color each of the six faces of a cube with either blue or red. note that two colorings are regarded the same if the cube looks identical after some rotation. how many different colorings can be made?

Someone biked 11 time as many miles as someone together they biked a total of 156 miles. 143 miles did they bike.

Miles:

The mile, sometimes called the international mile or statutory mile to distinguish it from others, is an imperial unit in the United Kingdom and a common unit of distance in the United States. Both are based on old English units that are 5,280 British feet or 1,760 yards long. The legal mile was standardized in 1959 by an international agreement between the British Commonwealth and the United States and formally redefined in SI units to be exactly 1,609.344 meters.

With the modifier, the mile is also used to describe or convert a wide range of units derived from or roughly equivalent to the Roman mile, such as the Chinese mile (now exactly 500 m). will be The Romans divided the mile into 5,000 Roman feet, but the growing importance of the furlong in Elizabethan England meant that in 1593 the legal mile equaled eight furlongs, or 5,280 feet. This form of the mile has since spread partially to the successor states of the British Empire, where they continue to use the mile. Most countries have replaced miles with kilometers when converting to the International System of Units (SI), but some countries still use international miles, such as Liberia, the United Kingdom, the United States, and countries with less than one mile. I'm here. Most of them are British or US territories or have close historical ties with the UK or the US.

According to the Question:

Let the distance Karly biked be x.

Then, someone biked 11x.

Now,

x + 11x = 156

x = 156/ 12

  = 13

Therefore,

Someone biked 11 × 13 = 143 miles

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-7.4 degrees celsius is less than the temperatures Susan recorded.

To explain, temperatures are measured on a scale, with 0 degrees celsius being the point at which water freezes and 100 degrees celsius being the point at which water boils. A temperature of -7.4 degrees celsius is therefore less than the recorded temperatures of -7.4 and 1.8 degrees celsius.

The temperature is a measure of the thermal energy of a substance or system, and is typically measured on a scale, such as the Celsius scale or the Fahrenheit scale.

In other words, the number -7.4 is less than 1.8 and -7.4 on the scale of temperature, meaning that -7.4 degrees celsius is less than the temperatures Susan recorded.

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Answer:

56.5 cm

Step-by-step explanation:

Circumfrence= pi× diameter

= 3.14×18 = 56.52 cm

3SF: 56.5 cm

Using the given function V(x) = 15,000(0.87)^x , the value of Mr.Dulaney's car 5 years after its purchase will be approximately equal to given option $7500.

A mathematical phrase, rule, or law that establishes the relation between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

A mathematical function is a rule that assigns a unique output, also called the function value, to each input value within a certain set called the domain. The output is determined by the instructions, also called the function rule, that defines the relationship between the input and output values. It can be represented by an equation, such as y = f(x), where x is the input, y is the output, and f is the function symbol. The graph of a function is a set of points, where each input in the domain corresponds to a unique output. It helps to express the relationship between two variables and allows to make predictions and analyze patterns in mathematical problems.

Given,

V(x) = 15,000(0.87)^x where x denotes number of years after its purchase.

So, to find the value of Mr. Dulaney's car 5 years after its purchase,

let x =5

so V(x) = 15,000(0.87)^5 = $7476.31

Which is approximately equal to given option , $7,500

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Answer:

250 and 10

Step-by-step explanation:

substitute x = 10 into the expressions

a = [tex]\frac{5x^2}{2}[/tex]

  = [tex]\frac{5(10)^2}{2}[/tex]

  = [tex]\frac{5(100)}{2}[/tex]

  = [tex]\frac{500}{2}[/tex]

  = 250

-----------------------------------------------

b = [tex]\frac{2x^2(x-5)}{10x}[/tex]

  = [tex]\frac{2(10)^2(10-5)}{10(10)}[/tex]

  = [tex]\frac{2(100)(5)}{100}[/tex] ( cancel 100 on numerator and denominator )

  = [tex]\frac{2(5)}{1}[/tex]

  = 10

Answer: 7/4

Step-by-step explanation:

The formula for slope is change in y/change in x.

So we substitute in the coordinates: -3-4/2-6

We can then simplify to -7/-4, or 7/4.

Answer: 7/4

Step-by-step explanation:

4-(-3)/6-2 = 7/4

Answer:

a. The length and width of the smaller wall are 14 feet and 8 feet, respectively.

b. The area of the smaller wall is 14 feet x 8 feet = 112 square feet.

c. The area of the larger wall is 20 feet x 8 feet = 160 square feet.

d. The total area of the four walls in the room is 112 square feet + 112 square feet + 160 square feet + 160 square feet = 544 square feet.

e. To find the cost of painting the room walls with two coats of paint, we need to know the total area of the walls, and the cost of one gallon of paint. We can use the information provided: a gallon of paint covers 350 square feet on average and the cost of one gallon of paint is $36.50.

