Three students, Arianna, Zachary, and Audrey, line up one behind the other. How
many different ways can they stand in line?

To convert 2/5 to a fraction, it is already a fraction in its simplified form, so we can leave it as is.

To convert 2/5 to a decimal, we can divide the numerator (2) by the denominator (5):

2 ÷ 5 = 0.4

Therefore, 2/5 is equivalent to the fraction 2/5 and the decimal 0.4.

The statement “For a set of decimals, the longest numeral will belong to the largest number” is false because it doesn't determine the value of a number.

In Mathematics and statistics, a numerical data can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.

In Mathematics and statistics, a numeral simply refer to the symbol and numerical figure that is used for representing or denoting a numerical data (number).

For instance, by using the numerical data (numbers) 8 and 9;

8 is represented as VIII in Roman numerals while 9 is represented as IX in Roman numerals. However, the numeral VIII for 8 is longer than the numeral IX for 9, but IX for the number 9 is greater than VIII for the number 8.

In conclusion, we can logically deduce that the given statement is false.

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Complete Question:

Is the statement “For a set of decimals, the longest numeral will belong to the largest number” true or false?

The diameter of the tin is 2/5D and the circumference of the tin is 0.4πD

Given the the scale factor of dilation is

Container = 2/5 smaller than in reality

This means that

Scale factor = 2/5

So, we have

Diameter = 2/5D where D = diameter in reality

Also, we have

Height = 2/5H where H = height in reality

The circumference is then calculated as

C = πD

So, we have

C = π * 2/5D

Evaluate

C = 0.4πD

Hence, the circumference is 0.4πD

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Complete question

The Ricoffy tin container with no dimensions indicated.The container is 2,5 times smaller than what it is in reality

Diameter of the tin on the picture = ? Height of the tin on the picture = ? Actual weight of coffee = 750 g 1.1 Measure the diameter of the tin in mm and write down the real diameter in mm​

1. Option a, c and e fulfill the Pythagorean triplet rule.

2. Option a, e, and f are the correct options.

3. Yes as per the Pythagoras theorem, all the sides will be proportional to the similar triangle.

The formula for the Pythagoras theorem is written as c² = a² + b², where c is the hypotenuse of the right triangle and a and b are its other two legs.

As a result, the Pythagoras equation can be used to any triangle that has one angle that is exactly 90° to create a Pythagoras triangle.

In question 1,

The Pythagorean triplets we have are:

5, 12, 13 as they fulfill the c² = a² + b², formula.

5, 10, 5√5 and 20, 99, 101

In the second question, we have the triplet 7, 24, 25

So the triangles similar to this will have proportionate sides.

So 14, 48, 50(sides have been doubled)

√7, √24, √25 (sides have been square rooted) and

35, 120 and 125(sides have been multiplied by 5)

are the sides that are proportional.

In the last question,

If the triangle has Pythagorean triplets, then for the other triangle to be similar the sides has to be multiples of the triplets or proportionate to them.

In this case its true, so the triangles are similar to each other.

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Answer:

We can use the formula for compound interest to find the balance in Eliana's savings account after 10 years:

A = P(1 + r/n)^(nt)

where A is the balance, P is the principal (initial deposit), r is the annual interest rate as a decimal, n is the number of times interest is compounded per year, and t is the time in years.

Substituting the given values, we get:

A = $700(1 + 0.04/12)^(12*10)

Simplifying, we get:

A = $700(1.0033333)^120

Using a calculator, we get:

A ≈ $1,038.81

Therefore, the balance in Eliana's savings account after 10 years is approximately $1,038.81.

Answer:

Let x be the cost of 1 kg of mushrooms and y be the cost of 1 kg of turnips.

From the given information, we can form two equations:

2x + 2.5y = 8.55 (Equation 1)

3x + 4y = 13.10 (Equation 2)

To solve for x and y, we can use the method of elimination. Multiplying Equation 1 by 4 and Equation 2 by -2, we get:

8x + 10y = 34.20 (Equation 3)

-6x - 8y = -26.20 (Equation 4)

Adding Equation 3 and Equation 4, we get:

2x + 2y = 8

Simplifying this equation, we get:

x + y = 4 (Equation 5)

Now we have two equations: Equation 2 and Equation 5. We can solve for x and y using substitution or elimination. Here, we will use substitution.

From Equation 5, we can express x in terms of y as:

x = 4 - y

Substituting this expression for x into Equation 2, we get:

3(4 - y) + 4y = 13.10

Simplifying and solving for y, we get:

y = £1.50

Substituting this value for y into Equation 5, we can solve for x:

x + £1.50 = 4

x = £2.50

Therefore, the cost of 1 kg of mushrooms is £2.50 and the cost of 1 kg of turnips is £1.50.

a) The cost of 1 kg of turnips is £1.50.

b) The cost of 1 kg of mushrooms is £2.50.

