Georgia loves to drop water balloons from her third-floor balcony into a dumpster located on the street below. Her brother filmed one balloon falling. He measured the height of the balcony rail. Then he used the video camera's time feature to figure out how far the balloon had traveled from Georgia's hand after each quarter of a second. He listed the times and distances in a table: Time 0.255 Distance 0.3 m 1.2 m 0.55 0.75 s 2.8 m 4.9 m 1.08 1.25 s 7.7 m 11.0 m 1.5 a . graph the distance the water balloon traveled over 1.5 seconds using the data georgia’s brother collected.

The percent of the US population lives in Exeter is 0.005%

A percentage is a number or ratio that can be expressed as a fraction of 100.

Given that, the population of Exeter is about 15 thousand people and the population of the United States is about 300 million people, we need to find what percent of the US population lives in Exeter

15,000 = 0.015 millions

The percentage of people who live in Exeter = 0.015 / 300 × 100

= 0.005%

Hence, the percent of the US population lives in Exeter is 0.005%

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The percent of the US population lives in Exeter is 0.005%, when the population of Exeter is about 15 thousand people. The population of the United States is about 300 million people.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

Given that, the population of Exeter is about 15 thousand people and the population of the United States is about 300 million people, we need to find what percent of the US population lives in Exeter

we know,

15,000 = 0.015 millions

now,

The percentage of people who live in Exeter = 0.015 / 300 × 100

                                                                           = 0.005%

Hence, the percent of the US population lives in Exeter is 0.005%

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The velocity of the car is given as follows:

2.83 m/s.

The kinetic energy is obtained as half the multiplication of an object's mass by the velocity squared of the object, that is:

K = 0.5mv².

The parameter values for this problem are given as follows:

K = 40000, m = 10000.

Hence the velocity of the car is obtained solving the equation for v as follows:

40000 = 0.5 x 10000v²

5000v² = 40000

v² = 8

v = square root of 8

v = 2.83 m/s.

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Answer:

Step-by-step explanation:

(64)5.45= 348.8    

Twelve dozen is referred to as a gross (122 = 144) and twelve gross (123 = 1,728, the duodecimal 1,000) is referred to as a great gross, a word most frequently used when shipping or purchasing products in bulk. The equivalent of 120 or ten dozen is a great hundred, commonly referred to as a small gross.

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Ratio: Because it has a meaningful zero point and allows for meaningful comparison of value differences, the volume of a backpack is a ratio level of measurement.

Ratio: A backpack's capacity is a ratio level of measurement because it has a meaningful zero point, or when an item (in this case, capacity) is absent, it has a value of zero. Additionally, it is possible to meaningfully compare value differences. As opposed to other levels of measurement like nominal or ordinal where the differences between two values may not be relevant, this means that differences in capacity between two backpacks may be compared properly.

For instance, the difference between two backpacks can be considered to be twice as great if one backpack has a capacity of 20 litres and the other has a capacity of 40 litres (20 liters). Ratio is the most suitable level of measurement for a backpack's capacity since other levels of measurement cannot account for this disparity.

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Option D is correct. The sum of the first 14 terms of arithmetic series is -2126.

What is arithmetic series?

The sum of a succession of numbers, such as 1, 2, and so forth, is known as an arithmetic series. Each term is calculated from the preceding one by adding (or subtracting) a constant.

The sum of the first 14 terms in the arithmetic series with first term (-18) and common difference (-9) can be calculated using the formula for the sum of an arithmetic series:

S_n = n/2 * (2a_1 + (n-1)d)

Plugging in the given values, we get:

S_14 = 14/2 * (2 * (-18) + (14 - 1) * (-9))

S_14 = 14/2 * (-36 + (13) * (-9))

S_14 = 14/2 * (-36 - 117)

S_14 = 14/2 * -153

S_14 = -2126

Therefore, the sum of the first 14 terms is -2126.Option D is correct.

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Option D is correct. The sum of the first 14 terms of the arithmetic series is -2126.

What is arithmetic series?

The sum of a succession of numbers, such as 1, 2, and so forth, is known as an arithmetic series. Each term is calculated from the preceding one by adding (or subtracting) a constant.

The sum of the first 14 terms in the arithmetic series with the first term (-18) and common difference (-9) can be calculated using the formula for the sum of an arithmetic series:

S_n = n/2 * (2a_1 + (n-1)d)

Plugging in the given values, we get:

S_14 = 14/2 * (2 * (-18) + (14 - 1) * (-9))

S_14 = 14/2 * (-36 + (13) * (-9))

S_14 = 14/2 * (-36 - 117)

S_14 = 14/2 * -153

S_14 = -2126

Therefore, the sum of the first 14 terms is -2126. Option D is correct.

