define the derivative of a funnction y = f(x) at the point a

For the given observation 5,6,7,8,9,11 the Median is 7.5

The median is one of the metrics of central tendency. The middle value in a group of numbers is known as the median. It divides a given data sample into the higher half and the lower half. At least half of the observations fall below the median and at least half of the observations fall above the median.

If a data collection contains an even number of observations, the median can be determined as follows:

Sort the information either by ascending or by descending.

Identify the (n/2)nd and [(n/2) + 1] th observations if there are an even number of observations (let's say n).

The median of the provided data is equal to the average of the top two observations (as determined in step 2).

Here n = 6, So [6/2 + (6/2)+1}/2

=>  Median = 7.5.

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Using the geometry of the right angle triangle. Since, The narrower hallway is 6ft. The answer is 6ft.

A subfield of mathematics called geometry examines the dimensions, placements, angles, and sizes of objects.

A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.

Larger hallway= 9 ft

narrower hallway=6 ft

Since, After turning in the corner, The pole should be carried through the 6ft wide hall. The maximum length of the pole is 6ft.

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The point from which all the points on a circle are equidistant is called the center of the circle, and the distance from that point to the circle is called the radius of the circle. A circle is named with a single letter, its center.

Every point in a circle is equally distance from the center. Similar to a sphere, every point on a sphere is equally distance from the center.

Two equal chords on a circle indicate that they are equally spaced from the circle's center.

The incenter of a triangle is the point that is equally far from each of its sides. A median is a line segment that has one of its endpoints in the vertex of a triangle and the other endpoint in the midpoint of the side opposite the vertex. The three medians of a triangle meet in the centroid.

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No, negative infinity and positive infinity are not the same. Negative infinity is a amount of number that is less than any other number, while positive infinity is a number that is greater than any other number.

Negative infinity is a number that is less than any other number. It is represented by a negative sign followed by an infinity symbol, and it is usually written as "-∞". Negative infinity is the opposite of positive infinity, which is a number that is greater than any other number. Positive infinity is usually written as "+∞". Negative infinity is used in mathematics to signify the smallest possible number or the lower limit of a range, while positive infinity is used to signify the largest possible number or the upper limit of a range. The two numbers are not the same, as they represent opposite extremes of a range. Negative infinity is the lowest possible number and positive infinity is the highest possible number.

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The root of the graph of f(x) = [tex](x-5)^{3} + (x+2)^{2}[/tex] touches the x axis at -2 and 5.

What is root of graph ?

A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph.

What is axis ?

An axis in mathematics is defined as a line that is used to make or mark measurements.

Have given ,  f(x) = [tex](x-5)^{3} + (x+2)^{2}[/tex]

⇒ [tex](x-5)^{3} * (x+2)^{2}[/tex]= 0.

But if ab = 0 ⇒ either a = 0 or b = 0 or both zero.

⇒ [tex](x-5)^{3}[/tex]= 0 and \[tex](x+2)^{2}[/tex] = 0

⇒ (x - 5) = 0 and x + 2 = 0

⇒ x = 5 and x = - 2.

The root of the graph of f(x) = [tex](x-5)^{3} + (x+2)^{2}[/tex] touches the x axis at -2 and 5.

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Answer:

$218.5

Step-by-step explanation:

its $218.5 because 250 - 56.50 = 193.5 and 193.5 + 25.00 + 218.5

The number of tickets sold will be equal to 29.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Let x represent the number of child tickets that were sold

Let y represent the number of adult tickets that were sold

5.30x +9.40y= 1206

The number of adult tickets sold was three times greater than the number of child tickets,

y= 3x

Substitute 3x for y in the equation,

5.40x + 9.40y= 974.40

5.40x + 9.40(3x)= 974.40

5.40x + 28.2x= 974.40

33.6x= 974.40

Divide both sides by the coefficient of x which is 33.5,

x= 974.40/33.6

x = 29

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The property that represents the commutative law of sets is given as follows:

d. (A ∪ B) ∪ C = A ∪ (B ∪ C)

The cumulative law of sets states that the order in which the union operation is made does not change the resulting set of these multiple union operations.

The symbol that represents the union operation is given as follows:

∪.

Hence statement d is the correct statement of the commutative law of sets, as:

For both cases, the resulting set is the same.

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Horizontal asymptotes is a horizontal line and its equation is y=k

vertical asymptotes is a vertical line and its eqaution is x=k

In these given lines we can find horizontal and vertical asymptotes.

To find the horizontal asymptotes ,we compare the degree of the numerator with the degree of denomenator.

f(x)=ax^n/bx^m

if degree of numerator is greater than degree of denominator then does not exist horizontal asymptotes.

To find  the vertical asymptotes , we use

f(x)= p(x)/q(x)

To set the denominator q(x) to zero ,and solve the value for x.

where p(x) and q(X) are polynomial functions and q(x) [tex]\neq[/tex] 0

vertical asymptotes is x=k where k represents real zero of q(x).