Combining the like terms of the expressions (x² - 4x+9)-(3x² - 6x-9) gives -2x² + 2x + 36

Algebraic expressions are simply described as those mathematical expressions that are known to consist of certain variables, coefficients, terms, factors and constants.

Algebraic expressions are also identified with arithmetic operations. These arithmetic operations are;

From the information given, we have;

(x² - 4x+9)-(3x² - 6x-9)

First, expand the bracket

x² - 4x + 9 - 3x² + 6x + 27

Now, collect the like terms

x²- 3x² - 4x + 6x + 9 + 27

Add or subtract

-2x² + 2x + 36

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Answer:

260

Step-by-step explanation:

First you find the area of the triangle

1/2×base×height

1/2×20×10

=100

Then you find the area of the rectangle

A=l×b

=20×8

=160

Then you add the area of the triangle with the area of the rectangle

160+100=260

The cost per ride is $1.50: True.

The situation can be represented by the equation y = 15x + 15: False, it can be be represented by y = 1.5x + 15.

The initial entrance fee was $15: True.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the slope formula, we have the following;

Slope (m) = (18 - 15)/(2 - 0)

Slope (m) = 3/2

Slope (m) = 1.50.

At data point (0, 15), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 15 = 1.50(x - 0)

y - 15 = -1.50(x)

y = 1.50(x) + 15

When x = 0, the y-intercept is given by;

y = 1.50(x) + 15

y = 1.50(0) + 15

y = 15.

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Answer:

$12.00

Step-by-step explanation:

We know that 1 pound = 16 oz.  Thus, we can create a proportion to find how many ounces (x) is 2.5 pounds:

[tex]\frac{1}{16}=\frac{2.5}{x}\\ x=(2.5*16)\\ x=40[/tex]

Since 2.5 pounds = 40 oz, we can now multiply 40 by 0.30 to find the price of 40 ounces of peacans priced at $0.30/ounce:

40 * 0.30 = $12.00

Answer:

40 5/8

Step-by-step explanation:

6 1/2 × 2 1/2

13/2 × 5/2= 65/4

65/4 × 2 1/2

65/4 × 5/2 = 325/8

325/8= 40 5/8

Answer:

40 5/8

Step-by-step explanation:

6 1/2 × 2 1/2

13/2 × 5/2= 65/4

65/4 × 2 1/2

65/4 × 5/2 = 325/8

325/8= 40 5/8

The factοrs οf the expressiοn is 4x(2xy+3y-4z).

Tο factοrise an algebraic statement, we first identify the terms' highest cοmmοn factοrs and then arrange the terms intο grοups in accοrdance with thοse grοups. In plain English, factοrizatiοn is the prοcess thrοugh which an algebraic expressiοn gets expanded in the οppοsite directiοn.

Here the given expressiοn is ,

=> [tex]8x^2y+12xy-16xz[/tex]

Nοw factοrizing the given expressiοn then,

=> 4×2×x×x×y+4×3×x×y-4×4×x×z

=> 4x(2xy+3y-4z)

Hence the factοrs οf the expressiοn is 4x(2xy+3y-4z).

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Hence, the angles' measurements are as follows: ∠1 = 147° , ∠2 = 33° and ∠3 = 147° as Interior angles on the same side of the transversal.

A geometric shape known as an angle is created by two rays or line segments that have a shared termination, or vertex. Angles, which express how much of a turn or rotation there is between two rays or line segments, are measured in degrees or radians. They are frequently employed in physics, engineering, geometry, trigonometry, and other disciplines.

given

The characteristics of parallel lines and transversals allow us to determine that:

Interior angles on the same side of the transversal: 1 + 2 = 180°; 2 + 3 = 180°.

We know that (1) = 147°, thus we can apply the first equation to determine 2:

∠1 + ∠2 = 180°

147° + ∠2 = 180°

∠2 = 33°

We can apply the second equation to determine 3 now that we know 2:

∠2 + ∠3 = 180°

33° + ∠3 = 180°

∠3 = 147°

Hence, the angles' measurements are as follows: ∠1 = 147° , ∠2 = 33° and ∠3 = 147° as Interior angles on the same side of the transversal.

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The fact that Jeri drew a polygon with precisely three sides serves as the representation of this claim.

A polygon is a closed shape made of line segments rather than curves on a two-dimensional plane.

