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For feet we will divide the given no. of inches by 12 and for inches we will multiply the given number of feet by 12.

Since 1 foot is equal to 12 inches, the given value (in feet) is converted to inches by multiplying by 12. To compare lengths given in different units or to perform arithmetic operations on them, it is crucial to learn how to convert feet to inches (ft to in).

We know that 1 feet = 12 inches.

And to find how many feet are in a given number of inches

We will divide the given no. of inches by 12.

And

To find how many inches are given in a number of feet

We will multiply the given number of feet by 12.

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Therefore, the function f is decreasing on the interval (- [infinity], -1].

A. (- [infinity], -1] only

We can use the first derivative test to determine where a function is increasing or decreasing. The first derivative test states that if the derivative of a function is positive, then the function is increasing, and if the derivative is negative, then the function is decreasing.

For this problem, the derivative of the function f is f'(x) = x^2 - 2/x.

We can see that for x < 0, the derivative is negative, so the function is decreasing on that interval. For x > 0, the derivative is positive, so the function is increasing on that interval.

Therefore, the function f is decreasing on the interval (- [infinity], -1].

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Answer:41,111

Step-by-step explanation:4-3=1 3-2=1 2-1=1 bring the 1 down and bring the 4down to and you got your answer

Answer: 3

Step-by-step explanation:

[tex]f(0)=3(0)-3=-3\\\\\implies g(f(0))=g(-3)=-(-3)=3[/tex]

The slope of the original line is 3/5.

What is the slope?

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

The slope of a line perpendicular to another line can be found by taking the negative reciprocal of the slope of the original line.

To find the slope of the original line, we need to convert the equation to the slope-intercept form (y = mx + b), where m is the slope.

To convert, we'll isolate y:

-3x + 5y = 20

5y = 3x + 20

y = (3/5)x + 4

The slope of the original line is 3/5. The slope of the line perpendicular to this line would be the negative reciprocal of this slope, or -5/3.

Hence, The slope of the original line is 3/5.

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The rate of the plane in still air is 1,000 kph and the speed of the wind is 250 kph. The result is obtained by using elimination and substituting method.

To eliminate equations, we can either add or subtract the equations. Substitution is substituting the value of one variable in the other equation.

A plane can travel:

Find the rate of the plane in still air and the speed of the wind!

Let's say

The speed of the plane with the wind is

v + w = 3750 km/3 h

v + w = 1250 kph ... (equation 1)

The speed of the plane against the wind is

v - w = 3750 km/5 h

v - w = 750 kph ... (equation 2)

Eliminate the equation 1 and 2!

v + w = 1250

v - w = 750 +

2v = 2000

v = 1000 m/s

Substitute the value of v in equation 1!

v + w = 1250

1000 + w = 1250

w = 1250 - 1000

w = 250 m/s

Hence, the speed of the plane when there is no wind and the speed of the wind respectively are 1000 m/s and 250 m/s.

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Answer:

Step 1: The nth term of an arithmetic sequence is given by an = a + (n – 1)d. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula. Step 2: Now, to find the fifth term, substitute n = 5 into the equation for the nth term.

Answer:

whats ..... representating

is it a continuous series?

12. i) By walking the 20 kilometers in the charity walk, Vreni raised $250 at a unit rate of $12.50 per kilometer.

12. ii) The total money raised by all participants in the charity walk was $3,100, using proportions.

12. iii) The percentage increase on the previous year's total is 26.53%.

Part B:

11. i) Based on a ratio of 3:2 of road and footpath distance, the road distance covered 12 kilometers.

11. ii) Using the distance, time, and speed formula, Vreni took 7 hours and 12 minutes to walk the 20 kilometers.

11. iii) Vreni's average speed is 2.78 km/h.

11. iv) Vreni finished the charity walk at 16:07.

Part C: The scale of the map to the total distance covered by Vreni was 1: 4 or a scale factor of 25%.

The ratio is the quotient of a value compared to another.

Ratios are proportionate values, which are equated to each other.

The average speed and scale factor show the ratios of one value and the whole.

