How long will it take a train to travel 50 km at an average speed of 40m/s? Give your answer in minutes and seconds.

The calculated scale factor from ABC to A'B'C is 1/3

From the question, we have the following parameters that can be used in our computation:

The triangles

From the triangles, we have the following parameters

A = (0, 3)

A' = (0, 1)

Using the above as a guide, we have the following:

Scale factor of the dilation = A'/A

So, we have

Scale factor of the dilation = (0, 1)/(0, 3)

Evaluate

Scale factor of the dilation = 1/3

Hence, the scale factor of the dilation is 1/3

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Answer will be 27.

Given,

3√81

Now, to solve the expression the squares of whole numbers and square roots for some numbers must be known.

For example, squares of

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81
10² = 100

Square roots,

√100 = 10

√81 = 9

√64 = 8

√49 = 7

√36 = 6

√25 = 5

√16 = 4

√9 = 3

√4 = 2

√1 = 1

Now ,

3√81 = 3× 9

= 27.

Thus the value is 27.

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Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

Answer:

The length of the diagonal of Stacy's ceiling was found to be 31 feet using both Pythagorean theorem and trigonometry.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let d represent the length of the diagonal, Usinng Pythagoras:

d² = 22² + 22²

d = 31 feet

Using trigonometric identity:

sin(45) = 22/d

d = 31 feet

The length of the diagonal of Stacy's ceiling was found to be 31 feet using both Pythagorean theorem and trigonometry.

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Step-by-step explanation:

As given, 23 × 22 .

multiplying we get,

2 3

× 2 2

= 5 0 6

(since 2×2=4, 3×2=6, then 6+4=10)

100×4 + 10(6+4) +1×6

= 400+ 100 + 6

= 506

Answer:

length of AC=32

Step-by-step explanation:

The total number of yards the friends who paddle the Adventure Mid travel is 8,580 yards

Number of friends who paddle Adventure Mid Trip = 40% of 15

= 0.4 × 15

= 6 friends

Total yards the friends who paddle the Adventure Mid Trip travel = Total length of travel

= 4 7/8 miles

Recall,

1 mile = 1760 yards

Total yards the friends who paddle the Adventure = 4 7/8 × 1,760

= 39/8 × 1,760

= (39 × 1,760) / 8

= 68,640 / 8

= 8,580 yards

Consequently, the task content is solved by converting number of miles to yards.

Complete question:

Great Adventures Canoe and Kayak company offers 3 different options as shown in the table. This afternoon a group of 15 friends paddle the different options in individual kayaks and 40% of the group paddle the Adventure Mid Trip. How many total yards will the friends who paddle the Adventure Mid Trip travel? (Hint: 1 mile = 1760 yards)

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The rate of change (or slope) of this linear function is -1/2.

A linear function is a mathematical function that has a constant rate of change, meaning that the output (y-value) changes at a constant rate for every unit increase in the input (x-value). In other words, the graph of a linear function is a straight line.

The general form of a linear function is y = mx + b, where m is the slope of the line (the rate of change) and b is the y-intercept (the point where the line crosses the y-axis). The slope represents how much the y-value changes for every one-unit increase in the x-value.

Linear functions can be used to model many real-world situations, such as distance vs. time or cost vs. quantity. They are also commonly used in economics, physics, and engineering.

The rate of change of a linear function represents the slope of the line. We can calculate the slope using the formula:

slope = (change in y) / (change in x)

Let's use the points (0, -3) and (2, -4) to calculate the slope:

slope = (-4 - (-3)) / (2 - 0)

slope = -1 / 2

Therefore, the rate of change (or slope) of this linear function is -1/2.

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The correct value of particle's acceleration at t = 2 seconds is -1/12 m/s^2.

To find the particle's velocity, we need to take the derivative of the position function with respect to time (t).

Given the position function:

s = √24 + 6t

To find the velocity, we differentiate the position function with respect to time:

v = ds/dt

Applying the power rule and chain rule for differentiation, we get:

v = (1/2) * (24 + 6t)^(-1/2) * 6

Simplifying further:

v = 3 / √(24 + 6t)

To find the velocity at t = 2 seconds, we substitute t = 2 into the velocity equation:

v = 3 / √(24 + 6(2))

v = 3 / √(24 + 12)

v = 3 / √36

v = 3 / 6

v = 1/2 m/s

So, the particle's velocity at t = 2 seconds is 1/2 m/s.