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The United States has the comparative advantage in producing footballs, while Canada has the absolute advantage in producing lumber. If the two countries specialize and trade, the United States produces 1000 footballs and Canada produces 8 tons of lumber.

(a)US Production Possibility Frontier:

Football (1000)  |  0  |  200  |  400  |  600  |  800  |  1000

Lumber (10)     | 10  |  8   |   6   |   4   |   2   |    0

Canadian Production Possibility Frontier:

Football (400)  |  0  |  100  |  200  |  300  |  400

Lumber (8)      | 8   |  7   |   6   |   5   |   4

(b) In autarky, if the United States wants to consume 500 footballs, it can consume at most 4 tons of lumber. This point is labeled A in the diagram. Similarly, if Canada wants to consume 1 ton of lumber, it can consume at most 300 footballs. This point is labeled C in the diagram.

(c) Canada has the absolute advantage in lumber production.

(d) The United States has the comparative advantage in lumber production.

(e) If each country specializes in the good in which it has the comparative advantage and there is trade, the United States produces 1000 footballs and Canada produces 8 tons of lumber.

(f) Yes, it is possible for the United States to consume 500 footballs and 7 tons of lumber. This point is labeled B in the diagram. It is not possible for Canada to consume 500 footballs and 1 ton of lumber at the same time. This point is labeled D in the diagram.

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Mountville High did 8 goals on Tuesday & 14 goals on Thursday. Here is the explanation below :

Given

Mountville High opponents total score - 14

Tuesday match won by Mounville High - 4 goals

Thursday match won by Mountville High - 4 goals

Mountville High total score on Thursday & Tuesday - 14+4+4 = 22

Let assume the Tuesday score of Mountville High - x

Thursday score of Mountville High- x+6

Here the solution below :

Tuesday score + Thursday Score = Total score

x+x+6 = 22

2x+6 = 22

2x = 22-6

2x = 16

x = 8

Tuesday Score of  Mountville High  - 8

Thursday Score of Mountville High - x+6 = 8 + 6 = 14

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Answer:

The radius of the circle when 0 = 90°, A = 20 cm² and when 0 = 30°, A = 35 cm² is 7 cm. This can be determined by using the information from byjus.com, which states that the Find the Value of X calculator is a free online tool that can be used to calculate the radius of a circle. Using the calculator, the radius of the circle when 0 = 90°, A = 20 cm² and when 0 = 30°, A = 35 cm² is 7 cm.

Step-by-step explanation:

According to medical research, teenagers' need to sleep,  (0.60, 0.70, and 0.80) is higher than 0.50, so they are less likely to occur.

The value of g that is least likely to occur is 0.50.

The article in the school newspaper claims that 50% of the 1,200 students at the high school are not getting enough sleep,

which would mean that P = 0.50.

However, the sample of 50 students is likely to differ from the population of 1,200 students,

So it's possible that the proportion of students in the sample who do not get enough sleep is different from 0.50.

The other values of g (0.60, 0.70, and 0.80) are higher than 0.50, so they are less likely to occur.

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The value of x is  log(49)/log(7³) in the equation  7³x+1 =49ˣ - 1

Two or more expressions with an Equal sign is called as Equation.

The given equation is 7³x+1 = 49^x-1​

7³ˣ + 1 = 49ˣ - 1

Take log on both sides

log(7³)ˣ + 1 = log(49)ˣ - 1

x log(7³) = x log(49)

x = log(49)/log(7³)

Hence, the value of x is  log(49)/log(7³) in the equation  7³x+1 =49ˣ - 1

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The solution of the equation is [tex]x = x^{1/3} + 80^{1/3}[/tex]

An equation is a mathematical statement that says that two things are equal. Solving an equation means finding the value of the variable that makes the equation true.

In this case, we want to solve for x in the equation x³ - x = 80.

To solve this equation, we can start by isolating the x terms on one side of the equation and the constant 80 on the other side.

To do this, we will add x to both sides of the equation to cancel out the subtraction of x on the left-hand side. The equation becomes

=> x³ = x + 80.

Next, we will take the cube root of both sides to isolate x on one side of the equation. The cube root of x³ is just x, so we get

[tex]x = x^{1/3} + 80^{1/3}[/tex]

Now, we have a simple equation in x and can use basic algebraic techniques to solve for x.

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Sketch lines through (0, 0) with slopes of 1 4, 1 2, 1 4, and 4 through the line with slope 4: y - 0 = 4 (x - 0), which reduces to y = 4x.

