what is the average rate of change

Answer:

Step-by-step explanation:

Although the answer is correct, the Step 3 is not correct.

$23.76 is the value of XYZ stock when the required return is 12 percent.

percentage, a relative value indicating hundredth parts of any quantity.

Let the price per share be P

growth rate, g = 8% = 0.08

D = Next years dividend = $0.88 × 1.08 = $0.9504

Required rate of return r = 12% = 0.12

P=D/r-g

P=0.9504/0.12-0.08

P=$23.76

Hence,$23.76 is the value of XYZ stock when the required return is 12 percent.

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Share of the each person is 1/12. And the above situation can be represented in the given picture.

Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire.

When we cut a piece of cake from the entire thing in real life, that could be the best example for Fractions.

To represent a fraction in a diagram we choose a closed polygon like a circle, square, etc.

First, divide the polygon into the number of parts as given in the denominator and shade the number of taken parts that are given in the numerator.

Here we have

6 people equally share 1/2 a pan of macaroni and cheese  

As we know 1/2 means half

By the given data, Half of the macaroni and cheese is shared by 6 people which means Half of the pan of macaroni and cheese again divided into 6 parts

=> (1/2) ÷ 6 =  [tex]\frac{ \frac{1}{2} }{6}[/tex]  = [tex]\frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex]  

Therefore,

Share of the each person is 1/12. And the above situation can be represented in the given picture.

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The missing numbers are 3 hours = 180 minutes 24 hours = 1 day

24 months = 2 years

What are numbers ?

A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them.

An arithmetic value used to indicate amount is called a number. A number is a mathematical concept that is used for counting, measuring, and labeling. Thus, mathematics is built on numbers. For instance, this is a single butterfly, and these are four.

1. 5 × x = 45

   45 / 5 = x

    x = 9

45 ÷ 5 = 9

2. 200 + 600 = 800

300 + 400 = 700

3. 3 hours = 180 minutes

     3 * 60 minutes

24 hours = 1 day

24 months = 2 years

12 * 2 = 24

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Answer:

                  1

log₂√2 = ------

                  2

Step-by-step explanation:

I'm assuming the equation looks like this:

2¹⁽² = √2

                  1

log₂√2 = ------

                  2

I hope this helps!

Answer:

C.

Step-by-step explanation:

For the first letter there are 26 choices, then, since one has been used, for the second letter there are only 25 choices left. And so on. You multiply them to get the total number of combinations.

For the digits, the initial choice is from 10 digits (0..9), which invalidates answer B.

Step-by-step explanation:

[tex](8 - 12) \times (8 \times 4) + {7}^{2} \\ [/tex]

[tex]( - 4) \times (32) + 49[/tex]

[tex] -12 8 + 49 =79 [/tex]

The value of (5x2−14x+24)÷(x−4)  is 5x + 6

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given ,

5x2 - 14x - 24

         x - 4    

  5x2 multiplied by 14x, then 24.

The first term is 5x2, and 5 is its coefficient.

The coefficient of the middle term, which is -14x, is -14.

"The constant," the final term, is -24.

Step 1: Multiply the first term's coefficient by the constant 5 • -24 to get a result of -120.

Find two factors of -120 whose combined value is equivalent to the middle term's coefficient, which is -14, in step two.

    -120    +    1    =   -119  

    -60    +    2    =    -58  

    -40    +    3    =    -37  

    -30    +    4    =    -26  

    -24    +    5    =    -19  

    -20    +    6    =    -14    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -20  and  6  

                   5x2 - 20x + 6x - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

                  5x • (x-4)

            Add up the last 2 terms, pulling out common factors :

                  6 • (x-4)

Step-5 : Add up the four terms of step 4 :

                 (5x+6)  •  (x-4)

Therefore  The value of (5x2−14x+24)÷(x−4)  is 5x + 6

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Simplified term is 5x + 6. Simplification is the process of reducing an expression/fraction/problem to a simpler form.

A mathematical expression is simplified when it is replaced with a simpler, typically shorter, equivalent statement.

Mathematical expressions are made up of different numbers and operations. To simplify them, we must first understand the rule known as the order of operations. It specifies the order in which operations must be performed when simplifying a mathematical expression.

Factoring  5x2 - 14x - 24

The first term is,  5x2  its coefficient is  5 .

The middle term is,  -14x  its coefficient is  -14 .

The last term, "the constant", is  -24

Multiply the coefficient of the first term by the constant   5 • -24 = -120

Find two factors of  -120  whose sum equals the coefficient of the middle term, which is   -14 .

