What does it mean if a function is continuous?

The conversion of 185 centimetres in feet is equals to the 6.06 feet. Thus, conversion factor from centimetres to feet is 6.06/185 = 0.032.

A conversion factor is a number used to convert one set of units into another set of units by multiplication or division. If conversion is necessary, a conversion factor suitable for equivalent value must be used. For example, to convert meters to centimetres, the appropriate conversion value is 100 centimetres equal 1 meter. It includes converting a value from inches to millimeters, for distance from miles to kilometers, feet or other units. How to convert centimeters to feet : One meter is a measure of length and equals approximately 3.28 feet. Thus conversion factor is 3.28 feet. So,185 meters

= 185 × 3.28 feet

= 606.8 feet --(1)

But we need to convert 185 centimeters to feet. So, change meters to centimeters. As you know, 1 meter = 100 centimeters, so 185 meters = 18500 centimeters --(2). Now from equations (1) and (2),

18500 centimeters = 606.8 feet,

Divide both parts by 100,

=> 185 centimetres = (606.8/100 ) feet

= 6.06 feet

Hence required value is 6.06 ft.

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The point on the curve y = x^2 - 3x + 5 where the normal is parallel to the tangent to the curve at the point (4, 9), we need to find the slope of the tangent at the point (4, 9) and then find the point on the curve where the slope of the normal is the same. The equation of the normal is y = -1/5x + 4.52.

First, find the derivative of the function y = x^2 - 3x + 5 to get the slope of the tangent:

dy/dx = 2x - 3

Next, plug in the x-value of the point (4, 9) to find the slope of the tangent at that point:

dy/dx = 2(4) - 3 = 5

The slope of the normal at any point on the curve will be the negative reciprocal of the slope of the tangent at that point. So, the slope of the normal at the point we are looking for will be -1/5.

To find the point on the curve where the slope of the normal is -1/5, set the derivative of the function equal to -1/5 and solve for x:

2x - 3 = -1/5

10x - 15 = -1

10x = 14

x = 1.4

Plug this x-value back into the original function to find the y-value:

y = (1.4)^2 - 3(1.4) + 5 = 4.24

So, the point on the curve where the normal is parallel to the tangent at the point (4, 9) is (1.4, 4.24).

Finally, to find the equation of the normal, use the point-slope form of a line:

y - y1 = m(x - x1)

y - 4.24 = -1/5(x - 1.4)

y = -1/5x + 4.52

So, the equation of the normal is y = -1/5x + 4.52.

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The nth derivative of each function is n!.

Taking the nth derivative of a function is the process of calculating successive derivatives and observing the patterns that occur.

In your example, the function given is f(x) = xⁿ. To find the nth derivative, you need to calculate the first few derivatives and observe the pattern that occurs.

The first derivative of the function f(x) = xⁿ is f'(x) = [tex]nx^{n-1}[/tex]

The second derivative is f''(x) = [tex]n(n-1)x^{n-2}[/tex]

From here, you can see that the pattern is that the exponent of x decreases by 1 each time, and the coefficient of x increases by n-1 each time.

Therefore, the nth derivative of

f(x) = xⁿ => f^(n)(x) = [tex]n(n-1)(n-2)...(n-(n-1))x^{n-n}[/tex] = n!x⁰ = n!.

This result is true for any value of n, so the nth derivative of f(x) = xⁿ is always equal to n.

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To find the axis of reflection for a given object or shape, follow these steps:

1. On a coordinate plane, draw the shape or object. You can do this with graph paper or a computer programme.

2. Find the reflection point or line. This will be the reflection axis. A line that divides a shape or object into two mirror images is referred to as the axis of reflection.

3. Determine the axis of reflection equation. If the axis of reflection is a straight line, the equation is x = a, where an is a constant. If the reflection axis is a horizontal line, the equation will be y = b, where b is a constant.

4. Reflect the shape or object across the axis of reflection to check your work. To accomplish this, flip the shape or object across the axis of reflection and ensure that it appears identical to the original shape or object.

You can also use an online axis of reflection calculator to find the axis of reflection for a given shape or object. To find an axis of reflection calculator, simply type "axis of reflection calculator" into your preferred search engine and select one of the results.