The slope of a line is a measure of its steepness or incline and is defined as the ratio of the rise (the vertical change) to the run (the horizontal change) between two points on the line. Slope is commonly represented as "m" in the equation of a line, y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).

The slope of a line can be calculated by dividing the difference in y-coordinates (rise) by the difference in x-coordinates (run) between two points on the line. If (x1, y1) and (x2, y2) are two points on the line, the slope is calculated as:

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

(b) To sketch the lines through (0,0) with slopes 1/4, 1/2, -1/4, and 4, we can use the point-slope form of a line: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. For each line, we can substitute the given slope and the point (0,0) to find the equation of the line:

Line with slope 1/4: y - 0 = 1/4 (x - 0), which simplifies to y = 1/4x

Line with slope 1/2: y - 0 = 1/2 (x - 0), which simplifies to y = 1/2x

Line with slope -1/4: y - 0 = -1/4 (x - 0), which simplifies to y = -1/4x

Line with slope 4: y - 0 = 4 (x - 0), which simplifies to y = 4x

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Sketch lines through (0, 0) with slopes of 1 4, 1 2, 1 4, and 4 through the line with slope 4: y - 0 = 4 (x - 0), which reduces to y = 4x.

The slope of a line is a measure of its steepness or incline and is defined as the ratio of the rise (the vertical change) to the run (the horizontal change) between two points on the line. Slope is commonly represented as "m" in the equation of a line, y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).

The slope of a line can be calculated by dividing the difference in y-coordinates (rise) by the difference in x-coordinates (run) between two points on the line. If (x1, y1) and (x2, y2) are two points on the line, the slope is calculated as:

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

(b) To sketch the lines through (0,0) with slopes 1/4, 1/2, -1/4, and 4, we can use the point-slope form of a line: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. For each line, we can substitute the given slope and the point (0,0) to find the equation of the line:

Line with slope 1/4: y - 0 = 1/4 (x - 0), which simplifies to y = 1/4x

Line with slope 1/2: y - 0 = 1/2 (x - 0), which simplifies to y = 1/2x

Line with slope -1/4: y - 0 = -1/4 (x - 0), which simplifies to y = -1/4x

Line with slope 4: y - 0 = 4 (x - 0), which simplifies to y = 4x

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Data categorization is a process of organizing and grouping data into meaningful classes or categories.

This process is often used to simplify data and make it easier to understand and analyze. Data categorization involves breaking down a large set of data into smaller, more manageable groups. For example, a company may group customers into categories based on their age, income, or location. Each group can then be analyzed separately to better understand customer behavior. Categorizing data can also help identify trends or patterns that may not be visible when looking at the data as a whole. Categorization can also be used to identify outliers or anomalies in the data. By breaking down the data into smaller groups, it becomes easier to see which elements don’t fit the pattern or are not part of the normal range. Categorizing data can be done using a variety of methods. For example, data can be divided into numerical ranges or grouped into categories such as low, medium, and high. Data can also be grouped using descriptive terms, such as customer type or product type. Once the data is categorized, calculations such as averages, medians, and modes can be used to analyze the data. This can help to identify patterns or trends that can be used to make decisions or draw conclusions.

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The value of RS would be 10.

What is an expression?

An expression is a mathematical phrase that can contain numbers, variables, and operators. It represents a value or a computation and can be evaluated to obtain a numerical result. For example, "2x + 3" is an expression where x is a variable and 2 and 3 are numbers, and the + and * symbols represent mathematical operations.

RS + ST = RT
x + 4 + 8 = 3x
3x - x = 12
2x = 12
x = 6

RS = x + 4
RS = 6 + 4

RS = 10

Hence, the value of RS would be 10.

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Answer:

average approximately 54

Step-by-step explanation:

215/4 = 53.75

assuming she's a robot & doesn't get tired LOL

Correct option is D, The greatest perimeter of hyperbola is in (D) ⇒ the perimeter = 60 units

When using hyperbola,

- A hyperbola's standard form of the equation with

transverse axis parallel to the x-axis and the center (h, k) are

[tex]\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2}[/tex]equals one.

The transverse axis' length is 2a.

The conjugate axis' length is 2b.

The asymptote rectangle's circumference is 2(2a + 2b).

* Let's review the results to determine the largest perimeter.

A)[tex]\frac{ (x - 4)^2}{11^2} - \frac{(y + 2)^2}{3^2} = 1[/tex]

* Compare it to the equation in standard form.

∵ a = 11 ⇒ 2a = 22

∵ b = 3 ⇒ 2b = 6

The circumference is 2(22 + 6) = 56.

