COFFEE A national coffee chain makes and serves 4 billion cups of coffee in a year. If the average cup of coffee costs $3.15, how much money does the coffee chain make in a year? Write your answer in scientific notation.

The volume of the solid with base bounded by the semi-circle and the x-axis whose cross sections perpendicular to the x-axis are squares is equal to 8π/3.

To find the volume of the solid with base bounded by the semi-circle and the x-axis whose cross sections perpendicular to the x-axis are squares is shown below.

The diagram shows that the cross-sectional area of the solid is a square of side x whose area is x². Since the base of the solid is bounded by the semi-circle and the x-axis, the radius of the semi-circle is equal to the side of the square as shown in the diagram.

The diameter of the semi-circle is equal to the width of the rectangle whose height is x, that is:2r = x

Substituting the value of r in terms of x in the formula for the area of a semi-circle, we have: A = πr²/2 = π(x/2)²/2 = πx²/8

Therefore, the volume of the solid is given by: V = ∫₀^4 πx²/8 dx

The limits of integration are from 0 to 4 since the semi-circle has a diameter of 4 units, which is equal to the width of the square whose area is the cross-sectional area of the solid.

Integrating, we have: V = [πx³/24]₀⁴V = (π/24) x (4³ - 0³) = (π/6) x 16 = 8π/3.

Therefore, The volume of the solid is 8π/3.

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The answer of the given question based on the greatest value is One such number is 3,043,728.

A number system is a system of representing and expressing numbers in a clear, concise, and organized way. The most commonly used number system is the decimal system, which is based on the numbers 0 through 9. However, there are many other number systems, including binary, octal, hexadecimal, and more.

Each number system has a set of rules and conventions for representing numbers. For example, in the decimal system, each digit can represent a value from 0 to 9, and the position of each digit determines its value.

The digit 3 in 143,728 has a value of 3 x 1000 = 3000. To find a number in which the digit 3 has a value that is 10 times as great as this, we need to find a number in which the digit 3 has a value of 10 x 3000 = 30,000.

One such number is 3,043,728. In this number, the digit 3 appears in the hundred thousands place, which means its value is 3 x 100,000 = 300,000. This is indeed 10 times as great as the value of the digit 3 in 143,728.

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The number 137 has the same relationship to the number 143 as the numbers 398,389,392, which have a digit 3 that is 10 times greater than the number 137.

A number's face value is the digit itself, while its place value is determined by its placement.

In order to answer the question, we must determine which of the following integers has a value for the digit 3 that is 10 times greater:

If we pay close attention, we can see that the number 137 has a third digit in its tens place while the number 143 has a third digit in its unit place. Additionally, there are 398,389,392, which has a digit 3 and is ten times bigger than the number 137.

These numbers will be written as follows if we now express their location and value in words:

143 = 1 × 100 + 4 × 10 + 3 × 1.

137 = 1 × 100 + 3 × 10 + 7 × 1.

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The complete question is:

In which number does the digit 3 have a value that is 10 times as great as the value of the digit 3 in 143,728? 137,982 142,398 292,389 392,097.

Answer:

Step-by-step explanation:

Okay so you've gotta start with the y-intersect. The line hits the y-axis at 7, so your B is 7 (y=mx+7).

Since the line is going down, it's a negative slope, so your m will be a negative (y=-mx+7)

The line matches up exactly with (1,4), which shows the line moving down 3 for every 1 movement to the right. That makes your equation for the line y=-3x+7 or y=-3/1x+7

Therefore, the area of P is 4 times bigger than the area of Q.

Area is a measure of the amount of two-dimensional space enclosed by a closed figure, such as a square, rectangle, circle, or triangle. It is typically measured in square units, such as square meters (m²) or square centimeters (cm²). The formula for finding the area of a figure depends on the shape of the figure. For example, the area of a rectangle is found by multiplying its length by its width, while the area of a circle is found by multiplying π (pi) by the square of its radius. Knowing the area of a figure can be useful in many situations, such as when calculating the amount of material needed to cover a floor or when determining the capacity of a container. It is also an important concept in geometry, where it is used to compare the sizes of different shapes and to solve problems involving the relationships between them.

