Victoria has a total of 65 dimes and quarters worth $10.70. How many of each type of coin does she have?

The value would be [tex]34^{-1} \pmod{47}=30[/tex]

What is the modulus in mathematics?

In mathematics, the modulus is the remainder of the division of one number by another. It is denoted by the symbol %, or in some cases, by the symbol mod.

Given that 13^-1 ≡ 29 (mod 47), we can use this information to find the inverse of 34 mod 47. The inverse of a number modulo m is a number x such that the product of the number and its inverse is congruent to 1 mod m.

In the case of the given equation, [tex]$13^{-1} \equiv 29 \pmod{47}$[/tex] is saying that 29*13 = 377 is congruent to 1 mod 47.

We can use this congruence to find the inverse of 34 mod 47. The inverse of 34 mod 47 is the number x such that 34*x = 1 mod 47. So we can write this congruence as [tex]$34x \equiv 1 \pmod{47}$[/tex]

We can use the given congruence of 13^-1 ≡ 29 (mod 47) to find the inverse of 34 mod 47.

Since [tex]$13^{-1} \equiv 29 \pmod{47}$[/tex], we can multiply both sides of the congruence by 34 as:

[tex]$13^{-1} * 34 \equiv 29 * 34 \pmod{47}$[/tex]

Now we can substitute the right side of the equation:

[tex]$13^{-1} * 34 \equiv (13*29) \pmod{47}$[/tex]

And now we can substitute the left side of the equation:

[tex]$34^{-1} \equiv (13*29) \pmod{47}$[/tex]

And since [tex]$13*29 = 377$[/tex] this is congruent to 30 (mod 47) the inverse of 34 mod 47 is 30.

Therefore, the value would be [tex]34^{-1} \pmod{47}=30[/tex]

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The value would be 13.

What is the modulus in mathematics?

In mathematics, the modulus is the remainder of the division of one number by another. It is denoted by the symbol %, or in some cases, by the symbol mod.

We can use the property of modular inverse that

[tex]$(ab)^{-1} \equiv b^{-1}a^{-1} \pmod{m}$[/tex]

So, [tex]$(13*34)^{-1} \equiv 34^{-1} \cdot 13^{-1} \pmod{47}$[/tex]

[tex]$13^{-1} \equiv 29 \pmod{47}$\\$(13*34)^{-1} \equiv 34^{-1} \cdot 29 \pmod{47}$So, $34^{-1} \equiv (13*34)^{-1} \cdot 13 \pmod{47}$$34^{-1} \equiv 1 \cdot 13 \pmod{47}$$34^{-1} \equiv 13 \pmod{47}$[/tex]

Hence, The value would be 13.

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The circle equations for circles with diameters of 12 units that lie on the y-axis are:

We want to find the equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis, now, remember that the general equation for a circle of radius R and a center (a, b) is:

(x - a)^2 + (y - b)^2 = R^2

If we want a circle that lies on the y-axis, then a = 0, and if the diameter is 12 units, then the radius is R = 6 units.

Then the equation is something like:

x^2 + (y - b)^2 = 6^2 = 36

The two circle equations with this form are:

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Answer:

see explanation

Step-by-step explanation:

A

for the triangles to be similar by the AA postulate then 2 angles in both triangles must be congruent.

In this case we are only given 1 pair of congruent angles.

Thus not able to say similar by AA postulate, therefore Sharon is incorrect in her assumption.

B

the sides are of different lengths but the ratios of corresponding sides are equal, that is

[tex]\frac{JK}{GH}[/tex] = [tex]\frac{8}{4}[/tex] = 2 and [tex]\frac{JL}{GI}[/tex] = [tex]\frac{10}{5}[/tex] = 2

If the ratios of 2 pairs of corresponding sides of 2 triangles are equal and the included angles are congruent , then the triangles are similar, so

Δ GHI and Δ JKL are similar by the SAS postulate

C

the ratios of corresponding sides are equal , then

[tex]\frac{KL}{HI}[/tex] = [tex]\frac{JL}{GI}[/tex]

[tex]\frac{KL}{7}[/tex] = [tex]\frac{10}{5}[/tex] = 2 ( multiply both sides by 7 to clear the fraction )

KL = 14

The number of mole O₂ is 2. Since the subscript of oxygen denotes the number of moles.

What is a diatomic element?

