Solve by the substitution method. (If there is no solution, enter NO SOLUTION. Use the parameters x and y as necessary.)
2x − 4y = 40
−x + 2y = −20
(x, y) =

Melanie's answer that 212 napkins were used in all and 433 napkins were left is reasonable and can be verified by using simple algebraic equations.

Yes, Melanie's answer is reasonable. She correctly determined that the total number of napkins used in lunch and dinner was 325-113 = 212. From this, we can also confirm that the total number of napkins left was 645 - 212 = 433. We can verify these answers by using simple algebraic equations to solve the problem. Using the equation 645 = 325 + x, where x is the number of napkins used at dinner, we can solve for x by subtracting 325 from both sides to get x = 320. Similarly, using the equation 645 = 433 + y, where y is the number of napkins used in all, we can solve for y by subtracting 433 from both sides to get y = 212. This confirms Melanie's answer that 212 napkins were used in all and 433 napkins were left.

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The angles 5 and 6 which are given in the diagram above are typical example of an adjacent angle.

An adjacent angle is defined as the type of angle that has a common sides which is shared by the two angles that are being compared.

A vertical angle is the type of angle that is usually opposite and they constructed by the intersection of two lines.

Therefore since a common sides exists between angle 5 and 6.

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The average allowance for each student is $9.25.

To find the average allowance for each student, we need to add up all the allowances and divide by the total number of students.

Adding up the allowances:

$7 + $12 + $8.50 + $10 + $7 + $8 + $10.50 + $11 = $74

There are 8 students, so we divide the total allowance by 8 to get:

$74 / 8 = $9.25

Therefore, the average allowance for each student is $9.25.

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The maximum errοr οf estimate is 0.092 years οr apprοximateIy 1 mοnth.

The standard deviatiοn is a measure οf the amοunt οf variatiοn οr dispersiοn οf a set οf vaIues frοm their mean οr average. It is caIcuIated as the square rοοt οf the variance.

Tο find the maximum errοr οf estimate, we need tο use the fοrmuIa:

Maximum errοr οf estimate = z * (standard deviatiοn / √(sampIe size))

where z is the z-scοre assοciated with the given cοnfidence IeveI, standard deviatiοn is the pοpuIatiοn standard deviatiοn (0.8 years), and sampIe size is the number οf TVs sampIed (445).

At a cοnfidence IeveI οf 95%, the z-scοre is 1.96.

Substituting the vaIues in the fοrmuIa, we get:

Maximum errοr οf estimate = 1.96 * (0.8 / √(445))

= 0.092 years (rοunded tο 3 decimaI pIaces)

Therefοre, the maximum errοr οf estimate is 0.092 years οr apprοximateIy 1 mοnth. This means that we can be 95% cοnfident that the true mean rate at which the TVs need tο be serviced οr repIaced is within 1 mοnth οf the sampIe mean οf 3.5 years.

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Answer:

Step-by-step explanation:

To calculate the amount of money Nathaniel needs to deposit today to fund this gift for his descendants, we can use the present value formula for a perpetuity:

Present Value = Annual Payment / Discount Rate

In this case, the annual payment is R380 000 and the discount rate (expected rate of return) is 6.45% in decimals, or 0.0645 as a fraction. So we can plug these values into the formula:

Present Value = R380 000 / 0.0645

This gives us a present value of approximately R5,899,225.68. Therefore, Nathaniel would need to deposit R5,899,225.68 today into the trust fund to provide R380 000 a year forever for his descendants, assuming a 6.45% expected rate of return.

Therefore, the coordinates of point B are approximately (12.67, 0.67).

In mathematics, an equation is a statement that asserts the equality of two expressions. Equations are written using an equal sign (=) between the two expressions that are being compared. The expressions on either side of the equal sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation. The equation is true if the LHS is equal to the RHS. Equations are used to represent various relationships and patterns in mathematics, and are an important tool in problem-solving and mathematical modeling.

Here,

(a) To calculate the length of OC, we need to find the coordinates of point O, which is the intersection of the diagonals of the parallelogram. The midpoint of AC is:

((12+5)/2, (0+5)/2) = (8.5, 2.5)

Therefore, the equation of the line passing through the midpoint of AC and perpendicular to AC is:

y - 2.5 = -(5-0)/(5-12) (x - 8.5)

Simplifying:

y - 2.5 = 5/7 (x - 8.5)

y = 5/7 x - 1

This is the equation of the line passing through O and parallel to AB. We can see that when x = 12, y = 5/7 * 12 - 1 = 7.4. Therefore, the coordinates of O are (12, 7.4).Using the distance formula, we can now calculate the length of OC:

OC = √((12-5)² + (7.4-0²) = √(109.96) ≈ 10.49

Therefore, the length of OC is approximately 10.49 units.