Now, let's find the particle's acceleration. Acceleration is the derivative of velocity with respect to time.

a = dv/dt

To find the acceleration, we differentiate the velocity function with respect to time:

a = d(3 / √(24 + 6t)) / dt

Applying the quotient rule and chain rule, we get:

a = -3 * (24 + 6t)^(-3/2) * 6

Simplifying further:

a = -18 / (24 + 6t)^(3/2)

To find the acceleration at t = 2 seconds, we substitute t = 2 into the acceleration equation:

a = -18 / (24 + 6(2))^(3/2)

a = -18 / (24 + 12)^(3/2)

a = -18 / 36^(3/2)

a = -18 / 36^(3/2)

a = -18 / 216

a = -1/12 m/s^2

So, the particle's acceleration at t = 2 seconds is -1/12 m/s^2.

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The scale factor and the value of x for each figure is given as follows:

A) Scale factor of 1/3, x = 7 m.

B) Scale factor 0.4747, x = 4.5 in.

For Figure A, we have that the ratio between the areas is given as follows:

510/4590 = 1/9.

As the area is measured in square units, while the side lengths are measured in units, the scale factor is the square root of 1/9, hence it is given as follows:

1/3.

Then the value of x is obtained as follows:

x = 21 x 1/3

x = 7 m.

For Figure B, we have that the ratio between the areas is given as follows:

16/71 = 0.22535.

The scale factor is then the square root of 0.22535, which is given as follows:

0.4747.

Then the value of x is given as follows:

x = 9.5 x 0.4747

x = 4.5 in.

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Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;

f(x) = 2x + 2         ⇒   (0, 2).

f(x) = 2x² - 2        ⇒   (-1, 0).

\(f(x) = 2\sqrt{x+1}\)   ⇒   (0, 2).

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;

For the ordered pair (0, 2), we have:

f(x) = 2x + 2

2 = 2(0) + 2

2 = 2 (True).

For the ordered pair (-1, 0), we have:

f(x) = 2x² - 2

0 = 2(-1)² - 2

0 = 2 - 2

0 = 0 (True).

For the ordered pair (0, 2), we have:

\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)

2 = 2 (True).

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Decentralization is a management approach that involves the delegation and assignment of decision-making rights from top levels of management to lower levels of management. Option A

It is an effective way to empower employees and to improve decision-making processes within an organization. The benefits of decentralization include the following:

It empowers more employees at lower levels of management: Decentralization allows employees to take ownership of their work, to be more accountable, and to make decisions that are in the best interest of the organization. This, in turn, leads to improved job satisfaction, employee engagement, and better overall performance.

It allows for better and more timely decision-making: Decentralization ensures that decisions are made closer to where the work is being done. This leads to faster decision-making, improved responsiveness to changes in the market, and better coordination between different departments and teams.

It trains future managers: Decentralization provides employees with the opportunity to gain valuable management experience, which can help prepare them for future leadership roles within the organization.

However, one benefit of decentralization that is not accurate is that it forces top levels of management to focus on individual units. In fact, decentralization can free up top management to focus on the big picture and long-term strategy, rather than getting bogged down in day-to-day operations.

In conclusion, decentralization is a useful management approach that can help organizations improve decision-making, empower employees, and train future managers.

By delegating decision-making rights to lower levels of management, organizations can improve overall performance and become more adaptable to changes in the market.

So Option A is correct.

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complete question:

The benefits of decentralization i.e. delegation and assignment of decision rights include all of the following except:

a it forces top levels of management to focus on individual units

b it empowers more employees at lower levels of management

c it allows for better and more timely decision making

d it trains future managers

Answer:

64cm³

Step-by-step explanation:

( 4 x 4 x 4) cm x cm x cm

Answer:

Step-by-step explanation:

You could do this 2 ways (NOT including going to a calculator and punching it in and getting the answer!). The first way is to use Newton's Method (which will give you an EXACT answer); the second is to use differentials (which will only approximate the answer). We'll do both here, beginning with Newton's Method. The formula for Newton's Method is

\(x_{1}-\frac{f(x_{1})}{f'(x_{1})}\) where x1 is your initial input.