A minimum of three line segments need to be joined end to end to produce a closed figure. As a result, a triangle and a 3-gon are both terms for a polygon with at least three sides.

The polygons are divided into many categories based on the sides and angles, including:

In this instance, Jeri's drawing of a polygon with precisely three sides serves as the symbolic expression of this argument.

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The number of triangles formed or the interior angle sum to each regular polygon:

Number of triangles formed is 4 - Regular octagon

Interior angle sum is 1,440 - Regular dodecagon

Interior angle sum is 1,800 - Regular decagon

Number of triangles formed is 6 - Regular hexagon

A triangle is a geometric shape that consists of three straight line segments that are connected to form three angles. The three line segments are called sides and the three angles are located at the vertices (corners) where the sides meet.

Here,

The number of triangles formed in a regular polygon is related to the number of sides it has. For a regular polygon with n sides, the number of triangles formed is (n-2). For example, a regular hexagon has six sides, so the number of triangles formed is (6-2) = 4. The interior angle sum of a regular polygon is related to the number of sides it has as well. The formula to find the interior angle sum of a regular polygon with n sides is: Interior angle sum = (n-2) x 180 degrees

For example, a regular dodecagon has 12 sides, so its interior angle sum is (12-2) x 180 = 1,800 degrees. Similarly, a regular octagon has 8 sides, so its interior angle sum is (8-2) x 180 = 1,080 degrees.

Therefore, based on the given information, we can match the number of triangles formed and the interior angle sum to each regular polygon as follows:

Regular octagon: Number of triangles formed is 4 (column 1) and Regular octagon is matched to 1 (column 2).

Regular hexagon: Number of triangles formed is 6 (column 1) and Regular hexagon is matched to 2 (column 2).

Regular decagon: Interior angle sum is 1,800 (column 1) and Regular decagon is matched to 3 (column 2).

Regular dodecagon: Interior angle sum is 1,440 (column 1) and Regular dodecagon is matched to 4 (column 2).

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As a result, the two new streets formed by reflecting and translating the expression original streets will be parallel and 5 units apart, with one to the left.

In mathematics, an expression is a group of representations, digits, and conglomerates that resemble a statistical correlation or regimen. An expression can be a real number, a mutable, or a combination of the two. Addition, subtraction, rapid spread, division, and exponentiation are examples of mathematical operators. Arithmetic, mathematics, and shape all make extensive use of expressions. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.  

If we reflect the line segment that represents Maple Street in the y-axis, the resulting street will be to the left of the y-axis, and if we translate it down 5 units, the new street will be parallel to but 5 units below the original Maple Street. Similarly, reflecting the line segment that represents Hazel Street in the y-axis results in a street to the right of the y-axis, and translating it down 5 units results in a new street parallel to the original Hazel Street but 5 units below it.

As a result, the two new streets formed by reflecting and translating the original streets will be parallel and 5 units apart, with one to the left.

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Step-by-step explanation:

Semi-annual means an interest period is 1/2 year

    1/2 *8% = 4% = .04

       effective annual interest rate is then

                    (1+ .04)^2  - 1  = .0816   or  8.16    (%)

a. The total length of cloth required to make shirts for 15 students is 345 meters.

b. At least 23 meters of cloth to make one shirt

c. The length of cloth required for one shirt in decimal form is 23.00 meters.

d. 13.25 meters of cloth is left after making 1 shirt from a piece of cloth that is 36.25 meters long.

What is total length?

Whole Length (TL) is the measurement taken in a straight line, with the fish lying on its side, from the tip of the snout to the end of the tail (caudal fin).

(a) Total cloth required = 15 × 23 meters = 345 meters

Therefore, the total length of cloth required to make shirts for 15 students is 345 meters.

(b) Number of shirts = 9.5 meters ÷ 23 meters/shirt ≈ 0.413

Therefore, only 0 shirts can be made from a piece of cloth 9.5 meters long. We need at least 23 meters of cloth to make one shirt.

(c) 23 meters = 23.00 meters

Therefore, the length of cloth required for one shirt in decimal form is 23.00 meters.

(d) Number of shirts = 36.25 meters ÷ 23 meters/shirt ≈ 1.576

The amount of cloth left over after making 1 shirt is:

Cloth left over = 36.25 meters - 23 meters = 13.25 meters

Therefore, 13.25 meters of cloth is left after making 1 shirt from a piece of cloth that is 36.25 meters long.

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Answer:

Step-by-step explanation:

According to the solving the area of the sidewalk is 138.16 square meters.

Size of a location on a surface is expressed in terms of area. As opposed to surface area, which refers to the area of an open surface or the border of a three-dimensional object, plane region or plane size refers to the area of a shape or planar lamina.