-120    +   1   =   -119

-60    +   2  =   -58

-40    +   3  =   -37

-30    +   4  =   -26

-24    +   5  =   -19

-20    +   6  =  -14  

Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -20  and  6

5x2 - 20x + 6x - 24

Add up the first 2 terms, pulling out like factors :

                   5x • (x-4)

Add up the last 2 terms, pulling out common factors :

                   6 • (x-4)

Add up the four terms of step 4 :

                   (5x+6)  •  (x-4)

Which is the desired factorization

Cancel out  (x-4)  which appears on both sides of the fraction line.

 5x + 6

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The value of x = 3.8 cm and y = 3.44 cm

What are some examples of consistency?

If two numbers can be placed exactly over one another, they are said to be "congruent." When placed one on top of the other, the two bread slices are the same size and form. Things that are precisely the same size and shape are said to be congruent.

What are the five different types of congruence?
Two triangles are congruent if they satisfy all five conditions for congruence. Right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS) are the four terms (RHS).

This can be solve by congruence

these two triangle can be congruent by AAS

so x = 3.8 com

in this triangle we have all angle 60 degree

so this is an equivalent triangle

hence down side = 3.8 cm

hence y = (3.8)^2-(1.6)^2 = 14.44 - 2.56 = √11.88 = 3.44

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The percentage of the council members who voted in favor of the tax is 50%.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, the council has 76 members out of which 38 members voted in favor of the tax.

The percentage amount of members who favor the tax is:
(38/76) × 100%

= 50%

Hence, the percentage of the council members who voted in favor of the tax is 50%.

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The equivalent expression is (x + 2√3i) (x - 2√3i).

What is a Polynomial Equation?

The equations formed with variables, exponents and coefficients are called as polynomial equations. It can have different exponents, where the higher one is called the degree of the equation.

Given polynomial is,

x² + 12

We need to find it's equivalent expression for that see the options

Solve the option (a)

(x + 2√3i) (x - 2√3i)

Now, solve this if we get equal to x² + 12 that means that option is answer

x(x - 2√3i) + 2√3i(x - 2√3i)

x² - 2xi√3 + 2xi√3 -  2√3i *  2√3i

x²  -  12 i²

we know, i² = -1

so, we get

x² + 12

We get the answer by 1st option. If you solve other options you'll get different answer.

Hence, the equivalent expression is (x + 2√3i) (x - 2√3i).

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Time taken by the bicyclist is 8 hours.

Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

Given slope = 35 / 2 = 17.5

Distance = 140 miles.

then time is calculated by 140 /17.5

 = 8 hours

The slope expresses how quickly the dependent variable changes when the independent variable changes. The Greek capital letter D or D is frequently used by mathematicians and economics to represent change. Slope contrasts the change in the vertical axis, y, with the change in the horizontal axis, x.

As x grows, there are 4 different sorts of slopes: negative, positive, zero, and undefined. The "average rate of change" can also be thought of as the slope of a line.

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For the third part of the batch, 1 :1/2 gallon of yellow is needed and for the second batch part 1/4 gallon is needed.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

Since we know that there should be the same amount of yellow and green (they are each 1/4 of the recipe) and there is a half a gallon of green there should same amount the yellow. Hence, the answer is 1/2 gallon.

For the second part of the question, we know that 2 gallons is 1/4 of the recipe, and we know that 1/4 * 2= 1/2 (2/4) we just have to multiply 2 by 2 and get 4, our answer.

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Answer:

third part of the batch 1 :1/2 gallon of yellow Second batch part 1: 4

Step-by-step explanation:

have a nice day.

By using trigonometry, it can be calculated that

Value of x is [tex]\frac{2\pi}{3}[/tex]

What is Trigonometry?

Trigonometry shows the relationship between sides and angles of a right angled triangle.

There are six trigonometrical functions. They are

[tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]

Trigonometry is a very important tool in mathematics.

Trigonometry has a very good application in heights and distance.

Trigonometry has also a very good application in calculus and differential equation and also in physics, trigonometry plays a very vital role

Here,

The trigonometric equation is

4cos x + 2 = 0 where 0 ≤ x ≤ π

4cos x = -2

cos x = [tex]-\frac{2}{4}[/tex]

cos x = [tex]-\frac{1}{2}[/tex]

cos x = cos [tex]\frac{2\pi}{3}[/tex]

x = [tex]\frac{2\pi}{3}[/tex]

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2/ ( 1 + x) ( 1 - x) is express  into partial fractions.

