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Augustus used a total of 12 gallons + 1.8 gallons = 12+1.8=13.8 gallons of chocolate syrup in the three mixtures.

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%.

Since Augustus used 10% chocolate syrup and 90% milk for the first mixture and 30% chocolate syrup and 70% milk for the second mixture, the total percentage of chocolate syrup he used in the first two mixtures is 10% + 30% = 40%.

Since Augustus made a total of 30 gallons of chocolate milk, he used 30 gallons * 40% =3040.01=12 gallons of chocolate syrup in the first two mixtures.

For the final mixture, Augustus used 15% chocolate syrup and 85% milk. The total percentage of chocolate syrup he used for the final mixture is 15%.

Since Augustus used a total of 12 gallons of chocolate syrup in the first two mixtures, he used an additional 12 gallons * 15% = 1215.01=11.8 gallons of chocolate syrup for the final mixture.

Hence, Augustus used a total of 12 gallons + 1.8 gallons = 12+1.8=13.8 gallons of chocolate syrup in the three mixtures.

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Answer:

Step-by-step explanation:

I hope this letter finds you in good health dear. I am doing well here.

It is been a long time since I haven’t written a letter to you, I finally got some time. I was actually occupied with some practical submissions. I am anyway going to start with the preparation for my exams. They are beginning from next week onward. What about yours?

This time I will be making my own notes by going through each and every topic so that I don’t miss out on topics. If you want I will share my notes with you. I am also going to refer to some extra books for easier explanations. My teacher gave me this idea. This will help me remember the basics in my own words and will help me understand each and every concept well.

Do write me back. I miss our long chats and I wish to hear from you.

Answer: Because the first washing machine is cheaper

Step-by-step explanation:

Find the first washing machine price by taking 550 times 0.7 = $385

The second machine is first down by 20%, so take 550 times 0.8 =$440

Then 10% off, so take 440 times 0.9 = $396

So the first washing machine is cheaper than the second one $11

Answer:

B

Step-by-step explanation:

h = 6.2w + 4.5

using forth week

h = 6.2(4) + 4.5

h = 24.8 + 4.5

h = 29.3

gives a close value

Answer:

The two expressions are equivalent, based on a direct numerical comparison (a) and (b) a methematical comparison.

Step-by-step explanation:

a)  The expressions can be shown to be equivalent by entering the numbers into each expression and comparing the results.  This is easy with a spreadsheet program.  Set up a table with the values of x in the left column.  Then enter the 2 equations in the first entry (-2) in each of two subsequent columns.  These expressions can be copied to the other rows by clicking on the first cell and dragging the lower right corner down until all rows are included.  The copied expressions will select the corresponding value of x for both expressions, as shown in the attached table.  It can be seen that both expressions yield the same results.

b)  Prove the equivalence mathematically:

In other words, do the two expressions equal each other?

(12x^2 - 27)/3  = -(-2x+3)(2x+3)   ??

Simplify both sides

(4x^2 - 9)           =   -(-4x^2 + 9)       ?

4x^2 - 9             =   4x^2 - 9            Yes.  They are equivalent

Answer: If two lines are parallel, it means that they have the same slope. Therefore, to find the value of x in this problem, you need to find the slope of line m and line n, and then set them equal to each other.

The slope of a line can be found using the formula:

slope = (y2 - y1)/(x2 - x1)

In this case, you are given the equation of line m in the form "x + 1", and the equation of line n in the form "7x - 5". To find the slope of each line, you can rewrite these equations in the form y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).

For line m, we have:

y = x + 1

The slope of this line is m = 1.

For line n, we have:

y = 7x - 5

The slope of this line is m = 7.

Since line m and line n are parallel, their slopes must be equal. Therefore, we can set these slopes equal to each other and solve for x:

1 = 7

This equation has no solution, which means that there is no value of x that will make these two lines parallel. Therefore, the answer is that there is no solution.