Here,

The area of a circle is given by the formula A = πr², where A is the area and r is the radius.

For shape P, the area is:

A_P = (3/4)π(20²) = 300π

For shape Q, the area is:

A_Q = (1/3)π(15²) = 75π

To find how many times bigger the area of P is than the area of Q, we can divide the area of P by the area of Q:

A_P / A_Q = (300π) / (75π) = 4

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there are n(n-1)(n-2)/2 simple paths of nonzero length in a tree with n vertices, where two simple paths are regarded as the same if they have the same edges.

In a tree with n vertices, there are (n-1) edges, since a tree is a connected acyclic graph.

To count the number of simple paths of nonzero length in the tree, we can consider each vertex as a starting point for a path and count the number of possible paths from that vertex.

Starting from any vertex, there are at most (n-1) paths that can be formed by moving to any of the neighboring vertices. From each of these neighboring vertices, there are at most (n-2) paths that can be formed by moving to a new neighboring vertex (excluding the vertex that was just visited).

This process can be continued until there are no more vertices to visit. However, to avoid counting the same path twice, we should only consider paths that do not backtrack on themselves.

Therefore, the total number of simple paths of nonzero length in the tree is the sum of all simple paths that start from each vertex:

(number of paths starting from vertex 1) + (number of paths starting from vertex 2) + ... + (number of paths starting from vertex n)

Using the reasoning above, we can see that the number of paths starting from each vertex is at most (n-1) * (n-2), since each path can visit at most (n-2) additional vertices after the starting vertex, and there are at most (n-1) vertices to choose from as the next vertex on the path.

Therefore, the total number of simple paths of nonzero length in the tree is at most n(n-1)(n-2).

However, we have counted each simple path twice (once in each direction), so the actual number of distinct simple paths of nonzero length is half of this maximum value, which is:

n(n-1)(n-2)/2

So, there are n(n-1)(n-2)/2 simple paths of nonzero length in a tree with n vertices, where two simple paths are regarded as the same if they have the same edges.

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Lila's height is 0.89 + 0.19 = 1.08m.

What is height ?

Height typically refers to the measurement of an object or person from the base to the top, usually measured vertically. It is often used in reference to the physical dimension of a person or object, such as the height of a building, tree, or individual.

According to the question:

In the context of the given problem, height refers to the height of Fatima, Charlotte, and Lila.

Fatima is 1.27 meters tall, Charlotte is 0.89 meters tall, and Lila is taller than Charlotte by half the difference between Fatima's height and Charlotte's height.
The difference between Fatima's height and Charlotte's height is 1.27 - 0.89 = 0.38m.

Half of that difference is 0.38/2 = 0.19m.

So, Lila is taller than Charlotte by 0.19m.

Therefore, Lila's height is 0.89 + 0.19 = 1.08m.

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Answer:

1 1/3 pounds of American cheese is equivalent to 4/3 pounds of American cheese.

2 1/4 pounds of turkey is equivalent to 9/4 pounds of turkey.

2/3 pound of cheddar cheese is equivalent to 0.67 pounds of cheddar cheese.

So the cost of each item is:

American cheese: (4/3) x $6.99 = $9.32 (rounded to the nearest cent)

Turkey: (9/4) x $5.99 = $13.48 (rounded to the nearest cent)

Cheddar cheese: 0.67 x $3.99 = $2.67 (rounded to the nearest cent)

To find the total cost, we add up these amounts:

$9.32 + $13.48 + $2.67 = $25.47

Therefore, the customer paid $25.47 for all the items.

The Average cost, after calculations, comes up to 210/x + 2.

To find the following functions such as Revenue, Cost, Profit and Average cost, we have given the equations as below:

Number of DVD's sold each day: n(x) = x

Selling price for each DVD: p(x) = 8.5 - 0.02x  Daily fixed costs: f(x) = 210  Daily variable costs: v(x) = 2x

To Find the following functions:

a. Revenue = R(x) = the product of the number of DVD's sold each day and the selling price of each DVD.

b. Cost = C(x) = the sum of the fixed costs and the variable costs.

c. Profit = P(x) = the difference between revenue and cost

d. Average cost = C (x) C¯(x) = the quotient of cost and the number of DVD's sold each day.