(b) The gradient of OC can be found using the coordinates of points O and C:

m = (y₂ - y₁)/(x₂ - x₁) = (7.4 - 5)/(12 - 5) = 0.4/1 ≈ 0.4

Therefore, the gradient of OC is approximately 0.4.

(c) The equation of line AB can be found using the coordinates of points A and B:

m = (y₂ - y₁)/(x₂ - x₁) = (y - 0)/(x - 12)

Simplifying and substituting the coordinates of point A:

0.4 = (y - 0)/(x - 12)

0.4(x - 12) = y

Therefore, the equation of line AB is y = 0.4x - 4.8.

(d) The coordinates of point B can be found by solving the system of equations formed by the equations of lines AB and OC. Equating y in both equations:

0.4x - 4.8 = 5/7 x - 1

Simplifying and solving for x:

0.3x = 3.8

x = 12.67

Substituting x in either equation:

y = 0.4(12.67) - 4.8 ≈ 0.67

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Using the supplementary angle theorem, the value for x so that points A, B, and C are collinear is 8.

What is a supplementary angle?

The definition of "supplementary" in mathematics relates to angles that combine to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles.

A line segment AC is drawn.

Point B is in between A and C.

A transversal DE is drawn passing through point B.

Points D, B, and E are collinear.

The measure of angle CBE is 148° and the measure of angle EBA is 4x°.

The angles ∠CBE and ∠EBA forms a pair of supplementary angles.

Their sum result in value of 180°.

Mathematically, this can be represented as -

∠CBE + ∠EBA = 180°

Substituting the values into the equation -

148° + 4x° = 180°

Solving for x, we get -

4x° = 180° - 148°

4x° = 32°

x = 32 / 4

x = 8

Therefore, the value for x is obtained as 8.

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In the given angles the required value of x is 17° respectively.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.

Angles created by two rays are in the plane where the rays are located.

The meeting of two planes also creates angles. We refer to these as dihedral angles.

Based on the measurement, there are many kinds of angles in geometry.

The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation.

So, we know that:

2x+5 + 8x+5 = Straight angle

2x+5 + 8x+5 = 180

Now, solve for x as follows:

2x+5 + 8x+5 = 180

10x+10 = 180

10x = 170

x = 17

Therefore, in the given angles the required value of x is 17° respectively.

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Required number of bags which have zips on them are 71.

Here given, A company makes 140 bags.

So, total number of bags = 140

It is also given, 47 of the bags have buttons but no zips 48 of the bags have zips but no buttons.

So, number bags which have buttons but no zips = 47 and number bags which have zips but no buttons = 48

and numbers of bags which have neither zips nor buttons = 22.

If we subtract number of bags which have no zips from total number of bags then we will get total number of bags which have zips

So, number of bags have zips on them

[tex] = 140 - 47 - 22 = 71[/tex]

Therefore, 71 bags have zips on them.

This is a problem of Subtraction.

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The order of the matrix is 2 x 2.

What is a matrix and what is meant by its order?

In the field of mathematics, matrices are rectangular arrangements of numerical values, symbols, or algebraic expressions, organized in rows and columns. Matrices are used in many areas of mathematics and science, as well as in engineering, physics, and computer graphics.

The term 'order' in the context of matrices refers to the dimensions of the matrix, which are determined by the number of rows and columns it contains. It is denoted by m x n, where m is the number of rows and n is the number of columns. To find the order of a matrix, we simply count the number of rows and columns. The order is usually written as a pair of numbers in the form m x n.

Determine the order of the given matrix:

In the given problem, we are asked to find the order of the matrix:

[tex]\begin{pmatrix}9 &6 \\-4 & 8\end{pmatrix}[/tex]

we count the number of rows and columns.

This matrix has 2 rows and 2 columns, so its order is 2 x 2.

Therefore, the order of the matrix is 2 x 2.

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(a) The value of sin 2θ is -3√(91)/50.

(b)  θ/2 is located in the third quadrant.

(c) The value of cos θ/2 is -√65/10.