Answer:

[tex]2ab(b+4a)[/tex]

Step-by-step explanation:

Given expression:

[tex]2ab^2+8a^2b[/tex]

Rewrite b² as b · b:

[tex]\implies 2abb+8a^2b[/tex]

Rewrite a² as a · a:

[tex]\implies 2abb+8aab[/tex]

Rewrite 8 as 2 · 4:

[tex]\implies 2abb+2 \cdot 4aab[/tex]

Rearrange:

[tex]\implies 2abb+2ab4a[/tex]

Factor out the common term 2ab:

[tex]\implies 2ab(b+4a)[/tex]

Answer: 5x-3=3x+9=4y+20

2x+6+20=180

answer is 74

Step-by-step explanation:

Anna can only fill the measuring cup a whole number of times, she will need to fill it 6 times to measure 78 cups of turnips.

What is division in mathematics?

Division is the process of splitting a number or an amount into equal parts.

To find the number of times Anna will need to fill the measuring cup, divide the number of cups of turnips by the size of the measuring cup:

78 cups/14 cups:

                            = 78/14

                              =5.57 measures

Hence, Anna can only fill the measuring cup a whole number of times, she will need to fill it 6 times to measure 78 cups of turnips.

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Answer:

x = 2, y = 3

Step-by-step explanation:

Solve the following system:

{-2 y + 3 x = 0 | (equation 1)

{-2 y + x = -4 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:

{3 x - 2 y = 0 | (equation 1)

{0 x - (4 y)/3 = -4 | (equation 2)

Multiply equation 2 by -3/4:

{3 x - 2 y = 0 | (equation 1)

{0 x + y = 3 | (equation 2)

Add 2 × (equation 2) to equation 1:

{3 x + 0 y = 6 | (equation 1)

{0 x + y = 3 | (equation 2)

Divide equation 1 by 3:

{x + 0 y = 2 | (equation 1)

0 x + y = 3 | (equation 2)

Collect results:

Answer: {x = 2, y = 3

Answer:

2x=4 x=2

Step-by-step explanation:

3x-x=2x

-2y-(-2y)=0

0-(-4)=4

2x=4

x=2

If x=2,3(2)-2y=0

On solving the provided question, we got that - y = 4, when x=2 and the hypotenuse of the resulting right triangle is 5.

[tex]AC^2 = AB^2 + BC^2[/tex] is the formula for the Pythagorean theorem, where AB is the perpendicular, BC is the base, and AC is the hypotenuse. All triangles with 90° angles are governed by the Pythagorean equation.

The hypotenuse formula can be used to define the relationship between the sides of a right triangle, making it a specific kind -

[tex]c^2 = a^2 + b^2\\or\\c^2 = x^2 + y^2[/tex]

where,

The triangle's hypotenuse, or c, is the side that faces away from the 90-degree angle.

while the sides closest to the 90° angle are denoted by a and b.

Given that the hypotenuse is 5 = c and one of the sides has a measure of 2 = x in the issue statement, we can calculate for y as follows:

[tex]y^2 = c^2 - x^2\\y^2 = 5^2 - 2^2\\y^2 = 21\\y = 4.58[/tex]

The number before the decimal is known as the natural number. As a result, the response is:

y = 4

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The address of element 0 is T₂₁ in the given matrix.

What are Matrices?

Matrices, the plural form of a matrix, are the arrangements of numbers, variables, symbols, or expressions in a rectangular table that contains various numbers of rows and columns. They are rectangular-shaped arrays, for which different operations like addition, multiplication, and transposition are defined. The numbers or entries in the matrix are known as its elements. Horizontal entries of matrices are called rows and vertical entries are known as columns.

We have given,

the matrix:

[tex]T = \left[\begin{array}{cc}4&2\\5&0\\11&-1\\8&3\end{array}\right][/tex]

To find the denotation of the element 0,

so,

A matrix is the arrangement of numbers in rows and columns in order to form an array.

The horizontal arrangement is called a row and the vertical arrangement is called a column.

If the matrix is denoted as  [tex][T]_{m \times n}[/tex] it means that the matrix T has m rows and n columns and the order of the matrix is m × n.

Each number in the matrix is called an element and the position of the element is represented as [tex]a_{mn}[/tex].

