Ashley’s math average decreased 12 points to 78. Then she completed an extra credit assignment and raised her final average by 5 points. Write an equation to show how Ashley’s average changed.

What was her starting average?
points

How much did her average increase or decrease, overall?
points

What was her final average?


points

The quotient of the two complex numbers is equal to z₁ / z₂ = (5 / 2) · [cos (- π / 3) + i sin (- π / 3)]. (Right choice: C)

In this problem we find two complex numbers, whose forms are introduced below:

z₁ = r₁ · (cos α + i sin α), z₂ = r₂ · (cos β + i · sin β)

Where α, β are angles, in radians.

Whose quotient is equal to:

z₁ / z₂ = (r₁ / r₂) · [cos (α - β) + i sin (α - β)]

If we know that r₁ = 5, r₂ = 2, α = π / 2, β = 5π / 6, then the quotient of the complex numbers is:

z₁ / z₂ = (5 / 2) · [cos (π / 2 - 5π / 6) + i sin (π / 2 - 5π / 6)]

z₁ / z₂ = (5 / 2) · [cos (- 2π / 6) + i sin (- 2π / 6)]

z₁ / z₂ = (5 / 2) · [cos (- π / 3) + i sin (- π / 3)]

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The regression equation is Y = 95.0 + 0.84X.The regression line is a mathematical model that is used to predict the value of a dependent variable (Y) based on the value of an independent variable (X).

In this case, the regression line is used to predict Y from X using the following data: X = 10, 20, 30, 40, 50, 60 and Y = 111, 109, 110, 94, 92, 93. By using a regression analysis tool such as StatKey, we can calculate the regression equation that best fits this data. The regression equation is Y = 95.0 + 0.84X, where 95.0 is the intercept and 0.84 is the slope. This equation can be used to make predictions about the value of Y for a given value of X. The rounded answer for the intercept is 95.0 and the rounded answer for the slope is 0.84.

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Step-by-step explanation:

The function is decreasing when f(x) decreases as x increases.

We can observe one section that is increasing, it is when:

So excluding this section, the decreasing sections are:

or, when x is:

The decreasing intervals of the graphed function are (-∝, -3) and (3, ∝)

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

The graphed function

From the graphed function, we can see that

Using the above as a guide, we have the following:

The decreasing intervals of the function are (-∝, -3) and (3, ∝)

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Explanation

We are given the following equations:

We are required to determine the value of x.

We can achieve this by using the elimination method as follows:

Hence, the value of x is:

The statement which best describes Gary’s error is; Gary did not use the greatest common factor in the equation.

This is the largest positive integer or polynomial that is a divisor of several different numbers. For instance, the greatest common divisor of 66, 30 and 18 is 6.

Gary's work:

66 + 36

Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

66 + 36

= 3 (22 + 12)

Gary did not use the greatest common factor in the equation.

The correct answer:

66 + 36

= 6(11 + 6)

Therefore, Gary did not use the greatest common factor in the equation.

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Answer:

144

Step-by-step explanation:

first digit of the code: only 2 and 4 are the only even numbers availible, so only 2 possibilities for the first digit.

2nd digit of code: 2,5,7,9,1 so 6 possibilities for the 2nd digit.

3rd digit of code: 2,5,7,9,1 so 6 possibilities for the 3rd digit.

4th digit of code: only 7 and 9 are greater tyhan 6 so only 2 possibilities for the 4th digit.

SO...

2 x 6 x 6 x 2 = 144

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\$3000\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 9.5\%\to \frac{9.5}{100}\dotfill &0.095\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years \end{cases}\)

\(3000=2000\left(1+\frac{0.095}{2}\right)^{2\cdot t} \implies \cfrac{3000}{2000}=1.0475^{2t}\implies \cfrac{3}{2}=1.0475^{2t} \\\\\\ \log\left( \cfrac{3}{2} \right)=\log(1.0475^{2t})\implies \log\left( \cfrac{3}{2} \right)=t\log(1.0475^{2}) \\\\\\ \cfrac{\log\left( \frac{3}{2} \right)}{\log(1.0475^{2})}=t\implies 4.37\approx t\qquad \textit{about 4 years and 4 months and a half}\)

Answer:

Step-by-step explanation:

3x  +  5  +  x  -  25  =  180

4x  -  20  =  180

4x  =  200

x  =  50

When performing a transformation to a point on the coordinate system, if the coordinates are multiplied by a constant k the resulting transformation will be a dilation.