B) [tex]\frac{(x - 2)^2}{4^2} - \frac{(y + 1)^2}{10^2} = 1[/tex]

* Compare it to the equation in standard form.

∵ a = 4 ⇒ 2a = 8

∵ b = 10 ⇒ 2b = 20

The circumference is 2(8 + 20) = 56.

C) [tex]\frac{(x + 5)^2}{5^2} - \frac{(y - 3)^2}{9^2} = 1[/tex]

* Compare it to the equation in standard form.

∵ a = 5 ⇒ 2a = 10

∵ b = 9 ⇒ 2b = 18

The circumference is 2(10 + 18) = 56.

D) [tex]\frac{(x - 7)^2}{8^2} - \frac{(y - 2)^2}{7^2} = 1[/tex]

* Compare it to the equation in standard form.

∵ a = 8 ⇒ 2a = 16

∵ b = 7 ⇒ 2b = 14

The circumference is 2(16 + 14) = 60.

* The largest boundary is in (D)

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b = 2 does not make the equation true

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

15 = 5b

when b=2,

15=5(2)

15 = 10

This is not true

So, b = 2 does not make the equation true

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The output of the given code will be: 15, 2, 15, -5.

The given code declares two integer variables max and min, with min initialized to 10. The expression 17 - 4 / 10 is evaluated as 17 - 0, since integer division returns the floor value, which is 0 in this case.

The expression max = max - 6 then sets max to 17 - 0 - 6, which is equal to 11. The expression min = max - min then sets min to 11 - 10, which is equal to 1. Finally, the println statements print out the values of max * 2, max - min, max, and min. These values are 15, 2, 11, and 1, respectively.

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Both analytical and Euclidean geometry have strengths and applications, and which technique to choose depends on the individual problem or job at hand.

Analytical geometry, often known as coordinate geometry, represents and analyses geometric objects using mathematical ideas such as algebra and calculus. It is especially useful for analysing objects with a distinct numerical representation, such as lines, circles, and conic sections. Analytical geometry, which provides a systematic framework for modelling and analysing things in any number of dimensions, may readily be extended beyond two dimensions.

Euclidean geometry, on the other hand, studies geometric objects such as points, lines, and planes using a set of axioms and definitions. This method is very beneficial for learning geometric concepts like congruence, similarity, and structures. Euclidean geometry is also beneficial for problem solving that necessitates visualisation, intuition, and spatial reasoning.

Analytical geometry is more helpful in real-world applications such as computer graphics, where objects are represented using mathematical equations and algorithms. Euclidean geometry, on the other hand, is more beneficial in fields like architecture and engineering, where a greater knowledge of geometric principles and spatial reasoning is necessary.

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Answer:

[tex]3.3k+1.6m[/tex]

Step-by-step explanation:

Subtract [tex]3.2k[/tex] from [tex]6.5k[/tex].

The critical point (0, 9) is a minimum and (0, -9) is a maximum.

Lagrange multipliers are a method used to find the maximum and minimum values of a function subject to a constraint.

To use Lagrange multipliers, we first write the function and constraint as a system of equations.

For the function

=> f(x, y) = y² − x²

and the constraint

=> 14x²y² - 81,

the system becomes:

y² − x² = λ(14x²y² − 81)

Next, we find the partial derivatives of both equations with respect to x and y and set them equal to zero to find the critical points.

Solving for x and y, we find that (0, ±9) are the critical points.

If the value is zero, the critical point is a saddle point.

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The mean value theorem does not apply to functions that are not continuous on a closed interval [a, b], or not differentiable on an open interval (a, b).

The mean value theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a point c in the interval (a, b) such that:

f'(c) = (f(b) - f(a)) / (b - a)

For example, the function f(x) = |x| is continuous everywhere, but it is not differentiable at x = 0. The interval [0, 1] does not satisfy the conditions for the mean value theorem to apply.

So, a possible function and interval for which the mean value theorem does not apply is f(x) = |x| on the interval [0, 1].