Let x = \(\sqrt{38}\) so

\(x^2=38\\x^2-38=0\) with a derivative of 2x. Fitting this into the formula with an initial input of 6, since 6-squared is 36 and that's pretty close.

\(6-\frac{6^2-38}{2(6)}=\frac{37}{6}\)  and use that answer in the next iteration:

\(\frac{37}{6}-\frac{\frac{37}{6}^2-38 }{2(\frac{37}{6}) }=\frac{2737}{444}\) and use that answer in the next iteration:

\(\frac{2737}{444}-\frac{\frac{2737}{444}^2-38 }{2(\frac{2737}{444}) }=6.164414003\) and use that answer in the next iteration:

\(6.164414003-\frac{.164414003^2-38}{2(6.164414003)}=6.164414003\)

Since we got the same number after that last iteration, the exact value of the square root of 38 is 6.164414003. Check your calculator for accuracy.

The next method is by differentials. the formula is

f(x + Δx) ≈ f(x) + f'(x)dx

We will let f(x) = √x with x = 36 and dx = 2 (36 is a perfect square and adding 2, the dx value, gets you back to 38, our number in question).

Filling in the formula:

f(x + Δx) ≈ √x + \(\frac{1}{2\sqrt{x} }\) dx

f(x + Δx) ≈ \(\sqrt{36}+\frac{1}{2\sqrt{36} }(2)\) and simplifying a bit:

f(x + Δx) ≈ 6 + \(\frac{1}{6}\)  which gives us 6.166666

Not quite as accurate as Newton's Method, but it works for mere approximations.

Answer:

Step-by-step explanation:

Area of a triangle is a*b divided by 2

Lets assume a = 8 and b= 9

8 *

9=72

72/2=36

Answer: 2/3, 3/4, 5/8, 5/6

Step-by-step explanation:

First,

We must turn all of them into denominators that can be divided by 1/2.

2/3 = 4/6. 3    1/3 = 2/6  

Now we see which is greater.  

2/3 > 1/2.  

3/4 > 1/2.

2/6 < 1/2.

1/3 < 1/2.

3/8 < 1/2.

5/8 > 1/2.

1/4 < 1/2.

5/6 > 1/2.

So the answers are 2/3, 3/4, 5/8, 5/6.

Answer:

x < -3 or x > 2

Step-by-step explanation:

x² + x - 6 > 0

Convert the inequality to an equation.

x² + x - 6 = 0

Factor using the AC method and get:

(x - 2) (x + 3) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x - 2 = 0

x = 2

x + 3 = 0

x = -3

So, the solution is x < -3 or x > 2

To the nearest inch, there are 4 inches in 10.16 centimetres.

The process of translating a measurement from one unit to another is known as a units conversion. This is frequently done when comparing measurements from various sources or when working with several unit systems. In order to communicate a measurement in a different unit of the same physical amount that is more suitable or useful for a specific context, units conversion is required.

If you are speaking with someone who uses the Imperial system of units, for instance, you may need to convert from metres to feet when estimating distance. If you are working with someone who utilises the American customary system, you may need to convert from kilogrammes to pounds when measuring weight.

In order to prevent mistakes in calculations and measurements, it is crucial to be precise and accurate while converting between units. Unit conversion is a crucial component of scientific and technological activity.

Since there are 2.54 centimetres in one inch, we may multiply 4 inches by 2.54 to convert them to centimetres:

4 inches * 2.54 centimeters per inch = 10.16 centimeters

We multiply by 2.54 to convert centimetres to inches:

10.16 centimeters / 2.54 centimeters per inch = 4 inches (rounded to the nearest inch)

Therefore, rounding to the closest inch, there are 4 inches in 10.16 centimetres.

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In the Unit conversion,to the nearest inch, there are 4 inches in 10.16 centimeters.

Describe Units Conversion?

The process of translating a measurement from one unit to another is known as a units conversion. This is frequently done when comparing measurements from various sources or when working with several unit systems. In order to communicate a measurement in a different unit of the same physical amount that is more suitable or useful for a specific context, units conversion is required.