We can divide the total area of the walls by the coverage of one gallon of paint, then multiply that by the cost of one gallon of paint.

544 square feet / 350 square feet/gallon * $36.50/gallon = $38.34

So the cost of painting the room walls with two coats of paint is $38.34.

Answer: [tex]18p^{4}[/tex]

Step-by-step explanation:

I wrote the steps in the image

The 100W bulb will have a lower brightness than the 60W bulb because the resistance of the 100W bulb is less than that of the 60W bulb, so it will have the lowest voltage drop.

Since the power of a lamp of nominal voltage V can be defined as [tex]\bold{P = \frac{V {}^{2} }{R}}[/tex], where R is the resistance to hot, this means that the resistance of the lamp is inversely proportional to its power, that is, the greater the power of the lamp, the lower its resistance.

Applying Kirchoff's second law to a series circuit with resistors R1 and R2 and power supply E we have:

[tex] \bold{E = I.R1 + I.R2}[/tex]

Since the current I is the same for all elements connected in series. In this expression we see that the smallest resistance will have the smallest voltage drop.

Now, in our circuit with two bulbs in series, the 100W bulb will have less resistance than the 60W bulb, so it will have less voltage drop. As it has a lower voltage drop, the power developed in the 100W lamp will be less than that developed in the 60W lamp and the 100W lamp will have a weaker brightness than the 60W lamp.

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The likelihood of selecting a second ball is 2/8 or 1/4 if that ball is now eliminated.

Probability theory, a subfield of mathematics, gauges the likelihood of an event or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty.  Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a comprehensive set of equally likely outcomes that result in a certain occurrence compared to the total number of outcomes.

given

The ratio of the number of balls of that color to all the balls is the likelihood of selecting a ball from a bag.

In the first case, the likelihood of a red ball is therefore 3/9, or 1/3. The likelihood of selecting a second ball is 2/8 or 1/4 if that ball is now eliminated.

Therefore, the chance of getting a white ball is 1/2*1 plus 1/2*49/99, or roughly 3/4.

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The final equation of the line using the point-slope formula is y = (1/5)x + (6/5) = (1/5)x + 1.2.

The point-slope form of a line is given by y - y1 = m(x - x1) where m is the slope of the line and (x1, y1) is a point on the line.

First, we need to find the slope of the line that is perpendicular to 5y = x − 4. A line is perpendicular to another line if the product of their slopes is -1. The slope of 5y = x − 4 is x/5y=-1. Therefore, the slope of the line that is perpendicular to 5y = x − 4 is 1/5

Now we can use the point-slope form of a line with a slope of 1/5 and the point (-2, 1) to find the equation of the line.

y - 1 = (1/5)(x + 2)

y = (1/5)x + (2/5) + 1

y = (1/5)x + (6/5)

To write the equation in slope-intercept form, we need to solve for y:

y = (1/5)x + (6/5) = (1/5)x + 1.2

That's the final equation.

Therefore, The final equation of the line using the point-slope formula is y = (1/5)x + (6/5) = (1/5)x + 1.2.

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The angles and sides are in order from smallest to largest is written as,

For first triangle;

Sides = ZY, XZ, XY

Angles = ∠X, ∠Y, ∠Z

For second triangle;

Sides = MQ, MP, PQ

Angles = ∠P, ∠Q, ∠M

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We know that;

In triangle, The opposite side of large angle is large and opposite angle of a large side is large.

So, By above conclusions we get;

The angles and sides are in order from smallest to largest is written as,

For first triangle;

Sides = ZY, XZ, XY

Angles = ∠X, ∠Y, ∠Z

For second triangle;

Sides = MQ, MP, PQ

Angles = ∠P, ∠Q, ∠M

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Finding the line that fits a set of data points the best is done using the linear regression approach. We can utilize the following procedures to apply linear regression to find an equation that would most effectively predict a fair home price depending on the square footage of the home:

Step 1 :The square footage of the house should be on the x-axis and the house's price in thousands should be on the y-axis of the graph you create in step one.

Step 2: Using the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, determine the equation of the line of best fit.

Step 3 :Find the slope and y-intercept by substituting the comps data into the equation in step three.

Step 4: The line of best fit has the equation y = mx + b, where m is the line's slope and b is its y-intercept.

Step 5: We must use the formula m = (NΣ(xy) - (Σx)(Σy)) / (NΣ(x^2) - (Σx)^2) to determine the slope (m).