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The completed table in the question used to prove the proportional BD/AB = BC/(AB + AC), when AD is an angle bisector can be presented as follows;

Statement                      [tex]{}[/tex]                   Reason

1. EB ║ AD, AD bisects ∠ABC   [tex]{}[/tex]      1. Given

2. ∠BEC = ∠DAC              [tex]{}[/tex]                2. Corresponding angles theorem

3. ∠C = ∠C   [tex]{}[/tex]                                     3. Reflexive property of congruence

4. ΔBEC = ΔDAC [tex]{}[/tex]                             4. AAA similarity postulate

5. DC/AC = BC/EC [tex]{}[/tex]                      5. Similar triangles have equivalent ratios

6. EC = EA + AC    [tex]{}[/tex]                             6. Segment addition postulate

7. DC/AC = BC/(EA + AC)[tex]{}[/tex]           [tex]{}[/tex] 7. Similar triangles have equivalent ratios

8. AD/AB = DC/AC [tex]{}[/tex]                           8. Triangle angle bisector theorem

9. BD/AB = DC/AC    [tex]{}[/tex]                         9. Substitution property

10. ∠EBA = ∠DAB [tex]{}[/tex]                             10. Alt int. angles theorem

11. ∠DAB = ∠DAC        [tex]{}[/tex]                      11. Definition of a bisector

12. ∠EBA = ∠BEC   [tex]{}[/tex]                           12. Alt int. angles theorem

13. ΔEBA is isosceles [tex]{}[/tex]                       13. Definition of isosceles triangles

14. CA = AB [tex]{}[/tex]                                       14. Side length of isosceles

15. BD/AB = BC/EC [tex]{}[/tex]                           15. Similar triangles have equal ratios

16. BD/AB = BC/(EA + AC) [tex]{}[/tex]                16. Substitution property

17. EA = AB [tex]{}[/tex]                                   17. Definition of isosceles triangle ΔEBA

18. BD/AB = BC/(AB + AC)  [tex]{}[/tex]               18. Substitution property

An angle bisector is an line that divides an angle into two angles of the same measure.

The details of the some of the reasons useds to prove the specified proportion are presented as follows;

Corresponding angles theorem

The corresponding angles theorem states that the corresponding angles formed between parallel lines and a transversal are congruent

Reflexive property of congruence

The reflexive property of congruence states that a geometric figure, such as an angle is congruent to itself

AA similarity postulate

The AA similarity postulate states that triangles are similar two angles in one triangle are congruent to two angles in the other triangles.

Similar triangles have equivalent ratios

Segment addition postulate

The segment addition postulate states that the point B is located between the points A and C on a segment, only if AC = AB + BC.

Ratios of corresponding sides ar

Triangle angle bisector theorem

The triangle angle bisector theorem states that an angle bisector of a triangle divides the side facing the bisected angle in the ratio of the lengths of the other two sides.

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Answer:

Answer: The length of the path would be 35 yds.

Step-by-step explanation:

We can use the formula for the area of a right triangle to find the length of the other leg. Once we know the lengths of both legs, we can use the Pythagorean theorem to find the length of the hypotenuse.

Let's call the length of the shortest side (the leg) "a", and let's call the length of the other side (the other leg) "b". We know that a = 21 yd and the area of the triangle is 294 yd^2. So we can use the formula for the area of a right triangle to solve for b:

area = (1/2) * a * b

294 = (1/2) * 21 * b

b = (2 * 294) / 21

b = 28

Now we know that a = 21 yd and b = 28 yd. We can use the Pythagorean theorem to find the length of the hypotenuse (c):

c^2 = a^2 + b^2

c^2 = 21^2 + 28^2

c^2 = 441 + 784

c^2 = 1225

c = sqrt(1225)

c = 35

Therefore, the length of the path along the longest side of the playground would be 35 yds.

Answer:

35 yards.

Step-by-step explanation:

We can use the Pythagorean theorem to solve this problem. Let's call the other leg of the triangle "x" and the length of the hypotenuse (the path the council would like to add) "c". Then we have:

Area of triangle = (1/2) * base * height

294 = (1/2) * 21 * x

x = 28

Now we can use the Pythagorean theorem to find "c":

c^2 = 21^2 + 28^2

c^2 = 441 + 784

c^2 = 1225

c = sqrt(1225)

c = 35

So the length of the path the council would like to add is 35 yards.

When the number"52" is divided by the number "2" , we get the answer as  26 .