With an example, what is a partial fraction?

The division of an algebraic fraction into smaller, "partial fractions," components is possible. Think about the algebraic fraction (3x+5) (2x2-5x-3). This formula can be broken down into its simplest form, [2/(x - 3)] - [1/(2x + 1)]. Partial fractions are the more straightforward pieces [2/(x - 3)] and [1/(2x + 1)].

                        The four categories of partial fractions are linear factors, degree 2 irreducible factors, repeated linear factors, and repeated irreducible degree 2 factors.

= 2/(1-(x^2))

= 2 / (1)² - (X)²

=  2/ ( 1 + x) ( 1 - x)

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The decision for rejecting the null hypothesis is μ = 8.4

In statistics the term hypothesis refers a tentative statement about the relationship between two or more variables.

Here we have given that engineer designed a valve that will regulate water pressure on an automobile engine and he is designed the valve such that it would produce a mean pressure of 8.0 pounds/square inch. Then it is believed that the valve performs above the specifications. Where the valve was tested on 24 engines and the mean pressure was 8.4 pounds/square inch with a standard deviation of 1.0 Here the level of significance of 0.05 will be used.

Here we have to determine the decision for rejecting the null hypothesis.

While we looking into the the given question we have identified the following values,

Standard deviation = 1.0

Mean pressure = 8.4 pounds/square

Level of significance = 0.05

Sample size = 24

According to these values the null and alternative hypothesis is written as,

H0 = μ = 8.4

Hx = μ ≠ 8.4

Therefore, H0 = μ = 8.4 is the decision for this one.

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Answer:

x = 222:2 and x = 2

Step-by-step explanation:

(2x-123):3=33

(2x – 123):3 = 33

2x – 123 = 33.3

2x – 123 = 99

2x = 99 + 123

2x = 222

x = 222:2

x = 111

200-8.(2x+7)=112

200 – 8.(2x + 7) = 112

-8.(2x + 7) = 112 – 200

-8.(2x + 7) = -88

2x + 7 = (-88):(-8)

2x + 7 = 11

2x = 11 – 7

2x = 4

x = 4:2

   x = 2

I hope my answer helps you.

The required value of the unknowns in the given sum of the matrix are w = -5, z = 15, and y = 1.

Given,
To determine the value of the unknowns in the matrix,

A matrix is a collection of numbers that are arranged in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics.

Here,
[tex]2\left[\begin{array}{ccc}w&2\\5&z\end{array}\right] +3\left[\begin{array}{ccc}2&x\\-2&-6\end{array}\right] = 4\left[\begin{array}{ccc}4&7\\y&3\end{array}\right][/tex]
From the above matrix,
Equation formed,
2w + 6 = 16,
w = 5,

2z -18 = 12
z = 15

10 - 6 = 4y
y = 1

Thus,  the required value of the unknowns in the given sum of the matrix are w = -5, z = 15, and y = 1.

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Answer:

q. point of intersection

Step-by-step explanation:

Both systems in two variables contains two lines that may be intersecting, parallel, or the same line.

The pressure of 28 inches of mercury occurs at 6.03 miles from the eyes of the hurricane

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

f(x) = 0.48 ln(x + 2) + 27

Also from the question, we have

Pressure = 28 inches

This means that

f(x) = 28

So, we have the following equation

0.48 ln(x + 2) + 27 = 28

Subtract 27 from both sides

0.48 ln(x + 2) = 1

Divide 0.48 from both sides

ln(x + 2) = 2.083

Take the exponent of both sides

x + 2 = 8.03

So, we have

x = 6.03

Hence, the distance is 6.03 miles

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Answer:

John = 14 ; Van = 26

Step-by-step explanation:

V = 12 + J

V - 2 = 2(J-2)

12 + J - 2 = 2J - 4

J + 10 = 2J - 4

2J - J = 10 + 4

J = 14

V = 12 + 14

V = 26

The following excel commands would give you the critical value is T.INV(0.95,25)

What is excel commands?

The following describe the commands in Excel: They carry out tasks the same way users do. They can change Excel settings, open, close, and edit documents, start recalculations, and other actions that users may perform (within the bounds of the interface being utilized). Excel's command menu interface is called the Ribbon. It logically and visually groups together frequently used actions. These make up the Ribbon's principal components. Related groupings of commands are grouped together by tabs.

Population sd is not available so we have to use t test.