Number of DVD's sold each day: n(x) = x

Selling price for each DVD: p(x) = 8.5 - 0.02x  Daily fixed costs: f(x) = 210  Daily variable costs: v(x) = 2x

a. Revenue = R(x) = the product of the number of DVD's sold each day and the selling price of each DVD.R(x) = n(x) × p(x) = x × (8.5 - 0.02x) = 8.5x - 0.02x2

b. Cost = C(x) = the sum of the fixed costs and the variable costs.C(x) = f(x) + v(x) = 210 + 2x = 2x + 210

c. Profit = P(x) = the difference between revenue and cost.P(x) = R(x) - C(x) = 8.5x - 0.02x2 - (2x + 210) = -0.02x2 + 6.5x

d. Average cost = C(x)C¯(x) = the quotient of cost and the number of DVD's sold each day. C¯(x) = C(x) / x = (210 + 2x)/x = 210/x + 2

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Ray's car will use 4.68 kiloliters of gasoline and travel 39.54 kilometers

Every week, Ray fills his car with 45 liters of gasoline. To calculate the total amount of gasoline used by Ray's car over two years, we must first convert liters to kiloliters. One kiloliter is equal to 1,000 liters, so 45 liters is equal to 0.045 kiloliters. Therefore, in two years, Ray's car will use 0.045 kiloliters x 104 weeks (2 years x 52 weeks per year) = 4.68 kiloliters of gasoline.

To calculate how many kilometers the car will travel with 4.68 kiloliters of gasoline, we need to know the car's fuel efficiency rating. Assuming the car has an average fuel efficiency rating of 8.5 kilometers per liter, we can calculate that the car will travel 8.5 kilometers x 4.68 kiloliters = 39.54 kilometers with 4.68 kiloliters of gasoline.

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In 1 km races, runner 1 on track 1 with time 2 min and 26.39 s appears to be faster than runner 2 on track 2 with 2 min and 26.53 s. The difference in the length of the tracks, ∆L = L₂ - L₁, is equals to the 0.95, to conclude that runner 1 is faster.

When a body is traveling and it displaces its place from one point to another point, then this displacement of the body for a period of time is known as the velocity of the body. For the calculation of the velocity, both magnitude and direction values should be known. Length of track 1 , L₁ = 1 km = 1000 m

Time of 1ˢᵗ runner, t₂= (2min, 26.39s)

= (2×60 + 26.39) seconds =146.39 s

Time of 2ⁿᵈ runner t₂ = (2min, 26.53s)

= (2×60 + 26.53) s = 146.53 seconds

By using the velocity equation, v = L₁ ×t₁

=> v = 1000 m/146.39 seconds

=> v = 6.8310 m/s

Now by using the same velocity we determine the length of 2ⁿᵈ track,v = L₂/ t₂

6.8310 m/s = L₂/ 146.53

=> L₂ = 146.53 ×6.8310 m/s

=> L₂ = 1000.95 m

So the difference in the length of the tracks, ∆L = L₂ - L₁

= 1000.95 m - 1000 m

= 0.95 m

Hence, required difference is 0.95 m.

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Complete question:

in 1 km races, runner 1 on track 1 (with time 2 min, 26.39 s) appears to be faster than runner 2 on track 2 (2 min, 26.53 s). however, length L₂ of track 2 might be slightly greater than length l of track 1. how large can L₂ - L₁ be for us to conclude that runner 1 is faster?

The correct option- The perpendicular bisector of AB has the slope -1/3.

The difference between the change in y-values and the change in x-values is known as the slope of a line. This figure represents the slope of a line.

Formula for slope m = (y2 - y1)/(x2 - x1)

Line segment AB coordinates :

A (1,5) and B (9,17).

Slope m1 = (17 - 5)/(9 - 5)

m1 = 12/4

m1 = 3

The line perpendicular to AB.

Let the slope of m2.