The Division is defined as a mathematical operation , which is used to find the quotient of two quantities. It involves dividing a given number (the dividend) by another number (the divisor) to find the result (the quotient) .

We have to divide , the number 52 by 2 ,

It is represented as : 52/2 ;

Let the answer after performing division be = "x" ;

which means ; x = 52/2 ;

⇒ x = 26 ;

Therefore , On dividing 52 by 2 , the answer is 26 .

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To divide 52 by 2, we can use the long division method. The quotient is 26.

To divide 52 by 2, you can use long division method. Write 52 as the dividend and 2 as the divisor. Divide 5 (the first digit of the dividend) by 2 (the divisor), which gives you 2 as the quotient. Multiply the quotient (2) by the divisor (2), which equals 4. Subtract 4 from 5 to get 1. Bring down the next digit, which is 2. Repeat the process by dividing 12 by 2, which gives you 6 as the quotient. Multiply the quotient by the divisor to get 12, and subtract from the remaining digit 2, which gives you 0. Therefore, 52 divided by 2 equals 26.

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To multiply mixed numbers, convert to improper fractions, cancel factors, multiply the remaining factors, and simplify if possible.

Increasing blended numbers can be tedious, yet there is an easy route that can work on the interaction. To duplicate blended numbers, convert them to ill-advised portions, then drop any elements that show up in both the numerator and denominator of the divisions. At long last, duplicate the leftover elements in the numerator and denominator and work on the subsequent division if conceivable. For instance, to duplicate 2 1/2 by 3 2/3, first proselyte them to inappropriate divisions, which are 5/2 and 11/3. Then, drop the variable of 2 in the numerator of the principal portion and the denominator of the subsequent division. The outcome is 55/3, which can be improved to 18 1/3. This alternate way can save time and assist understudies with taking care of augmentation issues all the more proficiently.

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Answer: 7 x 4 = 28

Step-by-step explanation: 7 + 7 + 7 + 7 = 28

An equation for each situation in terms of x include the following:

A = 3x + 65

B = 2x + 100

The number of miles driven that would make the cost of each company the same is $35.

Based on the information provided above, Company A charges an initial fee of $65 for the rental plus $3 per mile driven. Therefore, the total cost, A, can be represented by this equation:

A = 3x + 65

Since Company B charges an initial fee of $100 for the rental plus $2 per mile driven. Therefore, the total cost, A, can be represented by this equation:

B = 2x + 100

For the cost of each company to be the same, we have the following:

3x + 65 = 2x + 100

3x - 2x = 100 - 65

x = $35.

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the shaded segment PQR will be 18.265m².

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The sum of all angle of triangle = 180

the diagram shows a sector OPQR of a circle, centre O and radius 8 cm.

Area of shaded part = Area of quadrant − Area of triangle

=πr²/ 4 - 1/2 bh

= π × 8²/ 4  - 1/ 2 × 8× 8

= 18.265m².

Hence the shaded segment PQR will be 18.265m².

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Answer:

f(x) = -x^2 is a downward parabola.

Step-by-step explanation:

The f(x) = x^2 graph is a parabola pointing up. Therefore, f(x) = -x^2 is a downward parabola.

In general, whether or not an individual needs to file a tax return depends on a number of factors, including income, filing status, and age.

In the United States, for example, the IRS sets income thresholds each year, and individuals whose income exceeds these thresholds are generally required to file a tax return.

However, there are many exemptions and exceptions to this general rule, and individuals should consult the IRS website or a tax professional for more information specific to their situation.

Other countries may have different rules and requirements for filing tax returns, so it's important to check with the tax authority in your own country for specific guidance.

P.S Your question is incomplete, so I gave you a general overview to help you better understand filing tax returns.

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There are 0.625 (or approximately 5/8) gallons in 80 fluid ounces. It's worth noting that the conversion factor between fluid ounces and gallons can vary depending on the system of measurement used

There are 128 fluid ounces in a gallon in the US customary system of measurement. Therefore, to find out how many 80-ounce containers are in a gallon, you can use the following formula:

number of 80-ounce containers in a gallon = 128 / 80

Simplifying this expression, we can perform the division:

number of 80-ounce containers in a gallon = 1.6

This means that there are 1.6 (or approximately 1 and 3/5) 80-ounce containers in a gallon.

