees

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Answer:

About 28... I think.

Step-by-step explanation:

Based on the calculated test statistic and the degrees of freedom, you can find the p-value associated with the test statistic.

To determine if the average height of Kennesaw State University (KSU) students has changed since 2005, we can conduct a hypothesis test.

Here are the steps to perform the test:

1. Set up the null and alternative hypotheses:
  - Null hypothesis (H0): The average height of KSU students has not changed since 2005.
  - Alternative hypothesis (Ha): The average height of KSU students has changed since 2005.

2. Determine the test statistic:
  - We will use a t-test since we have a sample mean and standard deviation.

3. Calculate the test statistic:
  - Test statistic = (sample mean - population mean) / (sample standard deviation / √sample size)
  - In this case, the sample mean is 69.1 inches, the population mean (from 2005) is 68 inches, the sample standard deviation is 3.5 inches, and the sample size is 50.

4. Determine the p-value:
  - The p-value is the probability of obtaining a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

  - Using the t-distribution and the degrees of freedom (n-1), we can calculate the p-value associated with the test statistic.

5. Compare the p-value to the significance level:
  - In this case, the significance level is 0.05 (or 5%).
  - If the p-value is less than 0.05, we reject the null hypothesis and conclude that the average height of KSU students has changed since 2005. Otherwise, we fail to reject the null hypothesis.

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Step-by-step explanation:

The speed of the boat is absolute value of the velocity vector. To find the speed of the boat, take the magnitude of the velocity vector which is

\( \sqrt{ {a}^{2} + {b}^{2} } = {c}^{} \)

Where a and b is the vector

a is -4, b is 3

so

\( \sqrt{16 + 9} = \sqrt{25} = 5\)

So the speed of the boat is 5 meters per hour.

To find the direction of the vector, we need to find the angle it is traveling in.

Using trigonometry, we can do this.

\( \tan( \alpha ) = - \frac{3}{4} \)

\(arc \tan( - \frac{3}{4} ) = \alpha \)

\( \alpha = - 36.87\)

The boat is traveling at angle 36.87 degree clockwise.

An equation of the parabola whose vertex is (0, 0) and with directrix x = 2 is given by y² = -8x

Mathematically, the standard equation of the directrix lines for any parabola is given by this mathematical expression:

y = a(x - h)² + k.

Where:

Since the directrix is horizontal, the axis of symmetry would be vertical. Additionally, the distance (a) from directrix to vertex on the axis of symmetry is equal to -2.

4a = 4(-2) = -8

Therefore, the equation of this parabola would be modeled by this standard mathematical expression;

(y - k)² = 4a(x - h)

(y - 0)² = 4(-2)(x - 0)

y² = -8x

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Answer:

Step-by-step explanation:

357

987

457

hope that help

mark me brill !!

2/221 is the probability that a 2-card hand has two queens, two kings, or one of each.

Now, calculate the probability as follows:

Then, it can be either KK or QQ.

So required probability = 2king or 2 queen

Therefore, the probability that a 2-card hand (drawn from a standard deck of 52) has two queens, two kings, or one of each is 2/221.

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Answer:

2:5

Step-by-step explanation:

We know there are 2 girls so thats the first number now we have to find the total number of students which is boys + girls so 3 + 2 = 5 so it's 2:5 hope I could help :3

Answer:

2:5

Step-by-step explanation:

Because we are doing ratios of all the boys to girls at King Middle school this means there are three boys and two girls seeing that the boys to girls ratio would be 3:2 meaning that the total of all the students would be made by adding all the boys and girls making 5. we then remember there we only 2 girls meaning that there are two girls out of a total of five students at King Middle School.

To prove the equation (1 + sin(−θ))(sec θ + tan θ) = cos(−θ), the trigonometric indentities used are :  sec θ = 1/cosθ, tanθ = sin θ/cosθ, sin(−θ)=sin(θ), cos(−θ)=cos(θ), cos² θ + sin² θ=1.

To prove the equation is true follow these steps:

Hence, the given equation is true. The trigonometric identities used in the proof are: sec θ = 1/cosθ, tanθ = sin θ/cosθ, sin(−θ)=sin(θ), cos(−θ)=cos(θ), cos² θ + sin² θ=1.

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Ryan rides his bike for 30 minutes and travels a distance of 4 miles. He was traveling 8 miles per hours.

Ryan rides his bike for 30 minutes and travels a distance of 4 miles.

We have to determine how fast he was traveling.

Time = 30 minutes

First we convert the minutes in hours.

As we know that;

1 hour = 60 minutes.

So 1 minute = 1/60 hours

30 minutes = 30/60 hours

30 minutes = 1/2 hours

Distance = 4 miles

The formula of speed is;

Speed = Distance/Time

Speed = 4/(1/2) miles per hours

Speed = 4 × 2 miles per hours

Speed = 8 miles per hours

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Sebastian, this is the solution to the first problem you uploaded:

Let's recall that the interior angles of a triangle add up to 180 degrees.

Then if E =

The book "Problem Solving with C (Text Only) Edition: 10th" by Savitch Pearson, with ISBN 9780134448282, is available as a free PDF.

Explanation:

The book "Problem Solving with C" is a valuable resource for individuals looking to learn or improve their programming skills in the C language. Written by Savitch Pearson, the 10th edition focuses on teaching problem-solving techniques using C programming.