If k > 1 → the resulting dilation is an enlargment

If k < 1 →the resulting dilation is a reduction

For the given rule

(1.5x,1.5y)

The constant is k=1.5, the resulting transformation is an enlargement.

The proportion equation is y = 4x , where y is the total cost and x is the number of packs of honey

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

when y = 16 , x = 4

when y = 32 , x = 8

So , y = kx

Divide by x on both sides of the equation , we get

k = y/x

On simplifying the equation , we get

k = 16/4 = 4

k = 32 / 8 = 4

So , the constant of proportionality k = 4

Now , the equation will be y = 4x , where 4 is the constant of proportionality

And , the table of values is

y = { 16 , 32 , 48 , 64 , 80 }

x = { 4 , 8 , 12 , 16 , 20 }

Hence , the proportion is y = 4x

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f(4)=9*4-2 =34 & g(4)= -2*4 =-8 then,

f(4)- g(4) = 34+8= 42

Answer:

Here's an interesting project idea for mathematics that can relate three different topics:

Topic 1: Fractals

Topic 2: Chaos Theory

Topic 3: Differential Equations

Research Question: Can fractals be used to model chaotic systems described by differential equations?

In this project, you can explore the concept of fractals and their applications in modeling complex systems. You can also delve into chaos theory and differential equations to understand how they are used to describe chaotic systems. By combining these three topics, you can investigate whether fractals can provide a better understanding of chaotic systems by modeling them more accurately.

Your research paper can cover the following areas:

Introduction: Provide an overview of fractals, chaos theory, and differential equations, and explain their relevance to the research question.

Fractals: Discuss the properties of fractals and how they can be used to model complex systems. Provide examples of fractals in nature and technology.

Chaos Theory: Explain the concept of chaos and how it is described by differential equations. Discuss the importance of chaos theory in understanding complex systems.

Differential Equations: Provide an overview of differential equations and their applications in physics, engineering, and other fields. Explain how differential equations are used to model chaotic systems.

Combining the three topics: Explain how fractals can be used to model chaotic systems described by differential equations. Provide examples of fractals used in modeling chaotic systems and compare the results to traditional methods.

Conclusion: Summarize the findings of your research and discuss the implications of using fractals to model chaotic systems.

Overall, this project can be a challenging and rewarding exploration of the interplay between three different mathematical topics.

Step-by-step explanation:

The amount of debt per person in the small country is approximately $2,439. This means that, on average, each person in the country would be responsible for around $2,439 of the national debt.

To calculate the amount of debt per person in the small country, we divide the total national debt by the population and round the result to the nearest whole number. Let's perform the calculation.

The population of the small country is 2.457 million, which is equivalent to 2,457,000 people. The national debt is $5.99 billion.

To find the debt per person, we divide the national debt by the population:

$5.99 billion / 2,457,000 = $2,439.05 (rounded to two decimal places)

Since we want the answer in whole numbers, we round the result to the nearest whole number:

Debt per person = $2,439 (rounded to the nearest whole number)

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9514 1404 393

Answer:

  (d)  9

Step-by-step explanation:

The relation you're supposed to apply here is ...

  an exterior angle of a triangle is equal to the sum of the remote interior angles.

__

The exterior angle is 17x+7, and it is equal to the sum of the two marked angles inside the triangle.

  17x +7 = 13x +3 +40

  4x = 36 . . . . . . . . . . . . . subtract 13x+7 from both sides

  x = 9 . . . . . . . . . divide both sides by 4

Answer:

False

Step-by-step explanation:

This is all I can think of.

Multiply two matrices and obtain the identity matrix, it can be assumed the matrices are inverses of one another. so, this statement is true.

Inverse of matrix is a matrix derived from another matrix such that if you multiply the two you get a unit matrix. Square matrices with a an inverse are called non singular matrices while those without an inverse are called singular matrices (determinant is zero). Inverses and determinant are only calculated for square matrices.

Two matrices are said to be inverse of each other.

If A B = B A = I, where I is the identity matrix.

So, the matrices are inverses of one another if the product of two square matrices is the identity matrix.