The relation between the slopes of perpendicular lines:

m1 x m2 = -1

3 x m2 = -1

m2 = -1/3.

Thus, the slope of the line perpendicular to the given line AB is found as:  -1/3.

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Complete question:

AB in the coordinate plane has endpoints with coordinates A (1,5) and B (9,17). Which of the following is true?

The perpendicular bisector of  AB has slope 3/2.

The perpendicular bisector of AB has slope -2/3.

The perpendicular bisector of AB  has slope -2/3.

The perpendicular bisector of AB has slope -1/3.

The newborn department allows more patients per nurse than the surgical department.

Number is a mathematical object used to count, measure, and label. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers. Numbers can be represented in a variety of ways, including words, symbols, or images. Additionally, numbers are used in many different areas, including science, engineering, finance, economics, and computing.

The newborn department allows more patients per nurse than the surgical department. This is because the newborn department follows a lower nurse-to-patient ratio. The graph for the newborn department shows that for every two nurses, there are three patients, while the table for the surgical department shows that for every one nurse, there are two patients. This means that the newborn department has a ratio of 1:1.5 nurses to patients, while the surgical department has a ratio of 1:2 nurses to patients. This means that the newborn department allows more patients per nurse than the surgical department.

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The newborn department allows more patients per nurse than the surgical department.

Number is a mathematical object used to count, measure, and label. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers. Numbers can be represented in a variety of ways, including words, symbols, or images. Additionally, numbers are used in many different areas, including science, engineering, finance, economics, and computing.

The newborn department allows more patients per nurse than the surgical department. This is because the newborn department follows a lower nurse-to-patient ratio. The graph for the newborn department shows that for every two nurses, there are three patients, while the table for the surgical department shows that for every one nurse, there are two patients. This means that the newborn department has a ratio of 1:1.5 nurses to patients, while the surgical department has a ratio of 1:2 nurses to patients. This means that the newborn department allows more patients per nurse than the surgical department.

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complete questions as follows-

The answer is option a: a survey in which people are asked to indicate how much they trust a number of different politicians using a scale of 1-5, with 1 being the least amount of trust. This is an example of quantitative research.

Quantitative research requires participants to quantify their feelings and opinions using numerical values. It involves measuring variables and collecting numerical data, which can then be analyzed statistically. In this case, the survey data can be analyzed to measure the amount of trust people have in politicians.

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Answer: The cost of each small candle is $3 and the cost of each large candle is $6.

Step-by-step explanation:

Let's use variables to represent the cost of each small candle and each large candle. Let's call the cost of each small candle "x" and the cost of each large candle "y".

We can set up two equations based on the information given:

4x + 1y = 18 (equation 1)

5x + 2y = 27 (equation 2)

We can solve for one variable in terms of the other by using one equation to eliminate one variable. Let's solve for "y" in terms of "x" by multiplying equation 1 by 2 and subtracting it from equation 2:

5x + 2y = 27

(8x + 2y = 36)

-3x = -9

Dividing both sides by -3, we get:

x = 3

Now that we know the cost of each small candle is $3, we can substitute that value into one of the equations to solve for the cost of each large candle. Let's use equation 1:

4x + 1y = 18

4(3) + 1y = 18

12 + y = 18

y = 6

Therefore, the cost of each small candle is $3 and the cost of each large candle is $6.

The vertical distance between (2, 11/3) and (2, -4/3) is -5 units.

The distance formula is a mathematical equation used to find the distance between two points in a plane. It is derived from the Pythagorean theorem and is expressed as:

d = √((x₂- x₁)²+ (y₂ - y₁)²)

The distance formula can also be extended to three-dimensional space by adding an additional term to the equation.

The two points (2, 11/3) and (2, -4/3) have the same x-coordinate, which means they lie on a vertical line. To find the vertical distance between these two points, we simply subtract their y-coordinates:

Vertical distance = (y-coordinate of second point) - (y-coordinate of first point)

= (-4/3) - (11/3)

= -15/3

= -5

Therefore, the vertical distance between (2, 11/3) and (2, -4/3) is -5 units. Since this is a negative value, it means that the second point is located 5 units below the first point.