12) Charity Walk and Vreni:

The total distance walked = 20 kilometers

The unit rate of raising money per kilometer = $12.50

i) The total amount raised = $250 ($12.50 x 20)

Money raised in 12. 1 = 5/52 of the total money raised

ii) The total money raised in the charity walk = $3,100 ($250 ÷ 5/52)

iii) The total amount raised in the previous year = $2,450

The total amount raised in the current year = $3,100

Difference between current and previous year = $650 ($3,100 - $2,450)

Percentage increase on the previous year's total = 26.53% ($650/$2,450 x 100)

11b) Ratio of road and footpath walk = 3:2

The sum of ratios = 5

Road distance = 3/5 x 20 = 12 kilometers

Footpath distance = 2/5 x 20 = 8 kilometers

Vreni's walking speed along the road = 3 km/h

Road distance = 12 kilometers

Time to walk the road = 4 hours (12/3)

Vreni's walking speed along the footpath = 2.5 km/h

Footpath distance = 8 kilometers

Time to walk the footpath = 3.2 hours or 3 hours and 12 minutes (8/2.5) or 192 minutes (8/2.5 x 60)

Total time spent by Vreni = 7 hours and 12 minutes (4 hr + 3 hr + 12 min)

Vreni's average speed = Distance/Time

= 20 km/7.2 hrs

= 2.78 km/h

Starting time = 08:55

Total hours = 7 hours and 12 minutes

Finishing time = 16:07 (08:55 + 7 hrs + 12 min)

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The rate of increase of the depth of the water is 6.67 ft/min.

First, calculate the volume of the water tank:

Volume = (1/3) πr²h

Volume = (1/3) × 3.14 × 10² × 24

Volume = 7,040 ft³

Now calculate the rate of increase of the depth of the water:

Rate of increase of the depth = (Flow rate of water into tank / Volume of tank)

Rate of increase of the depth = (20 ft³/min / 7,040 ft³)

Rate of increase of the depth = 0.0028 ft/min

Finally, calculate the rate of increase of the depth of the water when the water is 16 ft deep:

Rate of increase of the depth = (Flow rate of water into tank / Volume of water)

Rate of increase of the depth = (20 ft³/min / 4,096 ft³)

Rate of increase of the depth = 0.0049 ft/min

Therefore, the rate of increase of the depth of the water when the water is 16 ft deep is 0.0049 ft/min, which is equivalent to 6.67 ft/min.

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The value of x using trigonometry is √6.

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

The area of mathematics known as trigonometry examines the link between the ratios of a right-angled triangle's sides to its angles. Trigonometric ratios, such as sine, cosine, tangent, cotangent, secant, and cosecant, are employed to analyze this connection.

The measurement of angles and issues relating to angles are covered in the fundamentals of trigonometry. Trigonometry has three fundamental operations: sine, cosine, and tangent. The cotangent, secant, and cosecant are three crucial trigonometric functions that may be derived from these three fundamental ratios or functions. These functions serve as the foundation for all the key ideas in trigonometry.

In the triangle base = [tex]\sqrt{2}[/tex] and height as x

The value of the angle is [tex]60\x^{o}[/tex]

so tanθ = tan[tex]60\x^{o}[/tex]

[tex]\frac{height }{base} = tan60\x^{o} \\[/tex]

⇒ x = √3 * √2

⇒ x = √6

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The differential equation for the time evolution of the toxic chemical in the pond is dy/dt = -200y + (100/2000)x

where y represents the amount (in kg) of the contaminant in the pond and x represents the amount of contaminant added to the pond per minute (5 kg/minute in this case). The negative sign in the equation indicates that the amount of contaminant is decreasing in the pond, while the positive term (100/2000)x indicates that the contaminant is being added to the pond at the rate of 5 kg/minute.

To solve for y, we can integrate the equation with respect to time. We start by multiplying both sides by dt, giving us the integral form of the equation: dy = -200y dt + (100/2000)x dt. Integrating both sides gives us the solution y = -200y(t) + (100/2000)x(t) + C, where C is an integration constant. Since we know the initial amount of contaminant in the pond is 5 kg, we can set y(0) = 5 and solve for C, giving us C = 5. Therefore, the solution to the differential equation is y(t) = -200y(t) + (100/2000)x(t) + 5.

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The probability that at least 3 copiers will break down on a given day is 0.0909.