Diatomic molecules—so named because they only contain two atoms of the same or different chemical elements—are molecules that are made up of two atoms. A diatomic molecule is considered to be homonuclear if it contains two atoms of the same element, such as oxygen (O₂) or hydrogen (H₂).

One mole consists of an Avogadro number of atoms. If you are aware of the mole quantity, you can convert a mole into grams.

The mole (symbol: mol) is the unit of material quantity used by the International System of Units. The amount of a substance determines how many elementary entities of that substance are present in an object or sample. The mole must contain precisely 6.02214076×10²³ elementary entities.

The subscript part of a chemical compound represents the number of moe of the chemical compound. The subscipt of O₂ is 2. Thus the number of mole is 2.

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If the circle's center is in one of the foci, the inverse of the hyperbola is a Limaçon with an inner loop.

A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.

A hyperbola is made up of two mirror images of one another that resemble two infinite bows.

These two sections are known as connected components or branches.

The hyperbola's equation is expressed as (y−k)2b2−(x−h)2a2=1.

The transverse axis is defined by b, the conjugate axis by a, and the center is defined by (h,k).

The section of a line that a hyperbola's vertices form.

The inverse of the hyperbola is a Limaçon with an inner loop if the circle's center is in one of the foci.

Therefore, if the circle's center is in one of the foci, the inverse of the hyperbola is a Limaçon with an inner loop.

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The measure of ∠B is (x - 25)° = (27 - 25)° = 2°.

What are supplementary angles?

Supplementary angles are two angles that add up to 180 degrees. They are angles that when placed together will form a straight line. They are called "supplementary" because they "supplement" each other to form a straight angle.

When two angles are supplementary, their measures add up to 180 degrees. So, if ∠A and ∠B are supplementary, then:

m∠A + m∠B = 180

Given that m∠A = (7x - 11)° and m∠B = (x - 25)°, we can substitute these values into the equation:

(7x - 11)° + (x - 25)° = 180

Simplifying this equation by combining like terms:

8x - 36 = 180

Adding 36 to both sides:

8x = 216

Dividing both sides by 8:

x = 27

Hence, the measure of ∠B is (x - 25)° = (27 - 25)° = 2°.

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The measure of ∠B is (x - 25)° = (27 - 25)° = 2°.

What are supplementary angles?

Supplementary angles are two angles that add up to 180 degrees. They are angles that when placed together will form a straight line. They are called "supplementary" because they "supplement" each other to form a straight angle.

When two angles are supplementary, their measures add up to 180 degrees. So, if ∠A and ∠B are supplementary, then:

m∠A + m∠B = 180

Given that m∠A = (7x - 11)° and m∠B = (x - 25)°, we can substitute these values into the equation:

(7x - 11)° + (x - 25)° = 180

Simplifying this equation by combining like terms:

8x - 36 = 180

Adding 36 to both sides:

8x = 216

Dividing both sides by 8:

x = 27

Hence, the measure of ∠B is (x - 25)° = (27 - 25)° = 2°.

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Answer:

4(3p - 7)

Step-by-step explanation:

First find the factors of 12 and 28:

12: 1, 2, 3, 4, 6, 12

28: 1, 2, 4, 7, 28

Notice any common factors: 1, 2, 4

Now, out of these factors, 4 is the GCF since it is the greatest common factor, so divide 12 and 28 by 4:

12/4 = 3.  28/4 = 7.

Hence, 12p-28 = 4(3p - 7)

Answer:

The median of the data is 1

The meaning of the 4! ( factorial ) in mathematics is equal to                    ( 4 × 3 × 2 × 1 ).

As given in the question,

Given expression in mathematics is written as :

4! ( factorial )

In standard form meaning of the n! ( factorial ) is given by multiplication of all the terms in decreasing order till 1.

It is expressed as:

n! = n × ( n - 1 ) × ( n - 2 ) × ( n - 3 ) × ........× 3 × 2 × (n - (n - 1) ).

Apply this formula for 4! ( factorial ) we get,

4! ( factorial )

= 4 × ( 4 - 1 ) × ( 4 - 2 ) ×( 4 - 3)

= 4 × 3 × 2 × 1

= 12

Therefore, the meaning of 4! ( factorial ) in mathematics is given by

4 × 3 × 2 × 1 .

The above question is incomplete , the complete question is :

What does 4! ( factorial ) mean in mathematics?

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The value 'k' for which '4x^2 + 8xy + ky^2 = 9' is the second degree equation of a pair of straight lines is 4.