Alternatively, you can convert the 80 ounces to gallons using the following formula:

number of gallons in 80 fluid ounces = 80 / 128

Again, simplifying this expression, we can perform the division:

number of gallons in 80 fluid ounces = 0.625

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The amount having half life=27 days  left after 54 days will be 122 gm.

What is a substance's half-life?

When we refer about half life, we mean the time it takes for exactly half of the radioactive material in question to decay.

More specifically, the time it takes for the radioactive material to lose exactly half of its mass.

Now,

As half-life=27 days

initial amount=488 gm

after 27 days, amount=488/2=244 gm

and after next 27 days amount=244/2

=122 gm

So, After 27+27=54 days the left substance will be 122gm of total initial amount=488gm.

hence,

           The amount left after 54 days will be 122 gm.

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Hello!

Answer:

A. The theoretical probability of flipping 3 heads on one flip of three coins is (1/2) * (1/2) * (1/2) = 1/8. Since you flipped three heads 7 times out of 50, the experimental probability of flipping 3 heads is 7/50.

B. To calculate the theoretical probability of flipping less than 3 heads, we can calculate the probability of flipping 0, 1, or 2 heads and add them together. The probability of flipping 0 heads is (1/2) * (1/2) * (1/2) = 1/8, since all three coins must come up tails. The probability of flipping 1 head is (1/2) * (1/2) * (1/2) * 3 = 3/8, since there are three ways to get one head (HTT, THT, TTH). The probability of flipping 2 heads is (1/2) * (1/2) * (1/2) * 3 = 3/8, since there are three ways to get two heads (HHT, HTH, THH). Therefore, the theoretical probability of flipping less than 3 heads is:

1/8 + 3/8 + 3/8 = 7/8.

So the theoretical probability of flipping less than 3 heads is 7/8.

The total number of pages in Rhett's book is 183 pages.

A solution to an equation is a number that can be substituted for the variable to provide a piece of true number information.

To determine the total number of pages in Rhett's book, we need to solve for p in the equation:

p + 31 = 214

First, we can separate p on one side of the equation by subtracting 31 from both sides:

p + 31 - 31 = 214 - 31

Simplifying:

p = 183

Therefore, the total number of pages in Rhett's book is 183 pages.

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Answer:

Step-by-step explanation:

The expression can be written as ⁴√y. The solution has been obtained by solving the radical expressions.

What are radical expressions?

A square root-containing expression is referred to as a radical expression. When a root other than a square root is being represented, the radical sign's 'V'-shaped component will have a superscript number.

We are given expression as y to the three fourths power, all over y to the one half power. This can be written as

[tex]\frac{y^{3/4}}{y^{1/2} }[/tex]

We know that

cᵃ ÷ cᵇ = cᵃ⁻ᵇ

So, using this we get

[tex]y^{3/4 - 1/2[/tex]

[tex]y^{1/4[/tex]

Since, we have to represent this in the radical form, we know that

b[tex]^{1/a}[/tex] = ᵃ√b

So, using this we get

[tex]y^{1/4[/tex] = ⁴√y

Hence, the expression can be written as ⁴√y.

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The Taylor series for sin(x) is an infinite series expansion that represents the trigonometric function sin(x) as a sum of infinite terms involving the powers of x.

The Taylor series for sin(x) can be written as:

where n! represents the factorial of n.

The series converges for all values of x, which means that it can be used to calculate the value of sin(x) to any desired degree of accuracy. The series is based on the idea that any continuous function can be represented as an infinite sum of terms involving the function's derivatives at a particular point, in this case, x=0.

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the ball will be traveling downward at a velocity of 24 feet per second after approximately 2.75 seconds.

What is velocity ?

Velocity can be defined as ratio of displacement and time taken.

To find the time when the ball will be traveling downward at a velocity of feet per second, we need to find the time when the velocity is equal to that value, which means the velocity is negative.

The velocity of the ball at any time t can be found by taking the derivative of the height function with respect to time:

v(t) = -32t + 64

We need to find the time t when v(t) = -24 feet per second. So we can set up the equation:

-32t + 64 = -24

Solving for t:

-32t = -88

t = 2.75 seconds (rounded to three decimal places)

Therefore, the ball will be traveling downward at a velocity of 24 feet per second after approximately 2.75 seconds.

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In linear equation,the number of customers who will pay by debit card will be 88.97.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                    The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Known as a linear equation, this type of equation has a highest power of one for each variable.