1. Calculate the probability that 0 copiers will break down:

P(0) = (1-0.66)^5

= 0.0729

2. Calculate the probability that 1 copier will break down:

P(1) = 5 * 0.66 * (1-0.66)^4

= 0.2221

3. Calculate the probability that 2 copiers will break down:

P(2) = 5C2 * 0.66^2 * (1-0.66)^3

= 0.3088

4. Calculate the probability that 3 copiers will break down:

P(3) = 5C3 * 0.66^3 * (1-0.66)^2

= 0.2197

5. Calculate the probability that at least 3 copiers will break down:

P(at least 3) = 1 - (P(0) + P(1) + P(2))

= 0.0909

The probability that at least 3 copiers will break down on a given day is 0.0909. This was calculated by first calculating the probability of 0 copiers breaking down (P(0)) which is (1-0.66)^5, then the probability of 1 copier breaking down (P(1)) which is 5 * 0.66 * (1-0.66)^4, and then the probability of 2 copiers breaking down (P(2)) which is 5C2 * 0.66^2 * (1-0.66)^3. Finally, the probability that at least 3 copiers will break down (P(at least 3)) was calculated by subtracting the sum of P(0), P(1), and P(2) from 1. This gives us the final result of 0.0909.

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Answer:

Step-by-step explanation:

It can include things like answers to equations, solutions to problems, and visualizations of data.

1. Input: The data and instructions a system receives.

2. Process: The manipulation of data and instructions to produce an output.

3. Output: The result of the system's processing of the data and instructions.

4. Feedback: Information from the output that is used to improve the system's performance.

1. Input: The first part of a system in mathematics is the input. This is the data and instructions that the system receives. It can include things like numbers, equations, formulas, and instructions for how to process the data.

2. Process: The second part of a system in mathematics is the process. This is where the data and instructions are manipulated to produce an output. This can include things like calculations, algorithms, and other mathematical operations.

3. Output: The third part of a system in mathematics is the output. This is the result of the system's processing of the data and instructions. It can include things like answers to equations, solutions to problems, and visualizations of data.

4. Feedback: The fourth part of a system in mathematics is the feedback. This is information from the output that is used to improve the system's performance. This can include things like error messages, suggested changes, and suggestions for optimization.

The four parts of a system in mathematics are input, process, output, and feedback. Input is the data and instructions a system receives. Process is the manipulation of data and instructions to produce an output. Output is the result of the system's processing of the data and instructions. Feedback is information from the output that is used to improve the system's performance.

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Answer:

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

The scale factor is 2, since each side is twice the initial length.

There are 4 congruent copies, as we can see on the picture.

The dilated area is 12*4 = 48 square units, since the area is the product of two dimensions, each dimension is twice the initial value therefore the area is 2*2 = 4 times greater.

Answer:

simple 5×-5 the answer divide by -5

Answer:

If two triangles are similar, the ratio of their corresponding side lengths is the same as the ratio of their areas.

We know that the area of the first triangle is 18 cm^2, and the area of the second triangle is 8 cm^2. So, the ratio of their areas is 18/8 = 9/4

We also know that one of the sides of the first triangle is 4.5 cm.

So the ratio of the corresponding side of the second triangle to the first triangle is:

(length of corresponding side of second triangle) / 4.5 = 9/4

We can cross-multiply and solve for the length of the corresponding side of the second triangle:

4.5 * (9/4) = 9 * (9/4) / 4 = 9 * 2.25 / 4 = 20.25 / 4 = 5.0625 cm

So, the length of the corresponding side of the second triangle is 5.0625 cm.

so the sample space will be simply all the cookies in the jar, namely 5 + 6 + 9 = 20.

the probability that Mark will NOT pick a Peanut Butter one hmm, that means that Mark will pick either a Chocolate Chip or an Oatmeal one, now this is an OR case so that means sum. so what are the chances Mark will pick either one?  P(Chocolate) + P(Oatmeal)

[tex]\stackrel{P(Chocolate)}{\cfrac{5 }{20}}~~ + ~~\stackrel{P(Oatmeal)}{\cfrac{9}{20}}\implies \cfrac{5+9}{20}\implies \cfrac{14}{20}\implies \cfrac{7}{10}\implies 0.7~\hfill \text{\LARGE 70\%}[/tex]

The statement, "two triangles with corresponding congruent angles are congruent," is true.