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The probability of drawing a marble that is not blue is 7/9.

Probability is a measure of the likelihood or chance of a particular event or outcome occurring

There are a total of 8 + 6 + 12 + 10 = 36 marbles in the bag.

The probability of drawing a blue marble is 8/36, or 2/9.

To find the probability of not drawing a blue marble, we need to subtract the probability of drawing a blue marble from 1 (since the sum of the probabilities of all possible outcomes must equal 1).

So the probability of not drawing a blue marble is

1 - 2/9 = 7/9

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7/9

Step-by-step explanation:

Answer:

To find the vertex of the quadratic function y = -2x² - 4x - 5, we can use the formula:

x = -b/2a

where a = -2 and b = -4 are the coefficients of the quadratic term and the linear term, respectively.

x = -(-4)/(2*(-2)) = -(-4)/(-4) = 1

To find the y-coordinate of the vertex, we substitute x = 1 in the function:

y = -2(1)² - 4(1) - 5 = -2 - 4 - 5 = -11

Therefore, the vertex of the quadratic function is (1, -11).

Answer:

(-1, -3)

Step-by-step explanation:

There are no real solutions to the equation 0 = x² + 5, and the graph of y = x² + 5 does not intersect the x-axis.

To find the solutions of 0 = x² + 5, we need to find the values of x that make the equation true. One way to do this is by solving the equation algebraically using methods like factoring, completing the square, or using the quadratic formula.

We cannot use the graph of y = x² + 5 directly to find the solutions of 0 = x² + 5, since the graph shows the values of y that correspond to different values of x, not the values of x that satisfy the equation 0 = x² + 5. However, we can use the graph to help us visualize the solution to the equation.

Since 0 = x² + 5 is equivalent to x² = -5, we know that the solutions to the equation must be imaginary numbers, since the square of any real number is always non-negative. Therefore, there are no real solutions to the equation 0 = x² + 5, and the graph of y = x² + 5 does not intersect the x-axis.

In summary, we cannot use the graph of y = x² + 5 directly to find the solutions of 0 = x² + 5, but we can use the graph to see that the equation has no real solutions.

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The height of the image after being scaled down by 80% three times is 76.8mm, which is not within the required range for a U.S. passport photo.

Scaling is the process of increasing or decreasing the size of a picture by dividing or multiplying its dimensions. An picture is expanded when it is scaled up, and its size is decreased when it is scaled down. An picture is affected by scaling when its size and, consequently, appearance, are altered. An picture may become pixelated or fuzzy if it is scaled up or down excessively, and information may be lost if it is scaled down too much. The aspect ratio of an image—the proportion of its width to its height—can also be impacted by scaling. The picture could look stretched or squished if the aspect ratio is modified.

Given that the image is 150 mm in height.

Thus, 80% of the image is:

150mm x 0.8 = 120mm

The scaling is performed 3 times, thus:

120mm x 0.8 = 96mm

96mm x 0.8 = 76.8mm

Hence, the height of the image after being scaled down by 80% three times is 76.8mm, which is within the required range for a U.S. passport photo.

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The complete question is:

The mathematician William Jones is credited with first using the Greek letter π

The mathematician William Jones is credited with first using the Greek letter π to represent the ratio of a circle's circumference to its diameter in a 1706 publication. He wrote, "there is no other more proper than Pi," and thus the symbol caught on among mathematicians. However, it's important to note that the concept of pi and its calculation had been around for thousands of years prior to Jones' use of the symbol.

Ancient Egyptian, Babylonian, and Indian mathematicians all had methods for approximating pi, and Archimedes famously used a geometric method to calculate it to a high degree of accuracy in the third century BCE.

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If four students use different instruments to measure the length of the same pen, the measurement which implies the greatest precision is 160.0 mm. Correct option is A.

To determine which measurement implies the greatest precision, we need to look at the number of significant figures in each measurement. The greater the number of significant figures, the greater the precision of the measurement.

In this case, we have four measurements:

(a) 160.0 mm

(b) 16.0 cm

(c) 0.160 m

(d) 0.00016 km

We can see that all of these measurements represent the same length in different units, and they are all written with the same number of decimal places. However, the number of significant figures is different for each measurement.