If you are speaking with someone who uses the Imperial system of units, for instance, you may need to convert from meters to feet when estimating distance. If you are working with someone who utilises the American customary system, you may need to convert from kilograms to pounds when measuring weight.

In order to prevent mistakes in calculations and measurements, it is crucial to be precise and accurate while converting between units. Unit conversion is a crucial component of scientific and technological activity.

Since there are 2.54 centimeters in one inch, we may multiply 4 inches by 2.54 to convert them to centimeters:

=> 4 inches * 2.54 centimeters per inch = 10.16 centimeters

We multiply by 2.54 to convert centimeters to inches:

=> 10.16 centimeters / 2.54 centimeters per inch

=> 4 inches (rounded to the nearest inch)

Therefore, rounding to the closest inch, there are 4 inches in 10.16 centimeters.

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Answer: 4

Step-by-step explanation:

1 third of 30 is 10 and 2/5s of 10 is 4

The mirror is a square. The diagonal of the mirror is 10 inches long . The length of the mirror can be calculated below

Therefore, the length is

The ordered pair that solves the system of equation is (0, 0).

To solve this system, we can substitute the first equation into the second equation to eliminate y:

x = 2x

Solving for x, we get x = 0.

Substituting x = 0 into the first equation, we get y = 0.

Therefore, the ordered pair that solves the system is (0, 0).

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Step-by-step explanation:

54x^2-144x

18x(3x-8) is your answer

The linear function there after 18 minutes of calls, then the credit was = $29

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Given that,

Slope = -0.16

There linear function is $29.00 in credit remaining on the card after 25 minutes of calls

There after 18 minutes of calls?

Slope m = -0.16

Let us assume,

x = 25 minutes

y = $29.00 in credit

Substitute this values,

So,

We can write,

y = mx + b

$29.00 = (-0.16) (25) + b

$29.00 = -24.84 + b

b = $29.00 + 24.84

b = $53.84

We can substitute b value,

y = mx + b

y = (-0.16) x + $53.84

y = \(-0.16x\) + $53.84

y = (-0.16)(25) + $53.84

y = -24.84 + $53.84

y = $29

Therefore,

The linear function there after 18 minutes of calls, then the credit was = $29

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Use the combination formula.

5 C2 = 5!/5!3! = 10

The answer is 10

Answer:

10

Step-by-step explanation:

We are given the radius of the scoop and asked to find the volume of ice cream in one scoop. By using the formula for the volume of a sphere and substituting the given radius, we can calculate the volume. The final answer is approximately 33.49 cubic inches.

a) The problem asks for the volume of ice cream in one scoop.

b) The given fact is that the radius of the scoop is 2 inches.

c) The formula to be used is the volume of a sphere, which is given by V = (4/3)πr³, where V is the volume and r is the radius.

d) Number Sentence:

  - Given: Radius (r) = 2 inches

  - Formula: V = (4/3)πr³

  - Substituting the value: V = (4/3)π(2)³

  - Simplifying: V = (4/3)π(8)

  - Evaluating: V = (4/3)(3.14)(8)

  - Multiplying: V = 33.49333333 (approx.)

e) Final answer: The volume of ice cream in one scoop is approximately 33.49 cubic inches.

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Answer:

The last answer choice

Step-by-step explanation:

Interpretation of internet users

Middle East - about 100 million

North America - about 250 million

Europe - about 500 million

Asia - over 1 billion

Now lets look back at the question.

If Africa has 170 million internet users, according to the graphs, which statement is true.

"Africa has fewer users than the middle east"

This is false as Africa has 170 million users whereas The middle east has about 100 million users

170 mil > 100 mil therefore the statement is false

"Africa has more users then Asia"

This is also false as Asia has the most internet users at 1 billion

Africa has no where near as many users at 170 million users therefore the statement is false

"Africa has more users than Europe but fewer than Asia."

We have already identified that Africa has fewer users than Europe so this one could be it if the other part is true.

"Africa has more users than Europe" This is false as Europe has 500 million internet users while Africa only has 170 million users

Therefore this statement is false

"Africa has more users than the Middle East but fewer users than North America."

Africa has more internet users than the Middle East ( 170 mil > 100 mil ) and fewer users than North America ( 250 mil > 170 mil )

therefore this is the correct statement