Step 6: We must apply the formula b = (y - m(x)) / N to determine the y-intercept (b).

Step 7: Using the information provided in the question, we will determine the slope and y-intercept. m = (3* (108+133+120) - (1400+1700+1500)(3)) / (3 (1400+1700+1500)(2)) = 0.09 b = (108+133+120 -0.09*(1400+1700+1500))/3 = 111.33

   Therefore, y = 0.09x + 111.33 is the equation that would most accurately forecast a reasonable property price based on the home's square footage.

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hope this helps you understand !!

Answer:

x + 2

Step-by-step explanation:

Ben : x cm

Kieran: (x + 8) cm

Bianca: (x - 2) cm

Mean of their heights = [tex]\frac{Sum of their heights}{Number of people} = \frac{x + (x + 8) + (x - 2)}{3}[/tex]

                                   = [tex]\frac{x + x + 8 + x - 2}{3}[/tex]    (Expand the brackets)

                                   = [tex]\frac{x + x + x + 8 - 2}{3}[/tex]  (Bring all the like terms together)

                      = [tex]\frac{3x + 6}{3}[/tex] (Simplify the two sets of like terms)

                        = [tex]\frac{3(x + 2)}{3}[/tex]  (Extract the common factor '3' in the numerator)

                      = (x + 2) cm  ([tex]\frac{3}{3} = 1[/tex])

The function is decreasing in the interval (-∞,-3/2) and (3/2, ∞) and increasing in the interval (-3/2, 3/2).

What is a function?

A function is a mathematical relation between a set of inputs (often called independent variables, or the domain) and a set of outputs (often called dependent variables, or the range). A function assigns exactly one output for each input. It can be represented by an equation, such as y = f(x), where x is the input and y is the output.

To find the interval(s) in which the function is increasing and decreasing, we can first find the critical points of the function by setting the derivative equal to 0 and solving for x.

The derivative of y = |2x² + x - 6| is not a defined function, it is not differentiable, it is a piece-wise defined function, it has a break at x = -3/2

Hence, the function is decreasing in the interval (-∞,-3/2) and (3/2, ∞) and increasing in the interval (-3/2, 3/2).

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The cost in dollars if a cab ride 49 miles long is $ 110.

The question is not complete, a table of travel costs and distance data should be provided. A table that is similar to the table that should be provided is in the attachment. From the table, it can be seen that if the mileage increases by 5 miles, the cost will increase by $ 12.5. The data graph will be in the form of a straight line.

The equation of the line if two points are known

(y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)

(c - c₁)/(c₂ - c₁) = (d - d₁)/(d₂ - d₁)

(c - 12.5)/(25 - 12.5) = (d - 5)/(10 - 5)

(c - 12.5)/12.5 = (d - 5)/5

5 × (c - 12.5) = 12.5 × (d - 5)

5c - 62.5 = 12.5d - 125

5c = 12.5d - 125 + 62.5

5c = 12.5d - 62.5

c = 2.5d - 12.5

If a cab ride is 49 miles long,

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Correct answers are - A, B, D, F, G.The volume of oblique cone is same as normal cone and volume of oblique cylinder is same as normal cylinder due to Cavalier's principle.

Cavalieri's principle is a method for determining the volume of an object by comparing it to the volume of another object of known volume. It was introduced by the Italian mathematician Bonaventura Cavalieri in the early 17th century. The principle states that if two solids have the same height and the same cross-sectional area at every height, then the two solids have the same volume.

The principle is based on the idea of slicing the solids into thin slices and comparing the areas of the cross-sections of the slices. If the cross-sectional areas are the same at every height, then the solids have the same volume.

Cavalieri's principle was one of the early precursors to the development of calculus and the concept of the definite integral. It is also a powerful tool in geometry and is used in many problems involving the calculation of volumes of irregular shapes.

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The complete question is as follows:

The equation be 38.67 + 13.6 then we get 52.27.

A different way to represent a fractional value in mathematics is to use decimal notation. It denotes that base-10 fractional representation is being used. It is possible to change fractions into decimals and vice versa.

The same thing applies to decimals: they each represent a portion of a whole number. The distinction is in the notation used to write decimals vs fractions. By using decimal notation, we can graphically express how much of a whole number we are working with.

The decimal point must be moved till it is to the left of the first non-zero number in order to be written in scientific notation. The exponent is the amount of places the decimal point advances since each movement signifies a "power of 10".

Let the equation be 38.67 + 13.6 then we get 52.27.