Therefore the answer is 4.

A general second-degree equation of a pair of straight lines is given by:

ax² + 2hxy + by² + 2gx + 2fy + c = 0

Where a, b, c, d, e, and f are constants, x and y are variables.

For the equation to represent a pair of straight lines, the following conditions must be met :

abc + 2fgh - af² - bg² - ch² = 0

In the equation 4x^2 + 8xy + ky^2 = 9, a = 4, h = 4, b = k, g = f = 0 and c = -9.

That is 4×k×(-9) + 2×0×0×4 - 4×0² - k×0² + 9×4² = 0

4×k×9 = 9×4²

k = 4

--The question is incomplete, complete question is given below--

"For what value of k is 4x^2 + 8xy + ky^2 = 9 the equation of a pair of straight lines?"

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Equation = P(1+r)^x, where P is the initial amount invested, r is the fixed interest rate, and x is the number of years.

It is important to note that the equation provided is the formula for compound interest. P is the initial principal, r is the annual interest rate, and x is the number of years the money is invested. The equation gives the total amount of money in the account after x years.

It should be also noted that the interest rate is given as a decimal and not a percentage.

For example, if the interest rate is 5%, then r = 0.05.

In order to use this equation, the value of P, r and x should be known

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Answer  

x=-1/2,=29/4

explanation

1. To maximize the profit :

28 jars of salsa and

0 jars of tomato sauce should be made.

which  make maximum profit of $42.

2.  In order to maximize the total monthly profit

2300 units of T₁ type table and and

600 units of T₂ type table should be made

which provide maximum profit of $273000.

In Algebra, inequality is a Mathematical statement that shows the relation between two expressions using the inequality symbol. The expressions on both sides of an inequality sign are not equal. It means that the expression on the left-hand side should be greater than or less than the expression on the right-hand side or vice versa. If the relationship between two algebraic expressions is defined using the inequality symbols, then it is called literal inequalities.

1. Let x be the numbers of jars of tomato sauce

Let y be the number of jars of salsa sauce

Profit P(x, y)=2x+1.5y

x≥0

y≥0

10x+5y≤140

x + y ≤13

​The solution set of the system of inequalities above the vertices of the feasible solution set obtained are shown below.

A at (0,13)

B at (0,28)

C at (14,0)

D at (15,0)

E at (15, -2)

Evaluate profit P(x, y) at each vertex

A at (0,13):P(0,13)=$19.5

B at (0,28):P(0,28)=$42

C at (14,0):P(14,0)=$28

D at (15,0):P(15,0)=$30

E at (15, -2):P(15,-2)=30-3=$27

The maximum profit of $42 is at vertex B.

Which means production of 28 jars of salsa and 0 jars of tomato sauce provides maximum profit of $42.

2. Let x be the number of tables of type T₁

​and y the number of tables of type T₂

​Profit P(x, y)=90x+110y

x≥0

y≥0

2x+4y≤7000

x+2.5y≤4000

2x+1,5y≤5500

​The solution set of the system of inequalities above the vertices of the feasible solution set obtained are shown below.

A at (0,0)

B at (0,1600)

C at (1500,1000)

D at (2300,600)

E at (2750,0)

Evaluate profit P(x, y) at each vertex

A at (0,0):P(0,0)=0

B at (0.1600):P(0,1600)=90(0)+110(1600)=176000

C at (1500,1000):P(1500,1000)=90(2500)+110(1000)=245000

D at (2300,600):P(2300,600)=90(2300)+110(600)=273000

E at (2750,0):P(2750,0)=90(2750)+110(0)=247500

The maximum profit of $273000 is at vertex D.

which means production of 2300 tables of type T₁ and 600 tables of type T₂ makes maximum  profit.

1. Hence, maximum profit is made by making

28 jars of salsa and

0 jars of tomato sauce getting

$42 of profit.

2. Hence the company needs to produce

2300 tables of type T₁ and

600 tables of type T₂,

in order to maximize its monthly profit which is equal to $273000.

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The longest side of a triangle is always opposite to the largest angle because  the endpoints of the lines on either side are going to be further apart if the angle is wider .

What is Triangle  ?

The triangle can defined as a three-sided polygon that consists of three edges and three vertices.

Let the angle opens up to its opposite side.

So , the larger the angle, the wider will be it's opening. which means that the endpoints of lines on either side of the angle are going to be further apart if angle is wider.