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By using the property of combination, it can be calculated that -

This is a problem of combination.

There are 15 ways to choose the students who will go to the meeting

What is combination?

Combination is the process of selection some objects from a group of items where the order of the selection do not matter

This is a problem of combination

Number of seniors = 6

Number of students will go to the all district meeting = 2

Number of ways to choose the students who will go to the meeting =

                                                                                                       [tex]{6 \choose 2}[/tex]

                                                                                                = [tex]\frac{6!}{(6 - 2)! \times 2!}[/tex]

                                                                                                = 15

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Answer: I think it's 13

Step-by-step explanation: So we need to fill in the distance formula. It's d=√((x_2-x_1)²+(y_2-y_1)²).

-6=x_1

-3=y_1

6=x_2

2=y_2

Now you plug in your coordinates to the formula, so you get d=√((6--6)²+(2--3²)

(6-(-6)²=144

(2-(-3²)=-7

So now 144+25=169

The square root of 169 is 13, so d=13. That should be your answer! Let me know if it's right

Answer:

Step-by-step explanation:

360

Answer:

The tree is 10.77 meters tall.

Step-by-step explanation:

The given diagram is an example of similar triangles. Look at the image I attached to my response to see this problem in terms of triangles.

The triangle that is formed by Alyssa and her shadow and the triangle that is formed by the tree and its shadow is an example of similar triangles because they both share an internal angle.

As per the similar triangles theorem, the ratios of the corresponding sides of both sides are proportional.

Thus, we have to make a proportion of the corresponding sides of both triangles to solve for the height of the tree. Let x = the height of the tree.

Proportion: [tex]\frac{BE}{BC} = \frac{DE}{AC}\\[/tex]

BE = 4.25 meters

BC = 27.75 meters

DE = 1.65 meters

AC = x meters

[tex]\frac{4.25}{27.75} = \frac{1.65}{x}[/tex]

Now, cross multiply to solve for x.

[tex]4.25x = 1.65(27.75)\\4.25x = 45.7875\\x = 10.77[/tex]

∴ The tree is 10.77 meters tall!

The height of the tree to the nearest hundredth of a meter is,

⇒ 10.77 meters

We have to given that;

Alyssa is 1.65 meters tall. At 11 a.m., she measures the length of a tree's shadow to be 27.75 meters. She stands 23.5 meters away from the tree.

Now, we can make a proportion of the corresponding sides of both triangles to solve for the height of the tree.

And,  Let us assume that,

x = the height of the tree

Hence, We get;

⇒ (27.75 - 23.5) / 27.75 = 1.65 / x

Solve for x;

⇒ 4.25 / 27.75 = 1.65 / x

Cross multiply we get;

⇒ 4.25x = 1.65 x 27.75

⇒ 4.25x = 45.78

⇒ x = 10.77 meters

Thus, The height of the tree to the nearest hundredth of a meter is,

⇒ 10.77 meters

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The required solution would be h = 3Vr²/3.14 for h, where V is the volume of a cone.

The volume of a cone is defined as the amount of space occupied by a cone in a three-dimensional plane.

The volume of the cone (V ) = 1/3πhr²

We have been given that the volume of a cone is (1/3)3.14r²h

We have to determine the solution for h

As per the given question, we have

⇒ V = (1/3)3.14r²h

Multiply by 3 into the above equation,

⇒ 3V = 3.14r²h

Divided by 3.14 into both sides

⇒ 3V/3.14 = r²h

⇒ h = 3Vr²/3.14

Therefore, the required solution would be h = 3Vr²/3.14.

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The  average rate of change in concentration of b from t= 0 s to t = 212 s as calculated from the data given above is 0.004811  m/s.

The average rate of change is given by the formula ,

concentration change / time change.

First we will calculate the rate of change for A

rate change = 0.140 - 0.650 = -0.510 M

time difference = 212 s − 0 s = 212 s

Rate of concentration change = -0.510 M / 212 s = -0.002405 M/s

The - sign indicates that the [A] is decreasing with time.

In order to calculate the concentration rate of B we will write it in the form of stoichiometry

B = 2 x 0.002405 = +0.004811 m /s

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The number of ways in a class of size 60 where no two students will have the same birth date is 365 x 364 x 363 x 362 x ........... x 306.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of students = 60

We will assume 365 days in a year.

Now,

The first student will have 365 possible days for his birthday.

The second student will have 364 possible days for his birthday.

In this way,

The last student will have (365 - 59) possible days for his birthday.

Now,

The number of possible ways for 60 students.