Last week there were

87 + 24 + 7 = 118 customers.

That means that the fraction of the customers, who paid by debit card, was

7/118  

In situations like that, when we use historical data and try to predict future behaviour, we use that past experience and extrapolate to a predicted result.

we simply say that we expect the same fraction, 7/118 if customers use credit cards

for the absolute number of predicted debit  card customers we multiply the predicted number of customers by the expected fraction

1500  × 7 / 118 = 88.97

Therefore the number of customers who will pay by debit card will be 88.97.

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In length 5.4 feet is equivalent to 164.592 centimeters.

Firstly, it is important to understand that length is a physical quantity that describes the size or distance of an object. The unit of length can vary depending on the system of measurement used. The Imperial system, which is commonly used in the United States, measures length in feet, whereas the metric system, which is used worldwide, measures length in centimeters.

Now, to convert 5.4 feet into centimeters, we need to use a conversion factor. One foot is equivalent to 30.48 centimeters, so we can multiply 5.4 feet by 30.48 to get the equivalent length in centimeters.

5.4 feet x 30.48 cm/1 foot = 164.592 cm

It is important to note that when dealing with measurements, it is crucial to use the appropriate unit of length to ensure accuracy and consistency.

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Answer:whitch one are they talking about I think it might be answer 3

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Formula is number of possibilities = n (n-1) (n-2) ....1

Here, n = 4

So, number of possibilities = 4 x 3 x 2 x 1 = 24

You can also use following method to count:

ABCD

ABDC

ACBD

ACDB

ADBC

ADCB

--------

BACD

BADC

BCAD

BCDA

BDAC

BDCA

---------

CABD

CADB

CBAD

CBDA

CDAB

CDBA

--------

DABC

DACB

DBAC

DBCA

DCAB

DCBA

--------

Total 24 combinations

The five steps to solving an inequality are as follows:

1.Identify the inequality - In the equation, the inequality symbol should be identified first.

2.Isolate the variable - The inequality should be rearranged so that the variable is on one side, and all other terms are on the other side.

3.Simplify the inequality - Multiplication and division rules should be used to simplify the equation.

4.Solve the inequality - The simplified inequality can be solved for the variable.

5.Graph the solution - The solution should be graphed on a number line in order to visualize it.

In summary, solving an inequality requires the identification of the inequality symbol, the isolation of the variable, the simplification of the inequality, the solving of the inequality, and the graphing of the solution. Following these steps carefully will ensure that the inequality is solved accurately.

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1. a. No, points A, C, and E are NOT coplanar.

This is because A and E are outside the plane)

b. The three lines are AE, CD, BC

c. The three collinear points are; A,B,E

d. The intersection of line AB and line CD is BE

A coplanar point is a point that lies in the same plane as one or more other points.

In three-dimensional space, a plane can be defined by at least three non-collinear points. Any additional point that lies on this plane is considered coplanar with those points.

In simpler terms, if you imagine a flat surface like a piece of paper, and you place some points on it, any additional point that you place on that same flat surface will be coplanar with the original points.

It's worth noting that coplanar points do not necessarily have to be in a straight line, as long as they all lie on the same plane.

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As per the line segment, the location point of M is option (c) (16/5,19/5)

To answer the question, it is important to understand what a line segment is. A line segment is a part of a line that connects two points, usually denoted by X and Y.

Here we have consider that in this case, the line segment XY is divided by Point M such that XM/MY is equal to 2/3.

As we all know that this means that the ratio between the two parts of the line segment is 2:3. Therefore, the location point of M is (-16/5,19/5).

Therefore, the correct option is (c).

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The difference between the two pots is 4731.761 cm^3

How to determine this?

1 gallon = 3785.41 cm^3

2 gallons = 3785.41 cm^3 *2

= 7570.82 cm^3

And also,

1 quart = 946.353 cm^3

3 quarts = 946.353 cm^3 * 3

= 2839.059 cm^3

So, the difference between the two

= 7570.82 cm^3 - 2839.059 cm^3

= 4731.761 cm^3

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Answer:60

Step-by-step explanation:

8x+2x=10x

10*6=60

Answer:

60

Step-by-step explanation:

If x=6, and the equation is 8x + 2x =?, we can simply insert 6 into the equation:

Solving the parenthesis:

Therefore, the answer is 60.