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Answer:

2

Step-by-step explanation:

Given expression is

[tex]\mbox{\large \left(\dfrac{4^{\frac{5}{4}}\cdot \:4^{\frac{1}{4}\:}}{4^{\frac{1}{2}}}\right)^{\frac{1}{2}}}[/tex]

Let's take the term in parenthesis and simplify

[tex]\dfrac{4^{5/4} \cdot 4^{1/4}}{4^{1/2}}[/tex]

Numerator [tex]4^{5/4} \cdot 4^{1/4}[/tex] can be simplified to [tex]4^{5/4 + 1/4} = 4^{6/4} = 4^{3/2}\\\\[/tex]

The entire expression on parentheses becomes:
[tex]\dfrac{4^{3/2}}{4^{1/2}} = 4^{3/2 - 1/2} = 4^1 = 4\\[/tex]

Therefore
[tex]\left(\dfrac{4^{\frac{5}{4}}\cdot \:4^{\frac{1}{4}\:}}{4^{\frac{1}{2}}}\right)^{\frac{1}{2}}} = (4)^\dfrac{1}{2} }= \sqrt{4} = 2[/tex]

So the entire expression simplifies to 2

The expression  [tex](\frac{4^\frac{5}{4}.4^\frac{1}{4} }{4^\frac{1}{2} })^\frac{1}{2}[/tex] is equivalent to 2, option C is correct.

An expression is combination of variables, numbers and operators.

The given expression is [tex](\frac{4^\frac{5}{4}.4^\frac{1}{4} }{4^\frac{1}{2} })^\frac{1}{2}[/tex]

Let us solve the numerator in parenthesis

[tex]4^\frac{5}{4}.4^\frac{1}{4}[/tex]

When bases are same then powers will be added

[tex]4^{\frac{3}{2} }[/tex]

So the expression will be [tex](\frac{4^\frac{3}{2}}{4^\frac{1}{2} })^\frac{1}{2}[/tex]

[tex](4^\frac{3}{2}} ^-^\frac{1}{2} )^\frac{1}{2}[/tex]

We get [tex]4^\frac{1}{2}[/tex]

√4=2

Hence, the expression  [tex](\frac{4^\frac{5}{4}.4^\frac{1}{4} }{4^\frac{1}{2} })^\frac{1}{2}[/tex] is equivalent to 2, option C is correct.

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E(aX + b) = aE(X) + b, which shows that E(ax + b) = aE(X) + b, as stated.

What is integration ?

An integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration.

This statement can be shown using the linearity property of expectation. According to this property, if X is a random variable and a, b are constants, then E(aX + b) = aE(X) + b.

Applying this property, we have:

E(aX + b) = aE(X) + b

= a(E(X) + b/a)

= aE(X) + ab/a

= aE(X) + b

So, E(aX + b) = aE(X) + b, which shows that E(ax + b) = aE(X) + b, as stated.

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The total amount that Noah paid for the cartridge is $30.35

A sales tax is one that applies to the purchase of goods and services for consumers and to the sale of goods and services for businesses.

Given that, Noah bought a computer cartridge for $28.50. Sales tax on the cartridge was 6.5%.

We need to find the total amount that Noah paid for the cartridge,

Total amount = sales tax + original cost

Total amount = 6.5% of 28.50 + 28.50

= 6.5 / 100 × 28.50 + 28.50

= 30.35

Hence, the total amount that Noah paid for the cartridge is $30.35

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By "graph representation," we only mean the process of storing a particular graph in a computer's memory.

An adjacency matrix is used in sequential representation to show how the graph's vertices and edges map to one another. The undirected graph, directed graph, weighted directed graph, and weighted undirected graph may all be represented using an adjacency matrix.

Edges in a directed graph represent a particular route between two vertex locations. If a path connects vertex A to vertex B, then vertex A serves as the starting point and vertex B serves as the ending point.

It is similar to an adjacency matrix representation of a directed graph except that instead of using the '1' for the existence of a path, here we have to use the weight associated with the edge.

Correct question: What is graph traversal and representation for the graph? write down the adjacency list representation.

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By using the concept of permutations and combinations, we can conclude that the shop can create 150 different sandwiches

We are given a deli that offers 5 fillings, 6 types of bread, and 5 condiments. Also, each sandwich consists of a filling, a type of bread, and a condiment.
We are asked to find the number of different sandwiches that the shop can create.

Here, we are gonna use the concept of permutations and combinations.

Number of different fillings = 5

Number of different beads = 6

Number of different condiments = 5

Number of different sandwiches = Number of different fillings x Number of different beads x Number of different condiments = 5

                                     = 5 x 6 x 5

                                     =  150 sandwiches

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Answer:

19 feet

The length of the storage area is 19 feet.

Step-by-step explanation:

Volume of a rectangular prism (a box shape) is given by:

Volume = length * width * height

We are given three out of four of these numbers. Fill them in and solve for the missing number.

570 = x * 6 * 5

570 = 30x

divide by 30

19 = x

The length is 19 feet. The storage area is 19 feet long.

Answer:

19 feet

Step-by-step explanation:

because I took this question already