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The equation to determine the number of hours it will take to fill the pool, given the current level of the pool, the rate at which the pool is being filled, and the pool's capacity can be found using the following steps.

To write an equation that can be used to find the number of hours it will take to fill the pool from its current level, we need to use the following information:

The pool's capacity: 43,000 gallons

The current level of the pool: 20,000 gallons

The rate of filling the pool: 130 gallons per minute

We can start by using the formula:

time = (amount needed to fill)/(rate of filling)

The amount needed to fill the pool is the difference between the pool's capacity and the current level of the pool.

amount needed to fill = 43,000 - 20,000 = 23,000 gallons

Now we can substitute this value in the formula above:

time = (23,000 gallons)/(130 gallons/minute)

To convert the time to hours, we divide the time in minutes by 60

time = (23,000 gallons)/(130 gallons/minute) × (1 hour/60 minutes)

So, the equation that can be used to find h, the number of hours it will take to fill the pool from its current level is:

h = (23,000 gallons) / (130 gallons/minute) × (1 hour/60 minutes)

Note that this equation is not simplified, you can simplify it by canceling out common factors, you'll get:

h = (23000 / 130) × (1/60)

This equation can be used to find the number of hours it will take to fill the pool, given the current level of the pool, the rate at which the pool is being filled, and the pool's capacity.

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Answer:

Let x be the length of one side of the square field.

Since the field is divided into two squares, the total length of the fencing is 2x + 2x = 4x.

And since the problem states that it takes 406 yards of fencing to enclose the field,

we can set up the equation: 4x = 406.

Solving for x, we get x = 101.5

So the dimensions of the field would be 101.5 yards by 101.5 yards.

Step-by-step explanation:

The mean number of accidents that would be expected to be more than 7 accidents is 0.6554.

By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.

A statistical measurement known as the Z-score indicates how closely a value relates to the mean of a collection of values. The Z-score is calculated using standard deviations from the mean. When a data point's Z-score is 0, it means that it has the same score as the mean. One standard deviation from the mean would be indicated by a Z-score of 1.0.

Given that mean is 6.4 and the standard deviation is 1.5.

The z score is used to determine the accidents:

z = 7 - 6.4 / 1.5

z = 0.4

Using the table of normal distribution we have, P(x > 7 ) = P(z > 0.4) = 0.6554

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Eleri wants to be fit for the adventure holiday and to achieve that she runs 2 laps of a running track. Each lap is 400m and she thinks she has run 1km in total. To determine if Eleri is correct, we must first understand the basic units of measurement for distance and how they relate to one another.

A lap of a running track is a distance of 400m. The prefix "kilo" in the unit "kilometer" represents 1000. Therefore, a kilometer is equal to 1000 meters. To convert meters to kilometers, we divide the number of meters by 1000. To convert kilometers to meters, we multiply the number of kilometers by 1000.

To determine the total distance Eleri ran, we must multiply the number of laps by the distance of each lap. 2 laps x 400m per lap = 800m. This is the total distance Eleri ran in meters.

To determine if Eleri ran 1km, we must convert 800m to kilometers. Therefore, to convert meters to kilometers, we divide 800 by 1000. 800m / 1000 = 0.8km.

Therefore, Eleri did not run 1km, she ran 0.8km.

To further demonstrate the accuracy of our calculation, we can use dimensional analysis by using the conversion factor of 1000m = 1km.

800m / (1000m/1km) = 0.8km

This confirms that Eleri ran 0.8km, not 1km.

In conclusion, Eleri is not correct in her assumption that she ran 1km. She actually ran 0.8km which is 800 meters. This was determined by understanding the basic units of measurement for distance, converting the distance from meters to kilometers, and using dimensional analysis to verify our calculations.

Answer:

Step-by-step explanation:

no she is not correct she only ran 0.8 km

The equation of function after a horizontal translation is y = 2*4ˣ⁺².

Initially, functions represented the idealized relationship between two changing quantities. A planet's position, for instance, depends on time. In the past, the idea was developed with the infinitesimal calculus at the end of the 17th century, and the functions that were taken into consideration until the 19th century were differentiable (that is, they had a high degree of regularity).

The realms of application of the concept of a function were substantially expanded at the conclusion of the 19th century when it was defined in terms of set theory.

An assignment of an element from set Y to each element of set X constitutes a function from set X to set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

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The correct dotplot for the given data is option D, which displays the number of errors for the week for each workstation.