According to the Triangle Congruence Postulate, if two triangles have three pairs of corresponding congruent angles, then the triangles are congruent.

This means that if two triangles have three pairs of corresponding congruent angles, all six angles are congruent and the triangles are exactly the same size and shape.

Thus, the statement, "two triangles with corresponding congruent angles are congruent," is true.

Congruence is determined by the congruence of angles, sides, and the overall shape of the triangle. If two triangles have the same angles and sides, then they are considered to be congruent.

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Answer:

80% of the flour is left.

Answer:

I hope may answer is correct! I am sorry if it is not!

The chef used 800g out of a 5kg bag of flour, so the amount of flour left is 5,000g - 800g = 4,200g. To find the percentage of flour left, divide the amount of flour left by the total amount of flour and multiply by 100: (4,200g / 5,000g) * 100 = 84%. So 84% of the flour is left.

According to the given information the detection angle is 72.

An angle is formed anytime two straight lines and rays meet at a single terminal. The intersection of two points at such an angle is known as the vertex. The word "angle" comes from the Latin word "angulus," which meaning "corner."

Degrees are a measure representing circularity or rotation and are used to express angles. You would turn 360° in order to face back in the exact direction after completing a full revolution. As a result, a quarter-circle, or straight angle, is 90°, and a half-circle is 180°. The sum of any two or maybe more angles on the a straight line is 180°.

[tex]\begin{aligned}5\theta & =360^{\circ} \\\theta & =\frac{360^{\circ}}{6} \\& =72^{\circ}\end{aligned}[/tex]

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The absolute value of a number is always positive or zero because it represents the distance of a number from zero on a number line, and the distance between two points can never be negative.

The absolute value of a number is defined as the distance of that number from zero, regardless of its sign. For example, the absolute value of -5 is 5 and the absolute value of 5 is also 5. When we apply the absolute value function to a number, the result is always positive or zero.

Additionally, the definition of absolute value is |x| = { x if x >=0, -x if x<0 }

if x is greater or equal to 0, the absolute value of x is x, otherwise is -x, which is positive.

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As, the moon has an elliptical orbit around a planet, the maximum distance between the planet and its moon is 88.54 Mm.

What is an elliptical orbit?

When an object moves around another object in an oval shaped path (ellipse), it is known to be revolving in an elliptical orbit.

The standard form of the equation of an ellipse with center at the origin (0,0) and x - axis major axis is given by

x²/a² + y²/b² = 1

Now,

Given that a moon's elliptical orbit around a planet is modeled by the equation 225x² + 576y² = 176,400, where distance is measured in megameters (Mm). and the planet is the center of the orbit's path.

Since the equation of the path is the equation of an ellipse, we write it in standard form

As standard form of the equation of an ellipse with center at the origin (0,0) and x - axis major axis is

x²/a² + y²/b² = 1  (1) where

a = vertex of major axis and

b = vertex of minor axis

So, converting 225x² + 576y² = 176,400 into standard form, we have

225x² + 576y² = 176,400

225x²/1764,000 + 576y²/1764,000 = 176,400/1764,000

x²/7840 + y²/3062.5 = 1  (2)

Comparing equation (2) with (1), we have that

a² = 7840 and b² = 3062.5

⇒ a = √7840 = 88.54 and

⇒ b = √3062.5 = 55.34

Since a = 88.54 is greater than b = 55.34, so, a is the major axis, and the maximum distance between the planet and its moon is 88.54 Mm

So, the maximum distance between the planet and its moon is 88.54 Mm

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Since the moon's has an elliptical orbit around a planet, the maximum distance between the planet and its moon is 88.54 Mm

How to find the maximum distance between the planet and its moon?

x²/a² + y²/b² = 1  (1) where

a = vertex of major axis and

b = vertex of minor axis

o, converting 225x² + 576y² = 176,400 into standard form, we have

225x² + 576y² = 176,400

225x²/1764,000 + 576y²/1764,000 = 176,400/1764,000

x²/7840 + y²/3062.5 = 1  (2)