This edition of the book provides a comprehensive introduction to C programming, covering fundamental concepts, data types, control structures, functions, arrays, and more. It emphasizes the development of problem-solving skills through practical examples and exercises, allowing readers to apply their knowledge in real-world scenarios.

The availability of a free PDF version of the book offers a convenient and accessible option for those who wish to learn or reference the material without the need to purchase a physical copy. It provides flexibility for self-study, as readers can access the book digitally from various devices.

By studying "Problem Solving with C," readers can gain a solid foundation in C programming, enhance their problem-solving abilities, and prepare themselves for further exploration in the field of computer science.

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Dyscalculia is a learning disorder that affects a person’s ability to do the math.

A learning problem called dyscalculia diminishes a person's capacity for math. Similar to how dyslexia impairs reading-related brain regions, dyscalculia interferes with the knowledge and skills connected to math and numbers. Although dyscalculia often first manifests in childhood, it can even affect adults who are unaware of it.

The signs of this condition typically emerge in childhood, particularly as kids start to master the fundamentals of math. However, many adults who suffer from dyscalculia are unaware of it. When forced to do the math, people with dyscalculia frequently experience mental health problems like anxiety, depression, and other distressing emotions.

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1993.5232 ml chocolate milk will the container hold if it is filled to the top.

volume is the amount of space in a certain 3D object

Given:

h= 15.5 cm, d= 12.8 cm , r= 6.4 cm

Volume of cylinder,

=πr²h

=3.14*6.4*6.4*15.5

=1993.5232 cm³

=1993.5232 ml

Hence, 1993.5232 ml chocolate milk will the container hold if it is filled to the top.

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Answer:

y = 5/2x - 5

Step-by-step explanation:

Step 1: Write equation

5x - 2y = 10

Step 2: Solve for x

Answer:

y = (5/2)x - 5

Step-by-step explanation:

5x-2y = 10

Subtract 5x from both sides

-2y = 10 - 5x

Rearrange

-2y = -5x + 10

divide both sides by -2 to isolate y

y = (5x/2) + (10/-2)

y = (5/2)x - 5

Answer:

-8

Step-by-step explanation:

The correct answer is C. -1 ≤ r ≤ 1. The correlation coefficient, r, is a measure of the strength and direction of a linear relationship between two variables. It can take on any value between -1 and 1, inclusive.

A correlation coefficient of -1 indicates a perfect negative correlation, where as one variable increases, the other variable decreases in a perfectly linear fashion. A correlation coefficient of 0 indicates no linear relationship between the two variables. A correlation coefficient of 1 indicates a perfect positive correlation, where as one variable increases, the other variable increases in a perfectly linear fashion.

Therefore, statement A is not correct as it only includes the positive values of r. Statement B is not correct as it does not include negative values of r. Statement C is correct as it includes all possible values of r.

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Answer:

It's B

Step-by-step explanation:

Given that we have the graph of f(x), we want to see which one is the graph of its inverse. i just had that question and i got a 100 on it

As per the addition formula, the value of the trigonometric function is -0.809.

In statistics, function is defined as a relationship between inputs where each input is related to exactly one output.

Here we have to find the value of the trigonometric function cos(13/15)cos(-/5)-sin(13/15)sin(-/5)  by using the addition and subtraction formula.

Here we have the following trigonometric function:

=> cos(13/15)cos(-/5)-sin(13/15)sin(-/5)

Now, we have to use the trigonometric addition formula,

=> Cos (A+B) = Cos A Cos B - Sin A Sin B

To solve the given function,

Here let us rewrite the given function based on the addition formula, then we get,

=> Cos ( 13π/15 + (-π/5) )

=> Cos( 12π/5)

=> Cos(144°)

=> -0.809

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To prove the SSS Inequality Theorem using an indirect proof, we need to assume the opposite of what we are trying to prove and show that it leads to a contradiction.

The SSS Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Assume that there exists a triangle ABC where the sum of the lengths of two sides is not greater than the length of the third side. Without loss of generality, let's assume that AB + BC ≤ AC.

Now, consider constructing a triangle ABC where AB + BC = AC. This would mean that the triangle is degenerate, where points A, B, and C are collinear.

In a degenerate triangle, the sum of the lengths of any two sides is equal to the length of the third side. However, this contradicts the definition of a triangle, which states that a triangle must have three non-collinear points.

Therefore, our assumption that AB + BC ≤ AC leads to a contradiction. Hence, the SSS Inequality Theorem holds true, and for any triangle, the sum of the lengths of any two sides is greater than the length of the third side.

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This problem involves a variety of concepts in quantum mechanics, including energy eigenstates, linear combinations, time evolution, inner products, probabilities, and normalization.

In this problem, we are given two orthonormal energy eigenstates of a system, and we are asked to compute various quantities related to their linear combinations.

We are also asked to find the wavefunction at a later time if the initial state is one of these linear combinations, and to calculate the probabilities of measuring the particle in each of the two states at a later time. Lastly, we are asked to find the normalization constant of a given wavefunction.

To start with, we compute the inner products of the states (A) and (B) with themselves and with each other, and obtain the probabilities of measuring the particle in each of the states.

We then use the time evolution operator to find the wavefunction at a later time t, given the initial state at t=0. Finally, we calculate the probabilities of measuring the particle in each of the two states at a later time t, and sketch the probabilities as a function of time on the same graph. We also find the normalization constant of a given wavefunction by integrating over all space.

By working through this problem, we can gain a deeper understanding of these concepts and their applications in quantum mechanics.

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