Write an equation for the graph in slope-intercept form. Do not use spaces in the equation

The volume of a right cone is one-third of the product of the area of the base B and the

Since the area of the base and the height is already given, substitute the values in to the equation and then simplify.

We may also find the exact value by substituting the given values into the equation below.

where V is the volume, r is the radius, and h is the height.

To obtain the exact value of the height, we use the Pythagorean theorem.

where a and b are the legs of the formed right triangle while c is its hypothenuse.

From the figure, the slant height is the hypothenuse while the radius, 9 ft, serve as one of the legs. Thus, the other leg, which is the height of the cone can be solved as follows.

Therefore, the height of the cone is as stated above.

Substitute the obtained height and the radius into the second formula that was stated.

Simplify the right side of the equation. Evaluate the exponential expression.

Multiply the numerator and then divide it by 3.

Note that the value that we obtain at first, 1415,603, is slightly different from the one that we obtained, which is 1419.36, since there are values that we already rounded off before substituting the values in the equation.

Therefore, to be more exact, it is best to indicate that the volume of the given cone is approximately 1419.36 ft³.

The total number of students calculated with the method called simplification and who are playing volleyball is 206.

How simplification method work?

In mathematics, the simplification method is used for the equation formation for the problem statements. And it also convert the complicated expression into simpler one to make the calculation easy.

According to the question, the given survey data for the playing volleyball is written below and it is solved by the simplification method:

survey of students: 36

play volleyball: 17

As per question, the simplification expression for the given statement which state that, if the survey of 648 students how many students play volleyball?

Therefore, the required simplified expression can be written as:

Required expression: 648÷36= 18

Now, playing volleyball =18×17=206 students play volleyball

Hence, the total number of students calculated with the method called simplification who are playing volleyball is 206.

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Answer: -210 is your answer

Step-by-step explanation:

I took the test and worked it out

Answer: -210

Step-by-step explanation: remembered answering this question once and -210 was the right answer

Answer:

c>11

Step-by-step explanation:

you +12 on both sides then u now have 11 rather than -1 which leaves u with c>11

Answer:

first evening = 27 calls

second evening = 42 calls

third evening = 21 calls

Step-by-step explanation:

Total of 90 calls

f = first evening

s = second evening

t = third evening

f=t+6

s = 2t

t=t

f+s+t=90

t+6 + 2t + t

(2t+t+t)+6 = 90

4t+6 = 90

4t=84

t=21

=21+6

= 27

s = 2t

 = 42

t = t

= 21

A is defined as a subset of the sample space, that is, the universal set

a. A∩B = { E3, E9}

b. A∪B = {E,  E1, E2, E3,E7, E9}

c. Yes, the union of A and B is collectively exhaustible

Sets are defined as in mathematical and logical collection of elements or objects, numbers or functions.

The members of a set are listed in enclosed braces.

The elements and objects of a set are well-defined and fixed.

Given the sets as;

S= [E1, E2, E3, E4, E5, E6, E7, E8, E9, E10]

A = [E1, E3, E6, E9]

A is defined as a subset of the sample space, S

a. It is important to note that the intersection of two sets involves the elements or objects that are common between them.

Given that;

A = [E1, E3, E7, E9]

B = [E2. E3, E, E9]

A∩B = { E3, E9}

b. Note that the union of sets involves the collection of the elements of both sets without repetition.

A∪B = {E,  E1, E2, E3,E7, E9}

c. The union of the sets A and B are together exhaustive as it contains all the elements in both sets.

Hence, A is defined as a subset of the universal set.

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To solve this problem, we will use the conditional probability definition: Given events A,B such that P(B)>0 we have that

Where P(A|B) means the probability of A given B occurred. This also leads to the following

Now, let us define two events. Let M1 be the event that we select a male first and let F2 be the event that we select a female second. We want to calculate the following probabilty

Using the definition of conditional probability, this is the same as

Now, we will calculate P(M1). At the beginning, when we have not picked anyone yet, we have 37 people (21 Female and 16 Male). So the probability of picking a male first is simply

Now, we will calculate the second probability. Since we already picked one male, we have now 36 people (21 female and 15 male). Then the probability of picking a female is

So,

Answer:

c

Step-by-step explanation:

The features of the graphs are

Function 1

The equation of the function is given as

f(x) = 3(x - 4)^2 + 3

A quadratic equation can be represented as

f(x) = a(x - h)^2 + k

Where, the vertex is

Vertex = (h, k)

And the axis of symmetry is

x = h

By comparing the equations, we have

Vertex = (4, 3)