= 365 x 364 x 363 x 362 x ........... x 306

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The ratio of the error is; 0.3333

The Percent error of the given problem is;  33.33%

We are given;

Amount spent by John on shopping = $75

Amount expected to spend = $100

Since this is what was given then it means we will have the following;

The approximate value to be spent = 100 dollars

Exact Value  spent = 75 dollars

Therefore, the error made is;

Error = Approximate value - Exact value  

Error = 100 - 75

Error =  25 dollars

Thus, the error when it is absolute is;

Absolute Error = ±25 dollars

Now, the ratio will be;

Ratio(e) = Error/exact value spent

e = 25/75 = 0.3333

Percent Error = error * 100%

Percent error = 0.3333 * 100%

Percent error =  33.33%

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Answer:

Slope

Angle (degrees) Gradient Grade (%)

Therefore, the correct answer is 5.24

The five ways to prove the congruence theorem are listed as,

Here we have to find the 5 ways to prove congruence.

As we all know that, according to the concept of triangle, then term congruence referred as if two shapes are congruent if and only if they have the exactly the same sides and exactly the same angles.

Based on these we have derived 5 sub theorem, from the congruence theorem, they are listed as,

1) SSS   (side, side, side)

2) SAS   (side, angle, side)

3) ASA   (angle, side, angle)

4) AAS   (angle, angle, side)

5) HL   (hypotenuse, leg)

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Answer:

f(x)=19

Step-by-step explanation:

x=-5

f(x)=-3(-5)+4

f(x)=15+4

f(x)=19

I think this is how you do it, but I haven't done these problems in a while so I could be incorrect.

Answer: I believe 20.

Take one pair of lines. They will intersect at a point (no lines parallel). The other four lines will intersect at different points (no more than two lines through one point) giving four triangles. There are 6C2 = 15 different pairs of lines so 15*4 = 60 triangles. However, each triangle will come from three different points so we need 60/3 = 20 distinct triangles.

EDIT: Now that I’m more awake, it occurs to me there is a much easier answer. Since no two lines are parallel and no three lines are coincident, every combination of three lines must form a triangle. There are 6C3 = 20 triangles.

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

combinations

C(n,r)= n! / (r! * (n−r)!)

n = 6 : total number of lines

r = 3 : because its 3 lines to make a triangle

6 lines

6C3 = 20 triangles

quora glenn clemens

mathplanet

The volume of the pyramid with the given base area of square and height of the cube is given by: V = ( 1/3) × ( y)² × (h).

As given in the question,

Base of the given pyramid is square in shape.

Base area of the pyramid is given by:

Let 'y' be the side length of the square base.

Area of the square base = ( side length )²

                                         = y²

let 'h' be the height of the cube

Volume (V) of the pyramid = ( 1/3 ) × Base area × height

⇒Volume of the pyramid = ( 1/3 ) ×  y² × h

Therefore, the volume of the pyramid with square base and height of the cube is equal to Volume of the pyramid = ( 1/3 ) ×  y² × h.

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Answer:

x is 5 cm

Step-by-step explanation:

x is half of the diagonal and we can see that the diagonal is 10 cm

and half of 10 is

The denominator of a fraction represents the number of equal parts in a whole, while the numerator represents the number of parts considered.

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Answer: You are correct, because negative number don't have real square roots

Step-by-step explanation:

Answer:

increase 10.5 percent

Step-by-step explanation:

..

We can find out the missing values of the sides of a triangle by using trigonometry functions like sin, cos, and tan.

If one angle and perpendicular are given then the other side means hypotenuse can be found out by sin function.

Sin Ф = perpendicular/hypotenuse

If one angle and hypotenuse are given then the other side means base can be found out by the Cos function.

CosФ = base/ hypotenuse

If one angle and base are given then the other side means perpendicular can be found out by the tan function.

Tan Ф= perpendicular/ base

Therefore the missing sides can be found by trigonometric function while one angle is given.

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Therefore , the 2 year old children can able to count to 1 to 100 counting by making them learn.

The counting-on method can be used by mathematicians to add numbers. With this approach, a student first adds the larger number,

variable then "counts on" with the other addends to arrive at the sum. If the number sentence is 4 + 3, the student will understand that 4 is the greater number and will add three additional numbers, such as the integers "4... 5, 6, 7."

Here,

Every child is different in how they grow and learn, yet many

Children as young as two years old may count past ten and learn their numbers from 1 to 100.

They could be ready to try numbering in fives or using other skip counting strategies (5, 10, 15, 20, and so on).

As soon as you can, begin teaching your child how to recognise

numbers.

As a result, by making the toddlers study, two-year-olds can count to one hundred.

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Answer:

0

Step-by-step explanation:

Rise over run.

Difference between y is 0.

Difference between x is 5.

0/5 = 0.

Answer:

m = 0

Step-by-step explanation:

Slope is rise/run or (y2 - y1) / (x2 - x1)

We see the y stay the same, and the x decrease by 5, so the slope is

m = 0/5