If the endpoints are further apart, then the line connecting them, which makes up the side opposite will be going to be more longer.

So , the longest side will always be opposite to the largest angle

Similarly , the smallest angle will result in shortest side opposite side for the same reasons.

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[tex]\dfrac{15}{4} \div\dfrac{5}{8}[/tex]

In order to divide two fractions, you will need to use the KCF method.

Keep

Change

Flip

This means that we will keep the first fraction, change the division to multiplication, and flip the second fraction(reciprocal).

[tex]\dfrac{15}{4} \times\dfrac{8}{5}[/tex]

Multiply:

[tex]\dfrac{15}{4} \times\dfrac{8}{5}[/tex]

[tex]\dfrac{15\times8}{4\times5}[/tex]

[tex]=\dfrac{120}{20}[/tex]

Simplify:

[tex]120\div20[/tex]

[tex]=\fbox{6}[/tex]

Answer: 6

Step-by-step explanation:

1. 15/4 divided by 5/8 = 120/20

15/4 / 5/8 = 15/4 times 8/5 = 15 time 8 over 4 time 5 = 120/20

2. 120/6 = 6

Answer:

1.  $76,000

2. $58,000 + $2,000 * t

Step-by-step explanation:

2. Now, you might be questioning why we are going with the second question first, but this will be useful as it sets up our equation to make the first question easier. So, we will start with Luke's base salary of $58,000. Then, we will add $2,000 for every year he works at the company. If he works for t years and gains $2,000 on his salary per year, our equation will look like this:

$58,000 + $2,000 * t

That is the equation.

1. Now, using our previous equation, $58,000 + $2,000 * t, we will substitute 9 in for t. We get:

$58,000 + $2,000 * 9

Then, we simplify, giving us:

$58,000 + $18,000 = $76,000

The term "line of symmetry" refers to the fictitious axis or line that you fold a figure along to create its symmetrical halves.

A definition of symmetry states that whether one form is moved, rotated, or flipped, it looks precisely like the other shape. Just fold the paper, draw one-half of the heart at the fold, then cut it out to discover that the second half precisely matches the first half when you are instructed to cut out a "heart" from a sheet of paper. The heart-shaped carving is an illustration of symmetry.

Symmetry is defined in mathematics as "a mirror image." Symmetry is the property of an image that remains unchanged after a form has been rotated or flipped. There are patterns in it. In daily life, you may have heard the word "symmetrical" frequently. One half of a thing is the mirror image of the other half, which is a balanced and proportionate likeness. Asymmetrical refers to a form that is not symmetrical. In nature, architecture, and the arts, symmetrical things are all around us.

The term "line of symmetry" refers to the fictitious axis or line that you fold a figure along to create its symmetrical halves. In essence, it splits one thing into two mirror images. The symmetry line may run vertically, horizontally, or diagonally. There might be one or many symmetry lines.

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Answer:

1. Choose Your Shape: Start with a shape that you want to create a line of symmetry for. It could be a simple shape like a square, rectangle, or triangle.

2. Draw the Shape: Draw the shape neatly on a piece of paper using a pencil.

3. Identify the Line of Symmetry: Decide where you want to place the line of symmetry. This line should divide the shape into two equal halves.

4. Draw the Line of Symmetry: Draw a straight line through the center of the shape, from one side to the other. Use a ruler to ensure the line is straight and passes through the center.

5. Create the Mirror Image: To create the mirror image on the other side of the line, imagine that the line is a mirror. Reflect each point on one side of the line to the other side while maintaining the same distance from the line. You can also use a ruler or straightedge to guide you as you draw.

6. Check for Symmetry: Carefully examine both sides of the line to make sure they are mirror images of each other. The distances and angles should match.

7. Finalize the Drawing: Once you're satisfied with the symmetry, trace over your pencil lines with a pen or darken them to make your drawing more prominent.

8. Erase Construction Lines: Gently erase any construction lines or guidelines you drew in the earlier steps.

The minimal number of employees who did not get their preferred shift that week was 20.

Out of 50, 40% are on the day shift = 0.4*50 = 20 & 60% are on the night shift = 30.

But, 80% of 50 prefer day shift = 0.8*50 = 20 & 20% of 50 prefer night shift = 10.

We need to find the minimum no. of people who did not get their desired shift. Since slots for the night shift(30) are greater than the people who desired it (10). We can assume that among those 30-night shift slots, 10 were occupied by the ones who wanted the night shift. So, whoever wanted the night shift got the night shift.