Axis of symmetry: x = 4

See attachment 1 for the graph of the function

Function 2

The equation of the function is given as

f(x) = 5x^2 + 4x - 1

Differentiate the function

f'(x) = 10x + 4

Set to 0

10x + 4 = 0

This gives

x = -0.4

Substitute x = -0.4 in f(x) = 5x^2 + 4x - 1

f(-0.4) = 5(-0.4)^2 + 4(-0.4) - 1

Evaluate

f(-0.4) = -1.8

This means that

Vertex = (-0.4, -1.8)

Axis of symmetry: x = -0.4

See attachment 2 for the graph of the function

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Answer:

The answer would be £36

Step-by-step explanation:

12+12+12=36

Using proportions, the costs for the boats are given as follows:

Factory A:

Factory B:

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem using the standard operations such as addition, subtraction, multiplication and division with the unit rates to find the equivalent amounts.

Considering the costs per hour and the number of hours needed, the cost of a small boat at Factory A is given by:

15 x 1  + 11 x 0.5 + 12 x 0.2 = $22.9.

For example, 15 x 1 is because it requires one hour of cutting, and each hour of cutting pays of $15.

The cost of a medium boat at Factory A is given by:

15 x 1.6  + 11 x 1 + 12 x 0.2 = $37.4.

The cost of a large boat at Factory A is given by:

15 x 2.5 + 11 x 2 + 12 x 1.4 = $76.3.

The cost of a small boat at Factory B is given by:

13 x 1  + 11 x 0.5 + 10 x 0.2 = $20.5.

The cost of a medium boat at Factory B is given by:

13 x 1.6  + 11 x 1 + 10 x 0.2 = $33.8.

The cost of a large boat at Factory B is given by:

13 x 2.5 + 11 x 2 + 10 x 1.4 = $68.5.

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The correct function to represent the depth of the pond in inches x days after the dry season begins is f(x) = 81.6 - 0.02x

It is a question of functions.

Given that:-

Depth of pond in Luke's neighborhood = 81.6 inches.

Depth that pond loses everyday = 0.02 inches

Function written by Luke to represent the depth of the pond in inches x days after the dry season begins = f(x) = -0.02(x+81.6)

We have to find the error in Luke's function and then rewrite then correct function.

Let x be the number of days after the dry season begins.

We know that,

Depth of pond after x days = Initial depth of pond - (Depth that pond loses everyday)* (number of days after the dry season begins)

Hence, we can write,

f(x) = 81.6 - 0.02x

Luke has wrongly multiplied -0.02 with (x + 81.6) instead of only multiplying with x.

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In order to determine which equation shows direct variation, you take into account that a direct variation is a linear equation that can be written in the following form:

y= kx

here k is a constant fdifferent of zero. By comparing the given options you can notice that only the equation y = 2x

Hence, y = 2x shows a direct variation.

The coordinates of the vertices of the image triangle A'B'C' after a rotation 90° counterclockwise about the origin are: A' (10, 5), B' (-4, -8), C'(0, 2)

A rotation simply refers to a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

In Geometry, rotating a point 90° about the origin in a counterclockwise (anticlockwise) would produce a point that has the coordinates (-y, x).

By applying a rotation of 90° counterclockwise to triangle ABC, the coordinates of the vertices of the image triangle A'B'C' include the following:

(x, y)                    →            (-y, x)

Point A = (5, -10)   →  Point A' = (-(-10), 5) = (10, 5)

Point B = (-8, 4)   →    Point B' = (-4, -8)

Point C = (2, 0)   →     Point C' = (0, 2)

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the prime factors of a positive integer are the prime numbers that divide that integer exactly.

The answer is

(a) the fixed cost when zero items are produced is $500 .

(b) cost for making 25 items is $750  .

(c) the domain and range of cost function is [0,100] and [500,1500] respectively  .

It the question ,

it is given that

the cost function is C(x)=10x+500  

Part(a)

to determine the fixed cost when 0 items are produced

Since 0 items are produced , we substitute the value x=0 in the cost function , we get

C(0)=10(0)+500

= 500

the fixed cost is $500.

Part(b)

to find the cost of making 25 items , we substitute x=25

On substituting the x=25 , we get

C(25)=10(25)+500

= 250+500

=750

the cost for 25 items is $750.

Part(c)

to find the domain of the cost function C(x)

Given that the maximum cost allowed is 1500

So, 1500=10x+500

10x=1500-500

10x=1000

x=100

So minimum 0 items and maximum 100 items can be produced ,

hence the Domain is [0,100]

to find the range

substituting x=0, the cost = $500

on substituting x=100 , the cost = $1500

the Range is [500,1500]

Therefore , (a) the fixed cost when zero items are produced is $500 .