0.95 is for upper bound and 25 is df of t test.

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The minimum number of dogs that have a mass of more than 24kg is 6 and the maximum number of dogs that could have a mass of more than 24kg is 18  

Using fundamental algebraic principles, rearrange the function to get the value of x at the derivative value of 0. The maximum or minimum will be at the vertex of the function, which is indicated by the response's x-coordinate. Rewrite the answer into the original function to determine the minimum or maximum.    

Here we have

The given shows the masses of various dogs  

Mass (x) kg          frequency  

0 ≤ x < 10                    2

10 ≤ x < 20                  7

20 ≤ x < 30                12

30 ≤ x < 40                 6      

a) The minimum number of dogs that have a mass of more than 24kg.

If we observe the given table the mass of 24 kg will lie in class intervals 20 ≤ x < 30, 30 ≤ x < 40                      

In class interval 20 ≤ x < 30, mass ranges from 20 kg to 30 kg there is a possibility that the mass of dag will be less than 24 since it started from 20 kg,  

In class interval 30 ≤ x < 40, mass ranges from 30 kg to 40 here there is no possibility that the mass will be less than 24 kg.

So here we can take the frequency of class interval 30 ≤ x < 40 as the Minimum value or number of dogs that could have a mass of more than 24 kg

Therefore,

The minimum number of dogs that have a mass of more than 24kg is 6

b) The maximum number of dogs that have a mass of more than 24kg.

In the above case since we are calculating minimum value, we didn't consider class interval 20 ≤ x < 30.

In this case, to get the maximum value or a maximum number of dogs we will consider class interval 20 ≤ x < 30 as there is a possibility that the mass could be more than 24 kg

In class interval 30 ≤ x < 40 the mass will always be more than 24 kg.

Thus, the Maximum number of dogs with more than 24 kg = 12 + 6 = 18

Therefore,

The maximum number of dogs that could have a mass of more than 24kg is 18  

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Answer:

c. |11|

Step-by-step explanation:

When it comes to absolute value, we're talking about the distance from 0. Even though 11 is greater than -19 and -34, the distance from 11 and 0 is smaller than the distance from -19 and 0 and the distance from -34 and 0.

|11-0|=11

|0-19|=19-0=19

|0-34|=34-0=34

a) The mean of this distribution is of: 0.35.

b) The standard error of this distribution is of: 0.0382.

The sampling distribution of p is defined according to the Central Limit Theorem, which states that the sampling distribution of a proportion p in a sample of size n has mean and standard deviation defined as follows:

(the standard deviation can also be called standard error).

The sample size and the proportion for this problem are given as follows:

n = 156, p = 0.35.

Then the standard error for this distribution is calculated as follows:

s = square root(0.35 x 0.65/156) = 0.0382.

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It will take Omari 7 months to pay off the computer.

What is a percentage?

Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) besides the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.

To find the amount of the down payment, multiply the price of the computer by the down payment percentage:

down payment = $1,099 * 20% = $219.80

The remaining balance on the computer after the down payment is:

remaining balance = $1,099 - $219.80 = $879.20

To find the total number of months it will take Omari to pay off the computer, divide the remaining balance by the monthly payment:

total months = $879.20 / $144/month = 6.1 months

Since it is not possible to have a fraction of a month.

Hence, it will take Omari 7 months to pay off the computer.

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Answer:

C(-6, -3)

Step-by-step explanation:

In a square, all four sides have the same length and all four angles have the same measure (90 degrees). Therefore, the line segments connecting the vertices of a square are all perpendicular to each other and all have the same length.

Since the line segment AB has a length of 8 (the difference in the y-coordinates is 8) and a horizontal component (the difference in the x-coordinates is 0), the line segment CD must also have a length of 8 and a horizontal component of 0. This means that the x-coordinate of point C is the same as the x-coordinate of point A, which is 2.

The line segment CD also has a vertical component equal to the difference in the y-coordinates of points D and A, which is 5 - (-3) = 8. Therefore, the y-coordinate of point C is the same as the y-coordinate of point D minus 8, or -3.

Therefore, the coordinates of point C are (-6, -3).

The polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.x= -2, x=7 ,will be P(x)=x²-5x+14

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

It is given that the zeroes of the polynomial are, x= -2, x=7

The polynomial expression is obtained as,

=(x+2)(x-7)

=x²-7x+2x+14

=x²-5x+14

Thus, the polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.x= -2, x=7 ,will be P(x)=x²-5x+14.

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