We know that cos θ = 3/10, so we can find sin θ using the Pythagorean identity:

sin² θ + cos² θ = 1

sin²θ + (3/10)² = 1

sin²θ = 1 - (3/10)² = 91/100

sin θ = ±√(91)/10

Since 3π/2 < θ < 2π,

we know that sin θ < 0, so sin θ = -√(91)/10.

a) To find sin 2θ, we can use the double angle formula:

sin 2θ = 2 sin θ cos θ

sin 2θ = 2 (-√(91)/10) (3/10)

sin 2θ = -3√(91)/50

b) To find the quadrant in which θ/2 is located, we first need to find θ/2:

θ/2 = (3π/2 + 2π)/2 = 5π/4

5π/4 is in the third quadrant, so θ/2 is located in the third quadrant.

c) To find cos θ/2, we can use the half angle formula:

cos θ/2 = ±√((1 + cos θ)/2)

Since 3π/2 < θ < 2π, we know that cos θ < 0,

so we take the negative square root:

cos θ/2 = -√((1 + 3/10)/2)

cos θ/2 = -√(13/20)

Simplifying the radical by dividing both numerator and denominator by 4:

cos θ/2 = -√(13)/2√5

Multiplying numerator and denominator by √5 to rationalize the denominator:

cos θ/2 = -√65/10

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Answer: $11.60

Step-by-step explanation: Since ur finding the cost of one cd and she bought 6 and since is before tax you do 36.90/(divided by) 6 and boom #!

If the graph of a polynomial function P(x) has x-intercepts at x = -4, x = 0, x = 5, the following must be true for P(x): D. The degree of the polynomial is greater than or equal to three.

Based on the graph of the polynomial f(x), the following is not a factor: B. (x - 1).

In Mathematics and Geometry, a polynomial graph simply refers to a type of graph that touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

Generally speaking, the zero of a polynomial function simply refers to a point where it crosses or cuts the x-axis of a graph. Since the polynomial function with x-intercepts at x = -4, x = 0, and x = 5 cuts the x-axis at three (3) points. Therefore, the degree of this polynomial is either greater than or equal to three (3).

By critically observing the graph of the polynomial function shown above, we can logically deduce that its x-intercepts include the following;

x = -1 ⇒ x + 1 = 0.

x = -2 ⇒ x + 2 = 0.

x = 2 ⇒ x - 2 = 0.

x = 3 ⇒ x - 3 = 0.

Therefore, (x - 1) is not a factor.

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The measure or value of x = 55°. This is solved using the Tangent, Secant and Arc theorems.

Note that the Measure of and x (m∠x) = (Far Arc - Near Arc)/2

Where

Far Arc = 360 - 65 - 120 = 175°

Near Arc = 65°

thus, m∠x = (175-65)/2

m∠x  = 55°

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Answer: 3.5

Step-by-step explanation: sry if im wrong ):

For given coordinates,  the ordered pair describing the location of G'' is (3,-6).

What are coordinates?

Coordinates are a set of numbers that specify the position or location of a point or object in space, relative to a reference point or system. In two-dimensional space, coordinates are usually represented by a pair of numbers (x, y), where the first number represents the horizontal position of the point along the x-axis, and the second number represents the vertical position of the point along the y-axis. In three-dimensional space, coordinates are usually represented by a triple of numbers (x, y, z), where the first number represents the horizontal position of the point along the x-axis, the second number represents the vertical position of the point along the y-axis, and the third number represents the position of the point along the z-axis, which is perpendicular to the x-y plane.

Now,

When a point is reflected over the x-axis, the y-coordinate is negated. So the image of G(-3,6) over the x-axis is G'(-3,-6).

When a point is reflected over the y-axis, the x-coordinate is negated. So the image of G'(-3,-6) over the y-axis is G''(3,-6).

Therefore, the ordered pair describing the location of G'' is (3,-6).

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(x+2), (x+1), and (x-2) are factors of f(x) because they correspond to the roots of the polynomial.

What is Polynomial function ?

A polynomial function is a type of mathematical function that consists of a sum of terms, where each term is a product of a constant coefficient and one or more variables raised to non-negative integer powers. In other words, a polynomial function is an algebraic expression that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

Thank you for providing the graph of the polynomial f(x). Based on the graph, we can see that the polynomial has roots at x = -2, x = -1, x = 2, and x = 7. Therefore, (x+2), (x+1), and (x-2) are factors of f(x) because they correspond to the roots of the polynomial.