(b) cost for making 25 items is $750  .

(c) the domain and range of cost function is [0,100] and [500,1500] respectively  .

The given question is incomplete , the complete question is

The cost in dollars of making x items is given by C(x)=10x+500. The fixed cost is determined when zero items are produced.

(a) Find the fixed cost for this item.

(b) What is the cost of making 25 items?

(c) Suppose the maximum cost allowed is $1500. What are the domain and range of the cost function, C(x) ?

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The standard deviation of the discrete distribution of the number of defects in a day is of 0.75 defects.

From the distribution at the end of the answer, the mean is:

E(X) = 0.1667 x 4 + 0.3333 x 5 + 0.5 x 6 = 5.3333.

Hence the standard deviation is of:

S(X) = sqrt(0.1667 x (4-5.3333)² + 0.3333 x (5 - 5.3333)² + 0.5 x (6 - 5.3333)²) = 0.75 defects.

The distribution is missing, and is given as follows:

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Using probability we can calculate that the company must charge $697 for an expected return of 400 .

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

The probability that a 30 year old female lives throughout the year

= 0.99967

Death benefit = $900,000

Expected amount the company would pay = probability that a person dies × insurance amount.

Expected amount = (1 - 0.99967) × 900000 = $297

Now Company wants a profit of $400

Cost charged by company =$( 297 + 400 ) = $ 697

Therefore using probability we can calculate that the company must charge $697 for an expected return of $400 .

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°

the two triangles have a bisetor that makes the adjacent side equal, so based on this 25 = 5x- 10

25+ 10 = 5x

meaning your x = 7

but on the equation 5x-10 =0

we get that x = 10/5

x >2

so the range would be 2

The perimeter of the semicircle with different r values is:

So, the formula for the perimeter of the semicircle:

Now, insert values as follows:

(A) (When r = 2)

(B) (When r = 4)

(C) (When r = 12)

Therefore, the perimeter of the semicircle with different r values is:

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The correct question is given below:

2 mm. em. 4 em 12 Manam. Find the perimeter of the semicircle. Use 3.14 for it when needed.

To find the line that is perpendicular to the one we have, the first step is to rewrite the expression in the slope-intercept form.

The slope of this line is -4/5. The one that is perpendicular to it has a slope that is negative reciprocal to this one, which means that we need to invert the fraction and the signal.

The equation for the perpendicular line so far is:

To find "b" we need to replace the coordinates of (-4,-1) and solve for b.

The full expression is:

From the given equation :

This can be written in the slope-intercept form :

where m is the slope

and b is the y-intercept

Rewriting the equation :

The equation will be y = 1/2 x + 4

the slope is m = 1/2

nd the y-intercept is b = 4

Note that parallel lines have the same slope.

So the slope of parallel line is m = 1/2

Perpendicular lines have a slope of negative reciprocal with each other.

So the slope of perpendicular line to this line is m = -2

Equation of parallel line :

we have :

Let's say the line passes at the origin (0, 0)

If a line passes thru the origin, the y-intercept is always b = 0

Therefore, the equation of parallel line is y = 1/2 x

quation of perpendicular line :

we have :

Let's also say that the line passes at the origin (0, 0)

and the y-intercept is also b = 0

he equation of the perpendicular line is yy = -2x

raphing these equations will be :

Original line (Blue)

Parallel line (Orange)

Perpendicular line (Pink)

y-intercepts :

(0, 0) and (0, 4)

The number of different ways that the three positions can be filled is 504 ways.

From the information, there are 9 candidates for three positions at a restaraunt. Based on the data, one position is for a cook, the second position is for a food server and the third position is for a cashier.

Therefore, the number of ways will be:

= 9P3

= 9! / (9 - 3)!

= 9! / 6!

= 9 × 8 × 7

= 504

The number of ways is 504 ways.

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ANSWER.  B = 18,  A = B + 23 = 18+23 = 41.

Step-by-step explanation:

Answer:Note that at least means greater than or equal to (≥) . It was stated that you must be at least 48 inches tall to ride the roller coaster. Hence, the inequality is h≥48 h ≥ 48

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Yes (3,0) is the solution of the given equation.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given Data

Equation

3x - 2y-9=0

X + 8y-3 = 0

Solution(3, 0)

Finding the values of x,

x + 8y - 3=0

x = 3 + 8y...(1)

Substituting x in the equation

3x - 2y = 9

3(3+ 8y) -2y = 9

9 + 24y - 2y = 9

22y = 0

y = 0

Substituting the value in (1)

x = 3 + 8(0)

x = 3

Yes (3,0) is the solution of the given equation.

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