Representation of the standard matrix is:

[tex]A = \left[\begin{array}{ccc}a_{11}&a_{12}&........ a_{1n}\\a_{21}&a_{22}&........a_{2n}\\\\a_{m1}&a_{m2} &........a_{mn}\end{array}\right]_{m \times n}[/tex]

from the above information, we can say that the address of element 0 is

T₂₁.

Hence, the address of element 0 is T₂₁ in the given matrix.

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Answer: perpendicular bisector

Step-by-step explanation: Hope you see it helpful!

Answer:

22.31 minutes

Step-by-step explanation:

First simplify the numbers to decimals to make it easy : 2 1/3 = 2.30( estimated) ,  11 2/3 = 11.67 ( estimated ), and 4 2/5 = 4.4

The we divide how many miles by the total amount of minutes to get 5.07( estimated )

We then multiply it by 4.4 to get 22.308 to be exact.

So it will take him 22.31 minutes

P.S : Correct me if I am wrong. Apologizes.

By using the concept of function, it can be seen that the given graph represents a function.

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here the values on the  x axis represents the domain and the values on the y axis represents the Range.

From the graph it can be seen that

Every point of the domain maps to unique point on the range.

So this is a function

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Answer:

Bar chart; because job classification is categorical.

Step-by-step explanation:

Categorical data:  Data that can be divided into groups (categories).

Numerical data:  Data that is in the form of numbers (also called "quantitative data").

Therefore, "job classification" is categorical data since the classifications such as employee, manager, senior manager, etc. are categories rather than numbers.

Box plots are used to show distributions of numerical data values.

Bar charts are used to show a comparison of values across different categories of data.

Therefore, a bar chart should be used to represent the data as the data is categorical.

Answer:

Step-by-step explanation: Bar chart; because job classification is categorical.

The probability that the randomly selected numbers are divisible by 3 is 3/10.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

So, the probability that the randomly selected number is divisible by 3:

Numbers under 20 divisible by 3 are: 3, 6, 9, 12, 15, 18

Total numbers: 20

Probability formula: P(E) = Favourable events/Total events

Now, substitute values and calculate as follows:

P(E) = 6/20

P(E) = 3/10

Therefore, the probability that the randomly selected numbers are divisible by 3 is 3/10.

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Answer:

Step-by-step explanation:

Answer: CLICK TO VIEW

16x^3+5x?

Step-by-step explanation:

Functions can be represented as equations, and equations can be represented as functions.

The number of people that started the rumor is 10

The function is represented as:

To calculate the number of people that started the rumor, we simply set t to 0.

So, we have:

Evaluate the exponent of e

Express e^0 as 1

Multiply 39 and 1

Add 1 and 39

Divide 400 by 40

When t = 0, N(t) = 10

This means that 10 people started the rumor.

Hence, the number of people that started the rumor is 10

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The power of three halves is equal to 3.

What is power?
Power is the ability to influence or control the behaviour of others, and to make decisions that affect the outcome of any given situation. It is a form of force that can be both positive and negative, and can be used in various ways. Power can come from a variety of sources, such as money, status, knowledge, physical strength, and social standing. It is a form of authority that can be used to motivate and inspire others, or to manipulate and coerce them. Power is an important part of many social and political systems, and is essential for effective leadership. It is an essential tool for achieving desired outcomes and can be used for good or for ill. Ultimately, power is a form of influence, and its use depends on the individual wielding it.

In general, if a is a positive real number and n is a positive integer, then a^(n/2) is equal to the square root of a^n. This can be written as:
a^(n/2) = sqrt(a^n) = a^(1/2) * a^(1/2)
Therefore, 3^(3/2) is equal to 3.

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Answer:

First answer: 10

Second answer: 810 ft^2

Step-by-step explanation:

Hope this helps

The distance between the points (3,5) and a line with the equation 5x-3y+10=0 is 10/√34 units.

Given that,

We have to find the distance between the points (3,5) and a line with the equation 5x-3y+10=0.

We know that,

We have a formula that is

Let (x₁, y₁) be the point and ax + by + c = 0 be the line.