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The inequality that represents p, the number of people the theater can seat is p ≤ 25

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

A movie theater can seat a maximum of 25 people

This means that

Maximum =  25 people

In other words, the movie theatre can allow 25 or less people to attend a movie

In inequality, 25 or less means less than or equal to 25

When represented as an inequality expression, we have

≤ 25

Using the variable p, we have

p ≤ 25

Hence, the inequality is p ≤ 25

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x = 4sinФ is the correct trigonometric substitution for evaluating the integral.

Given the integral below

∫√16-x² dx

We need to determine the correct substitution for the given integral. Generally, if we have the integral ∫√a²-x² dx, the correct substitute will be a sine function that is x = a sinФ

Comparing both integral

a² = 16

a = √16

a = 4

Hence the correct trigonometric substitution for evaluating will be x = 4sinФ

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Answer:

Step-by-step explanation:

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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Answer:

3 of each gallon

Step-by-step explanation:

It worked for me on ttm

Answer:

4 of 1/3 and 1 of 1/6

Step-by-step explanation:

5/6+2/3=9/6

9/6+4/3=17/6

17/6+1/6=18/6

18/6=3

Hello!

We have the expression:

The first step is to write the number as a fraction, look:

Now, let's calculate the natural logarithm on both sides of the equation:

We can simplify it as:

Now, let's calculate it:

Alternative D. x = 1.96.

Answer:

Step-by-step explanation:

To find the new coordinate of a point after it has been scaled by a factor of 1/2, you can multiply the x- and y-coordinates of the point by 1/2.

For example, to find the new coordinate of point K', you can multiply the x-coordinate of K' (-8) by 1/2 to get the new x-coordinate, and multiply the y-coordinate of K' (8) by 1/2 to get the new y-coordinate. This gives you the new coordinate of K' as (-4,4).

You can use the same method to find the new coordinates of points L' and M'. The new coordinate of L' is (4,4) and the new coordinate of M' is (-2,4).

I hope this helps! Let me know if you have any questions.

The volcano is growing larger by 1 cm/year.

In order to determine if the volcano is growing or wearing down, determine the cm that the volcano wears down each year. To do this, we would be dividing the total cm the volcano wears down by the number of years.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.

The cm the volcano wears down each year = 20 cm / 5 = 4cm

10 / 2 = 5cm

5cm - 4cm = 1 cm

This means that the volcano is growing at 1 cm per year.

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Answer:

The machine can drill 50 holes in 25 minutes!

Explanation:  

6 by 4 is 24, which in this context will be 24 minutes. Therefore, multiply 12 by 4 to get the sum of 48. Then, to find the remaining 1 minute, divide 12 by 6 to get 2 which is the amount of holes per minute. Add 2 to 48 and that is your answer!  

Answer:

10

Step-by-step explanation:

Both angles will be equal as they are opposite angles

➝13x=130

➝x=130/13

➝x=10

Answer:

The table is 12 feet long

Step-by-step explanation:

If the table is 2 feet wide and the length is 6 times the width

we do 6(2) you get 12 which is the length

Answer:

no violet turned violet and so you would turn violet because the inside of a bluberry is more violet than it is blue

Step-by-step explanation:love yall please give me brainliest

Answer:

x = 16

Step-by-step explanation:

Opposite sides are equal in a parallelogram

AD = BC

5x - 12 = 3x + 20

5x - 3x = 20 + 12

2x = 32

x = 32/2

x = 16

Answer:

B is the answer for the question

1. It is false that when non-Standard unit used is small few unit's are

needed .

2. Objects with different shapes can have the same volume. True

3. Length, width and height and multiplied to find volume of a rectangular prism. True

4. It is false that volume is measured in square unit.

5. It is true that Volume is a measure of the amount of space inside an object.

6. The formula for volume of a rectangular prism is V = l × w × h. True

7. It is true that Standard units give a consistent and accurate measure of a container.

8. It is false that Non-Standard units cannot be used to measure volume.

9. Volume is measured in cubic units. True

Volume can be defined as the amount of space inside and object. the object can be in different form such as cone, rectangular prism, cylinder and many other shapes. Even though shapes are different, It is possible for different shapes or objects to have the same volume when measure.

Measurement of volume can be through standard measurement and non standard measurements such as a cup of rice. However, for consistency and the sake of accuracy, it is advisable to always use standard measurements of volume where possible to avoid error that may occur in non standard measurement. The acceptable and recognized unit of volume is cubic meter (\(m^3\)).

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