However, since there is no point on the graph where f(x) is equal to zero when x = -7, we can conclude that (-x+7) is NOT a factor of f(x).

Therefore, (x+2), (x+1), and (x-2) are factors of f(x) because they correspond to the roots of the polynomial.

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The equation's only solution is x = -17.

Simplifying the left-hand side of the equation:

-5 + x - 2 = -7 + x

Simplifying the right-hand side of the equation:

3x + 10 - x = 2x + 10

Substituting into the original equation, we get:

-7 + x = 2x + 10

Subtracting x from both sides, we get:

-7 = x + 10

Subtracting 10 from both sides, we get:

-17 = x

So the only solution to the equation is x = -17. Therefore, the correct statement about the solution(s) of the equation is:

• The equation's only solution is x = -17.

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Step-by-step explanation:

2  2/3 =  8/3

8/3 * 1/4  = 8/12 =   2/3 pound in each portion

The cost to operate Lee's Tv is 2.88 dollars.

Lee watches TV for 4 hours per day. During that time, the TV consumes 200 watts per hour. Electricity costs (12 cents)/(1 kilowatt-hour).

Therefore, the cost for Lee to operate in 30 days can be calculated as follows:

200 watt = 0.2 kilowatt

Therefore,

1 day = 4 hours

30 days = ?

cross multiply

number of hours = 120 hours.

Therefore, in 30 days he watches television for 120 hours.

Let's find the cost

0.12 dollars  = 12 cent

1 hour  = 0.2 kilowatt

120 hours =

kilowatt use in 30 days = 0.2 × 120 = 24 kilowatts

Therefore,

1 kilowatts = 0.12 dollars

24 kilowatts = ?

cost of Tv for a month of 30 days = 24 × 0.12

cost of Tv for a month of 30 days = 2.88 dollars

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Step-by-step explanation:

The equation 2x − 15 = 185 represents the relationship between Sam's and Martha's heights. We can solve for x, which represents Martha's height, by isolating x on one side of the equation:

2x − 15 = 185

Add 15 to both sides of the equation:

2x = 200

Divide both sides of the equation by 2:

x = 100

Therefore, Martha's height is 100 centimeters.

You will pay a total of $26.40 including the 20% tip.

To calculate the total amount including the 20% tip, you need to add 20% of the meal cost to the original meal cost:

A gratuity or a small amount of money given to someone for their service, such as a waiter or a hairdresser.

A piece of advice or a suggestion given to someone to help them do something better or more efficiently.

A pointed or tapered end of an object, such as the tip of a pen or a needle.

Tip amount = 20% of $22.00 = 0.2 x $22.00 = $4.40

Total amount including tip = $22.00 + $4.40 = $26.40

Therefore, you will pay a total of $26.40 including the 20% tip.

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Answer:

y = 5/6x + 1/6

Step-by-step explanation:

m = 5/6, x = 7, y = 6

y = mx + b

6 = 5/6(7) + b

b = 6 - 35/6

b = 36/6 - 35/6 = 1/6

y = 5/6x + 1/6

Answer:

Below

Step-by-step explanation:

Here is another way:

 Start with point ( 7,6)   slope ( m= 5/6)  form :

    (y-6) = 5/6 ( x-7)     expand

    y-6 = 5/6 x -  35/6     add 6 to both sides

       y = 5/6 x + 1/6     Done.

The shape of the distribution of the sample mean time is normal.

The standard error of the mean time is 0.5.

The percentage of the sample means that would be greater than 31.25 seconds is 0.621%.

The percentage of the sample means that would be greater than 28.25 seconds is 99.977%.

The percentage of the sample means that would be greater than 28.25 but less than 31.25 seconds is 99.357%.

Given the following data:

Mean = 30.

Standard deviation = 2.

Sample = 16 ads.

What is a normal distribution?

A normal distribution is also referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which shows that all data near the mean have a higher frequency than data far from the mean.

a. The shape of the distribution of the sample mean time is normal.

b. To calculate the standard error of the mean time, we would apply this formula:

Standard error = 0.5.

c. To calculate the percentage of the sample means that would be greater than 31.25 seconds:

P(Z>2.5) = 0.621%.

d. To calculate the percentage of the sample means that would be greater than 28.25 seconds:

P(Z>2.5) = 99.977%.

e. To calculate the percentage of the sample means that would be greater than 28.25 but less than 31.25 seconds:

P(-3.5<Z<2.5) = 99.357%.