Error in math is any mistake made in the process of solving a mathematical problem or problem-solving process. It could mean a mistake in the calculations, incorrect steps taken, or incorrect assumptions made. It can also include making a wrong interpretation of the problem, or not being able to solve it at all. Errors in math can occur due to a lack of understanding of the concepts, mistakes in calculations, errors in reasoning, or incorrect application of the rules and formulas. Errors can also be made in the process of writing down the equations, or in the process of simplifying the equation.

The graph begins with 0 and goes up to 254201 in intervals of 5. The data points for each work station are marked on the graph, showing the number of errors each work station made. This visual display of data points allows for an easy comparison of the number of errors across all workstations.

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Rate of the jet in still Air is 716 miles per hour and

wind speed is 80 miles/hour.

The velocity of an item in relation to another observer is known as its relative velocity. It is the pace at which one item's relative location changes in relation to another object over time. When two bodies are travelling in opposing directions, their relative velocity is at its highest. They are approaching one another.

Let ‘X’ be speed of jet and

'Y’ be speed of Wind

Relative velocity when jet travels against wind: X - Y = ( 2544 / 4 ) = 636 miles/hour

Relative velocity when jet travels with wind is: X + Y = ( 3184 / 4 ) = 796 miles/hour

By adding these two equations we will get

2 X = 1432 or X = 716 miles /hour and

or, Y = 796 - 716 = 80 miles/hour

Hence,

Rate of the Jet in still Air is 716 miles per hour and

Wind speed is 80 miles/hour.

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The coordinate point T' the reflection of T over the y-axis is (4, -5).

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given that, the point T is plotted on the coordinate grid.

The coordinate point on the grid is (-4, -5).

The reflection of point (x, y) across the y-axis is (-x, y).

Here, (-4, -5)→(4, -5)

Therefore, the coordinate point T' the reflection of T over the y-axis is (4, -5).

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Dalton made 10 number of  decorations. Dalton made 10 decorations using 1/2 of a meter of ribbon, which he cut into equal pieces.

1. Dalton used 1/10 of a meter of ribbon for each decoration.

2. He got this by cutting 1/2 of a meter of ribbon into equal pieces.

3. 1/2 of a meter is equal to 5/10 of a meter.

4. If 1/10 of a meter is used for each decoration, then 5/10 of a meter can make 5 decorations.

5. Therefore, 10 decorations can be made.

Dalton made 10 number of decorations using 1/2 of a meter of ribbon, which he cut into equal pieces.

Dalton made 10 decorations for each of the dancers in his year-end dance performance. He used 1/10 of a meter of ribbon for each decoration which he got by cutting 1/2 of a meter of ribbon into equal pieces. This meant that he was able to get 10 decorations out of the 1/2 of a meter of ribbon, as 1/10 of a meter was used for each decoration. He was able to do this by dividing the 1/2 of a meter of ribbon evenly into 10 pieces.

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Answer:

let the 2 unknown numbers be 'x' and 'y'

given: x+y=15 - equation 1

5x-3y=19 - equation 2

from equation 1 :

x = 15 -y

substitute this in equation 2

5(15-y) -3y = 19

75 - 5y - 3y = 19

75-8y=19

8y=56

y=7(substitute value of y in equation 1)

x+7=15

x=8

hence the two numbers are 8 and 7

Answer:

x = 8

y = 7

Step-by-step explanation:

let's assume the first number as x, and the second number as y

Now, according to the question,

x + y = 15

Moving on to the next statement,

five times the first number = 5x

three times the second number = 3y

Thus,

5x  - 3y = 19

Now that we have two equations, we can either write 'x' in 'y' terms, or y in 'x' terms.

For example, from the first equation:

x + y = 15

y = 15 - x

Now, let's put this value of y into the second equation, i.e.

5x - 3(15 - x) = 19

5x - 45 +3x = 19

8x = 19 + 45

x = 64/8

x = 8

Now, let's put this value of x into the first equation, i.e.

x + y = 15

8 + y = 15

y = 7

In conclusion, the two numbers, x and y, are 8 and 7 respectively

The expression will be;

n = 8 x 5 / 4.

The correct option is A.

Algebraic expressions shows us how to express an unknown value using letters such as t, a, y, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

Number of friends = 4

Bags sold = 8

Amount sold = $5

The expression will be;

n = (8 x 5) / 4

to find the amount sold for each of the friends.

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the rate of change of height at h = 15cm, 0. 0159 cm/s

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

Beads are dropped to create a conical pile such that the ratio of its radius to the height of the pile is constant at 2:3.

Volume is increasing at a rate of 5 cm3/s.

The volume of a Cone: 1/3 pi r^2 h

given r/h =2/3

V =0. 0159 cm/s

Hence the rate of change of height at h = 15cm, 0. 0159 cm/s

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