Measurement (a) has four significant figures, while measurements (b), (c), and (d) each have three significant figures. Therefore, measurement (a) implies the greatest precision, since it has the most significant figures.

So, the answer is (a) 160.0 mm, which implies the greatest precision among the given measurements.

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Complete question is:

Four students use different instruments to measure the length of the same pen. Which measurement implies the greatest precision?

(a) 160.0 mm

(b) 16.0 cm

(c) 0.160 m

(d) 0.00016 km

(e) Need more information

Answer:

Step-by-step explanation:

We simply have to divide 900 by 50 to get us 18. Now multiply 18 by 0.5 to get an answer of 9 inches. Hope this helped!

For square a of perimeter 24 cm and square b has an area equal to one-fourth the area of the square a, the perimeter of square b is 12 cm.

Given that a square has a perimeter of 24 cm. And another square b has an area equal to one-fourth of the area of square a. To find the perimeter of square b, we need to find the length of the side of square b using the area of square

Area of the square a = side² of the square a
The perimeter of the square a = 4 × side of the square a

Given that, Perimeter of square a = 24 cm⇒ 4 × side of square a = 24 cm⇒ side of square a = 24 / 4 cm⇒ side of square a = 6 cm.

Area of square b = 1/4 × Area of square a = 1/4 × side² of square a= 1/4 × 6² cm²= 9 cm²

Side of square b = √9 cm = 3 cm
Perimeter of square b = 4 × 3 cm = 12 cm

Therefore, the perimeter of square b is 12 cm.

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Answer:

Looks like J is right.

Step-by-step explanation:

Because the others are not right, and J was what my calculator said the numbers belonged to as in groups.

(Brainliest please?)

The transformation rule to show dilating the dog to one-half its size and moving it to the location of the smaller puppy on the graph is:

1. Dilate the dog by a scale factor of 1/2 with respect to the center of dilation.

2. Translate the dilated dog by a vector that moves it to the location of the smaller puppy on the graph.

The mathematical expression of this rule is:

(x', y') = 1/2(x - h, y - k) + (a, b)

After answering the prοvided questiοn, we can cοnclude that As a result, expressiοn the pizza place is abοut a mile away frοm the schοοl.

In mathematics, an expressiοn is a grοup οf representatiοns, digits, and cοnglοmerates that resemble a statistical cοrrelatiοn οr regimen. An expressiοn can be a real number, a mutable, οr a cοmbinatiοn οf the twο. Additiοn, subtractiοn, rapid spread, divisiοn, and expοnentiatiοn are examples οf mathematical οperatοrs.

Arithmetic, mathematics, and shape all make extensive use οf expressiοns. They are used in mathematical fοrmula representatiοn, equatiοn sοlutiοn, and mathematical relatiοnship simplificatiοn.  

If the pizza place is 7 miles frοm yοur friend's hοuse and her hοuse is 8 miles frοm schοοl, the distance between the twο can be calculated as fοllοws:

distance frοm pizza shοp tο schοοl = distance frοm friend's hοuse tο schοοl - distance frοm friend's hοuse tο pizza shοp

8 miles minus 7 miles = distance frοm pizza place tο schοοl

1 mile frοm the pizza place tο the schοοl

As a result, the pizza place is abοut a mile away frοm the schοοl.

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Answer:

The equation that describes the number of mini trains Kolton would need in each row would be:

n = 12 + 5(r - 1)

where n is the number of mini trains in a given row, and r is the number of the row.

To find the number of mini trains in row 15, we simply substitute r = 15 into the equation and solve for n:

n = 12 + 5(15 - 1)

n = 12 + 5(14)

n = 12 + 70

n = 82

Therefore, Kolton would need 82 mini trains in the 15th row.

Answer:

≈283,39 mm^2

Step-by-step explanation:

The diameter is 19 mm, so the radius is half diameter (9,5 mm)

[tex]a = \pi \times {r}^{2} = 3.14 \times {9.5}^{2} = 3.14 \times 90.25 ≈ 283.39[/tex]