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The p-value, under the assumption that the null hypothesis is correct, is the likelihood of receiving a test statistic that is as extreme as the one that was observed.

A declaration or assumption that there is no significant difference or association between two or more variables or populations being studied is known as the null hypothesis in statistics. The default hypothesis that is evaluated against an alternative hypothesis is known as the null hypothesis and is frequently represented as "H0." Typically, the null hypothesis is formulated in light of prior research, theoretical predictions, or accepted wisdom. It posits that any observed differences or correlations between groups or variables are the result of chance or random variation and serves as the foundation for evaluating a hypothesis.

given

We can use a standard format that includes the following details to present the z test results:

This is a claim regarding the population parameter being tested, or the null hypothesis.

In this instance, the null hypothesis is that the population of police officers' mean physical fitness score is equal to 73.

This assertion defies the null hypothesis, according to the alternative. The alternative hypothesis in this situation is that the sample of police officers' mean physical fitness score is higher than 73.

The p-value, under the assumption that the null hypothesis is correct, is the likelihood of receiving a test statistic that is as extreme as the one that was observed.

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Answer: N

Step-by-step explanation: The set of natural numbers is represented by the letter “N”.  A natural number is a number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number. The set of natural numbers, denoted N, can be defined in either of two ways: N = {0, 1, 2, 3, ...}

Therefore , the solution of the given problem of unitary method comes out to be  enable the current to travel, a connection, such as a wire or conductor, is required.

Utilizing previously well-known variables, this uniform convenience, or all crucial elements from a prior flexible study that followed a particular methodology event can all be used to achieve the goal. It will be possible to contact the entity again if the anticipated assertion outcome actually happens; if it doesn't, both important systems will surely miss the statement.

Here,

D. In order for a current to move, there must be an energy source, a recipient, and a connection.

Current is the movement of charged ions through a conductor, most frequently electrons.

The energy required to transport the charged particles is provided by an energy source, such as a battery or generator.

The current has a route through a recipient, which can be a machine or a circuit.

In order to finish the circuit and enable the current to travel, a connection, such as a wire or conductor, is required.

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Answer:

Step-by-step explanation:

Fractions are parts or pieces of a complete thing.

In this problem, the fractions start out with varying denominators, and then end with the same denominator.  In order to go from different denominators to the same denominator, we must find a common denominator.

A common denominator is a number that denominators of fractions can equal when multiplied by something else.  Ex:  1/3 + 2/ 7  Multiples of 3:  3, 6, 9, 12, 15, 18, 21   Multiples of 7:  7, 14, 21.  Both 3 and 7 have 21 in common, so this would be the common denominator.

A common denominator is needed so fractions with different denominators can be combined.  To get from 6, 3, and 7 to 42, the multiples of 2, 3, and 7 must be listed.

Multiples of 6:  6, 12, 18, 24, 30, 36, 42

Multiples of 3:  3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 29, 42

Multiples of 7:  7, 14, 21, 28, 35, 42

All three numbers have 42 in common, so that is their common denominator.  Whatever was done to the denominator, must be done to the numerator.  Now, we must take the number that can be multiplied by the denominator to reach 42 and multiply it by the numerator.

[tex]\frac{1*7}{6*7}}[/tex]

[tex]=\frac{7}{42}[/tex]

[tex]\frac{2*14}{3*14}[/tex]

[tex]=\frac{28}{42}[/tex]

[tex]\frac{3*6}{7*6}[/tex]

[tex]=\frac{18}{42}[/tex]

So, to sum it up, when trying to add fractions with different denominators, find a common denominator by listing multiples of the denominators and multiply the numerator by the number the denominator was multiplied by to get the common denominator.

The logic in this fraction addition problem is to find a common denominator for all the fractions and then add the numerators. In this case, the common denominator is the least common multiple of the denominators, which is 42.

Now that all the fractions have a common denominator of 42, we can add the numerators to get the final answer:

[tex]\begin{aligned} \sf \dfrac{1}{6} + \dfrac{2}{3} + \dfrac{3}{7} = \dfrac{7}{42} + \dfrac{28}{42} + \dfrac{18}{42} = \bold{\dfrac{53}{42}} \end{aligned}[/tex]

Therefore, the sum of the fractions is 53/42.

I hope this helps!