Then the distance between a point and a line will be

d=|ax₁+by₁+c|/√(a²+b²)

Here,

(x₁,y₁)=(3,5)

a=5, b=-3 and c=10

So, substituting

d=|5(3)+(-3)(5)+10|/√(5²+(-3)²)

d=|15-15+10|/√25+9

d=|10|/√34

d=10/√34

Therefore, the distance between the points (3,5) and a line with the equation 5x-3y+10=0 is 10/√34 units.

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The statement that ,"distribution of sample​ mean(μ) will be normally distributed if sample is obtained from population that is normally​ distributed, regardless of sample size(n)" is True .

What is Normal Distribution ?

A Normal Distribution is a distribution that describes a symmetrical plot of data around the mean value, where width of curve is defined by standard deviation.

the Central Limit Theorem states that , for a normally distributed random variable "X" , with mean "μ" and standard deviation "σ" , the sampling distribution of the sample means with size "n" can be approximated to a normal distribution with mean  and standard deviation  is s = σ/√n   .

So , sample size restriction is only for non normal underlying distribution,

Therefore , by Central Limit Theorem the given statement is True .

The given question is incomplete , the complete question is

The distribution of the sample​ mean (μ), will be normally distributed if the sample is obtained from a population that is normally​ distributed, regardless of the sample size . Is the statement True or False ?

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The domain of the given graph will be equal to -4≤ x ≤ 4. The correct option is A.

The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f. (x).

A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value.

The values that we can put in the function of the given graph images vary from -4 to 4.

In the y-axis, the value of x varies from -4 to 4.

Therefore, the domain of the given graph will be equal to -4≤ x ≤ 4. The correct option is A.

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Answer: 0.75x+0.8(x+10)=101

Step-by-step explanation:

Jared:   a=x*0.75

Zach: b= (x+10)*0.8

total a+b=101

final equation

0.75x+0.8(x+10)=101

The coordinates will be after applying the transformation,  L( 3, 1) --> (-5, 1) U(3, 5), -- > (-5, 5), and X(0, 5) --> (-2, 5)

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

It is given that:

The graph is shown in the picture.

From the picture the coordinates are:

L( 3, 1)

U(3, 5),

X(0, 5)

After transformation:

L( 3, 1) --> (-5, 1)

U(3, 5), -- > (-5, 5)

X(0, 5) --> (-2, 5)

Thus, the coordinates will be after applying the transformation,

L( 3, 1) --> (-5, 1) U(3, 5), -- > (-5, 5), and X(0, 5) --> (-2, 5)

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The completed reasons that justify the statements in the solution to the equation consisting of an algebraic expression are presented as follows;

Statements        [tex]{}[/tex]                             Reasons

1. (1/2)·x - 5 = 10                        [tex]{}[/tex]     1. Given

2. 2·((1/2)·x - 5) = 20   [tex]{}[/tex]                   2. Multiplication property

3. x - 10 = 20                                 4. Distributive property

4. x = 30                                        5. Additive property

An algebraic equation consists of a statement that sets two expressions, that (at least one) consists of algebraic term, as being equivalent or the same.

The details of the reasons used to justify the steps are presented as follows;

Multiplication property

The multiplication property of equality states both sides of an equation remain equal following the multiplication of both sides of the equation by the same property.

Distributive property

The distributive property states that the multiplication of the sum of two numbers by a specified number has equivalent result as multiplying the individual numbers in the addend by the number

Mathematically; a·(b + c)  = a·b + a·c

Additive property

The additive property states that the equality of both sides of an equation is still true following the addition of the same quantity to both sides of the equation.

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Answer:

??????????????????????

Answer:

5.36^2+5.36^3=182.720256

Step-by-step explanation:

g(×)=4x+1 when g(×)=4x​ then we are getting No Solution.

What is system of equations?

Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution. A solution is not assured even then.

[tex]$$\left[\begin{array}{c}g=4 x+1 \\g=4 x\end{array}\right]$$[/tex]

Substitute g=4 x

[4 x=4 x+1]

Refine 4 x=4 x+1

-1=0

-1=0 is false, therefore the system of equations has no solution

No Solution

Complete Question : Find the solution of the given function g(×)=4x+1 when g(×)=4x​.

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