But, for the day shifts the no. of slots (20) is less than the number of people who desired it (40). So, there are going to be 20 people who did not get what they desired.

Thus, 20  is the minimum number of staff members who failed to receive her preference of shift that week.

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Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.

The term "inequality" refers to a relationship between two expressions or values that is not equal to one another. Inequality originates from an imbalance, thus.

In order to get the variable on its own, you can solve a lot of straightforward inequalities by adding, removing, multiplying, or dividing the two sides. But as a result of them, the direction of the inequality will change: Using a negative number to divide or multiply both sides. right and left sides are switched.

An inequality results from the comparison of two or more algebraic expressions using the symbols, >, or. They are the mathematical expressions with unequal sides.

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Answer:0.23

Step-by-step explanation:

Answer:

77.4 inches

6 feet 4 inches

Step-by-step explanation:

what persent of 14 is 10.83 is 77.35

what persent of 84 is 77.3571428571 is 92.08

what is 92.08% of 84 is 77.34

77.34 inches to feet is 6 feet and 4 inches

The exact value is required. In this case, they don't have enough for 1 3/4 cups of flour.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

From the information, the person had 2/3 cup of flour in a bin and 7/8 flour was still in the bag. In this case, it should be noted that they also wanted to know of they had enough for 1 3/4 cups of flour.

This will be calculated thus:

= 2/3 + 7 / 8

= 16/24 + 21/24

= 37 / 24.

= 1 13 / 24

This is not enough for 1 3/4 cups of flour.

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The 7 stepd in problem-solving examples are:

Step 1: Read through the problem

Step 2: Draw diagram

Step 3: Assign variable to each unknown

Step 4: Translate information into an equation

Step 5: Check the equation

Step 6: Use algebra rules to solve the equations

Step 7: Check the final answer.

We know that the word problems are required to translate the real world problem into mathematical terms.

Everything mentioned in the word problem is important.

The seven necessary steps in problem solving examples:

Step 1: Read the problem throughly

Step 2: Draw picture / diagram / arrow diagram related to example

Step 3: Assign an alphabate to each unknown value

Step 4: Translate information into an equation

Step 5: Check the types equation

Step 6: solve the equations using algebra rules

Step 7: Check the final answer.

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An equation that could be used to determine the number of wreaths that Nicole could decorate using one spool of ribbon is:

                           W = S / R

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

An equation that could be used to determine the number of wreaths that Nicole could decorate using one spool of ribbon is:

W = S / R

where W is the number of wreaths, S is the total length of ribbon on the spool, and R is the length of ribbon used per wreath.

Plugging in the given values, we get:

W = 20 / 2.5

Solving for W, we get:

W = 8

So Nicole could decorate 8 wreaths using one spool of ribbon.

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So Dylan needs 1.375 liters of water more for his experiment.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

To find out how much more water Dylan needs, we can subtract the amount of water he currently has from the amount of water he needs for the experiment.

2.5 - 1.125 = 1.375 liters

So Dylan needs 1.375 liters of water more.

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Inverse of function is written by using notation f⁻¹

The function that can be reversed into another function is termed as inverse function. It is also called anti function. There are different types of inverse function such as inverse trigonometric function, inverse rational function, inverse log function and so on.

We can determine an inverse function by interchanging the elements that present in the given expressions.

Inverse of the function f is denoted by notation f⁻¹

let, we have given a function, f(x) = 8x + 9

now, we need to find the inverse of the above function.

in the first step we write the function using y and set equal to x

                      x = 8y +9

in the next step, we arrange to make the y subject,

                 x - 9 = 8y

               8y = x - 9

                y = (x - 9)/ 8

 use the notation f⁻¹ = (x - 9)/ 8

this is the inverse of function f.

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As you can see, 5y is an external angle of triangle ABC

we know that 5y=180-x

since angle B is 40, and angle A=x and C=x, we have

x%2Bx%2B40=180

2x=180-40

x=140%2F2

x=70

so, angle A=70 and C=70

then

5y=180-70

5y=110

y=110%2F5

y=22

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On solving the provided question, we can say that the sum of the two expressions will be -4n + 6

It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression) A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)It is possible to compare expressions and phrases.

Expression, Number/Variable, and Mathematical Operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.

let the two expression be

-4nand 6 and the sum will be -4n + 6

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