Comparing equation (2) with (1), we have that

a² = 7840 and b² = 3062.5

⇒ a = √7840 = 88.54 and

⇒ b = √3062.5 = 55.34

Since a = 88.54 is greater than b = 55.34, so, a is the major axis, and the maximum distance between the planet and its moon is 88.54 Mm

So, the maximum distance between the planet and its moon is 88.54 Mm

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The price of an adult ticket is $20

The price of a child's ticket is $19

Let x represent the price of a child ticket

Let y represent the price of an adult ticket

Three adults and four children must pay 136

3y + 4x= 136.........equation 1

Two adults and three children must pay $97

2y + 3x= 97.........equation 2

From equation13 1

3y+4x= 136

3y= 136-4x

y= 136-4x/3

Substitute 136-4x/3 for y in equation 2

2(136-4x) + 3x= 97

272-8x/3 + 3x/1= 97

272-8x+9x/3= 97

cross multiply

272-8x+9x=291

collect the like terms

-8x+9x= 291-272

x= 19

Substitute 19 for x in equation 1

3y+4x= 136

3y + 4(19)= 136

3y+ 76= 136

3y= 136-76

3y=60

y= 60/3

y= 20

Hence children tickets cost $19 and adult tickets cost $20

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Answer: A rectangle has two dimensions: length and width. The area of a rectangle is given by the formula A = L * W, where L is the length and W is the width.

Given the area can be represented by the expression 16x^4 + 48x^3 + 82, we can see that it's a polynomial of 4 degree.

So, one of the dimensions (L or W) must be represented by a polynomial of degree 4 and the other dimension by a polynomial of degree 3.

So the expressions that could represent one of the dimensions of the rectangle are:

L = 16x^4

W = 48x^3 + 82

It's important to note that this is just one of the possible representations of the dimensions of the rectangle, depending on the values of x.

Step-by-step explanation:

1. The area of the shaded part = 95π

2. The area of the half circle = 12.5π

3. the distance of the bicycle = 0.0675/π inches

4. The diameter of the circle = 9 unit

radius = 4.5

area = 20.25π unit²

A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.

The area of a circle = πr²

1. Area of the shaded part = area of big circle - area of small circle

= 12²π - 7²π

= 144π - 49π

= 95π

2. area of semi circle = 1/2πr²

= 1/2×5²× π

= 25π/2

= 12.5π unit²

3. The distance moved by the biycle =

S = tetha/r

tetha = 2π×100 = 200π

S = 200π/13.5

S = 14.8π inches

4. c = πd

c = 9π

d = 9

r =d/2 = 9/2 = 4.5

Area = 4.5²π

A = 20.25π unit²

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The distance travelled is 1035 meters, The period T is 1.67m/s and The wavelength is 0.575 meters.

Because sound is a wave, we can use the proper definitions of the terms to derive the relationship between the wavelength, frequency, and speed of a wave. The wavelength is the distance travelled by the wave in one time period of its cycle, whereas the frequency is the number of cycles per second.

Formula used:

Speed = Distance/time

Frequency of wave = 1/Time period of the wave

Wavelength = Distance travelled by the wave in one time period

Given,

a)The distance travelled is 2d,

where d is the distance to the wall

Thus d = 345 × 6/2= 1035 m

b)The frequency is 600 Hz thus the period T = 1/f= 1.67ms

c)The wavelength λ = Velocity/Frequency

= 345/600

= 0.575 meters

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Answer:

(- 1, 5 )

Step-by-step explanation:

y = x + 6 → (1)

y = 2x + 7 → (2)

since both equations have y on the left side, then equate the right sides

2x + 7 = x + 6 ( subtract x from both sides )

x + 7 = 6 ( subtract 7 from both sides )

x = - 1

substitute x = - 1 into either of the 2 equations for y

substituting into (1)

y = x + 6 = - 1 + 6 = 5

solution is (- 1, 5 )

Step-by-step explanation:

We would make these two equations equal to each other since both equations are in y= form

[tex](x + 6) = (2x + 7)[/tex]

Now to get numbers on one side and X's on the other.

Let's start by subtracting 6 from both sides

[tex]x = 2x + 1[/tex]

Next we can subtract 2X

[tex] - x = 1[/tex]

Last but not least, we can divide by -1 to reverse the signs

[tex]x = - 1[/tex]