The width of the circular sidewalk is 2 m, which means that the radius of the entire area, including the flower bed and the sidewalk, is 10 m + 2 m = 12 m.

To find the area of the sidewalk, we need to subtract the area of the flower bed from the area of the larger circle.

Area of larger circle = πr²

= 3.14 x 12²

= 452.16 square meters (rounded to two decimal places)

Area of flower bed = πr²

= 3.14 x 10²

= 314 square meters

Area of the sidewalk = Area of larger circle - Area of flower bed

= 452.16 - 314

= 138.16 square meters (rounded to two decimal places)

Therefore, the area of the sidewalk is 138.16 square meters.

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Answer:

Step-by-step explanation:

to find the the answer you need to put it on the graph then find the thing you need to do to find out the correct answer

The point on the graph that tells you the amount of sugar you'll use if you don't make any pies is (0, 0).

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

In order to have a proportional relationship, the variables representing the amount of sugar and time must have the same constant of proportionality:

Constant of proportionality, k = y/x

Constant of proportionality, k = 4/3

Constant of proportionality, k = 12.

Therefore, the required equation is given by:

y = kx

y = 4x/3

When x = 0, the value of y is given by:

y = 4(0)/3

y = 0 pies.

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The probability of the maximum number of black hats that could be present in the group is 2.

Since the probability of selecting a student with a green hat is the highest, it is likely that there are more green hats than any other color. Let's assume that there are 7 green hats. If there are 7 green hats, then there are only 5 hats left for the remaining colors. However, we know that there are only 2 red hats and 1 blue hat, leaving a maximum of 2 hats for the black color. Therefore, the greatest possible number of black hats in the group is 2, which would give a total of 2 red hats, 1 blue hat, 7 green hats, and 2 black hats. In conclusion, if the probability of selecting a student with a green hat is the highest, then the greatest possible number of black hats in the group is 2.

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Answer: X=55 and Y=125

Step-by-step explanation:

y is an external angle

so according to external angle property sum of two angles is equal to external angle. two angles are given- 35 and 90

90+35=y

y=125

now with angle sum property

90+35+x=180

125+x=180

x=55

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The linear equation that models the number of pages that he reads is:

y = 56*x

So we know that Mark reads 42 pages every 3/4 of an hour, and we want to write an equation that models the number of pages y that mark reads in x hours, to do so we needto get the unit rate.

Take the quotient between the number of pages and the time above to get:

u = (42 pages)/(3/4 hours) = 56 pages per hour.

Then the number of pages that he can read in x hours is modeled by the linear equation:

y = 56*x

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A 95% confidence interval that the t population mean number of books  is between 9.89 and 11.11 books.

What is confidence interval ?

A confidence interval is a statistical range that provides an estimate of the likely range of values for a population parameter (such as a mean, proportion, or standard deviation) based on a sample of data. It is calculated using a specific level of confidence, which represents the probability that the true population parameter falls within the calculated range.

Confidence intervals are typically expressed as a range of values with a margin of error or standard error. The margin of error represents the amount of random variation that is expected due to sampling error, while the standard error reflects the variability of the sample data.

According to the question:
C. There is 95% confidence that the population mean number of books read is between a lower bound of approximately 9.89 books and an upper bound of approximately 11.11 books.

To construct the confidence interval, we can use the formula:

[tex]CI =\bar x \± z* (s/\sqrt{n})[/tex]

substitute the values, we get:

CI = 10.5 ± 1.96 * (16.6/√1015)

CI = (9.89, 11.11)

This means that we are 95% confident that the  population mean number of books is between 9.89 and 11.11 books.

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The equation that represents dividing the rectangle into two equal parts is:

W * L/4 = A/2

Assuming that we want to divide the rectangle into two equal parts by a straight line passing through its center, we can represent the rectangle's dimensions as follows:

Let L be the length of the rectangle, and let W be its width. Then the area of the rectangle is A = L * W.

Therefore, to divide the rectangle into two equal parts, we need to draw a line that passes through the center of the rectangle and divides it into two parts with equal areas.

Let x be the distance of the dividing line from one of the shorter sides of the rectangle. Then, the length of the two parts of the rectangle is equal, which means:

L/2 - x = x

Solving for x, we get:

x = L/4

Therefore, the equation that represents dividing the rectangle into two equal parts is: W * L/4 = A/2

This equation says that if we take the width of the rectangle and multiply it by one-fourth of its length, we get half of the rectangle's area, which represents dividing it into two equal parts.

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Answer:6^21

Step-by-step explanation: