Mandy and 6 of her teammates each sold an equal number of
shirts to raise money for their tennis team. If a total of 56 shirts
were sold, how many shirts did each person sell?

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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Answer:(5,4) , (4,-2) , (-1,0) , (-2,-4)

Step-by-step explanation: Each input can only have one output

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

Answer:

c

Step-by-step explanation:

a) A vertical analysis of the income statement for AT&T is as follows:

                                                      AT&T        Percent

Revenue                                     $132,447        100%

Cost of Services (Expenses)         60,611        45.8%

Selling & Marketing Expense      39,697       30.0%  

Depreciation & other expenses 20,393        15.4%

Operating Income                       $11,746         8.9%

b) A vertical analysis of the income statement for Verizon is as follows:

                                                    Verizon      Percent

Revenue                                     $127,079       100%

Cost of Services (Expenses)         49,931        39.3%

Selling & Marketing Expense        41,016       32.3%

Depreciation & other expenses   16,533       13.0%

Operating Income                      $19,599       15.4%

A financial statement vertical analysis is a comparison of each line item on the financial statement as a percentage of the base figure.

For the income statement, the base figure is the revenue, which is set to 100%.  For the balance sheet, the base figure is the total assets or total liabilities and equity, which are set to 100%.

The vertical analysis uses the following formula = Financial statement line item divided by the total base figure X 100.

                                                      AT&T     Percent

Revenue                                     $132,447  100% ($132,447/$132,447 x 100)

Cost of Services (Expenses)         60,611  45.8% ($60,611/$132,447 x 100)

Selling & Marketing Expense      39,697  30.0% ($39,697/$132,447 x 100)

Depreciation & other expenses 20,393   15.4% ($20,393/$132,447 x 100)

Operating Income                       $11,746    8.9% ($11,746/$132,447 x 100)

                                                    Verizon    Percent

Revenue                                     $127,079  100% ($127,079/$127,079 x 100)

Cost of Services (Expenses)         49,931   39.3% ($49,931/$127,079 x 100)

Selling & Marketing Expense        41,016  32.3% ($41,016/$127,079 x 100)

Depreciation & other expenses   16,533  13.0% ($16,533/$127,079 x 100)

Operating Income                      $19,599  15.4% ($19,599/$127,079 x 100)

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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)

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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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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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.  B = 18,  A = B + 23 = 18+23 = 41.

Step-by-step explanation:

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:

New coordinate are P(0,0) ,Q(-4,2) ,R(6,6)

A coordinate plane is a two-dimensional surface made up of two number lines. It is produced when a horizontal line crosses the origin, which is the location where the X- and Y-axes meet. The numbers on a coordinate grid are used to find points. Using a coordinate plane, you may graph points, lines, and many other things. It functions as a map and gives precise driving instructions between two locations. The definition of a coordinate plane is as follows: A coordinate plane, also known as a rectangular coordinate plane grid, is made when the X-axis and Y-axis, two horizontal lines, cross.

Given that :P(0,0) , Q(-2,1) , R(3,3)

(x,y)→(2x,2y)

P(0,0)

Q(-4,2)

R(6,6)

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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 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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We get 1.37 when we evaluate log 23.6

Given,

log 23.6

We have to evaluate this using a calculator or desmos.

Desmos:

Desmos is a free math teaching and graphing application that is accessible on the web, iOS, and Android. There are classroom activities available to assist students in learning about a number of arithmetic concepts in addition to graphing equations.

Evaluation of logarithms:

You can use a calculator to assess logarithms by utilising the change of base formula, M = log a, M log a, and selecting either the common log or the natural log.

Lets evaluate log 23.6

log 23.6 = 1.372912003

Lets round to 2 decimal places:

log 23.6 = 1.37

That is,

We get 1.37 when we evaluate log 23.6

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The common difference of each given sequence is:

a. -3

b. 3

c. -4

d. 5

An arithmetic sequence or progression is defined as a series of numbers whereby each term of the sequence is determined by adding a constant (known as the common difference) to the previous term to get the next term in the sequence.

The common difference is the number that is added to each term of an arithmetic sequence to get the next term of the sequence.

The common difference, d = difference between two consecutive terms in the sequence.

Subtract the first term from the second term or the second term from the third term to get the common difference of the sequence.

a. Common difference = 7 - 11 = 4 - 7 = 1 - 4 = -3.

b. 23 - 20 = 26 - 23 = 29 - 26 = 3.

c. 12 - 16 = 8 - 12 = 4 - 8 = -4.

d. 3 - (-2) = 8 - 3 = 13 - 8 = 5

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Answer:

a. -3

b. 3

c. -4

d. 5

Step-by-step explanation:

Have a good day!

The conversion of dry measurements are:

a. 352 quarts

b. 48 pints

c. 3.03 bushels

d. 140 pecks

a. 11 bushels to quarts

32 quarts make up one bushel, which is a unit of dry volume.

1 bushel = 32 quarts

11 bushels = (32 × 11) quarts = 352 quarts

b. 3 pecks to pints

A peck, which equals 16 dry pints in imperial and American usage, is a unit of dry volume.

1 peck = 16 pints

3 pecks = 3 × 16 = 48 pints

c. 97 quarts to bushels

As we know, 1 bushel = 32 quarts

1 quart = 1/32 bushel

97 quarts = 97/32 ≅ 3.03 bushels

d. 1,120 quarts to pecks

A peck is an imperial and American customary dry volume measurement unit that is equal to 8 dry quarts.

1 peck = 8 quarts

So, 1 quart = 1/8 peck

1120 quarts = 1120/8 pecks = 140 pecks

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The quotient of 550six and 50six​ is obtained by the calculation to be   11 six

We know that the result that we obtain after we have carried out a division operation is called a quotient. In this case, we have been required to carry out the operation of division in base six.

We could start by converting the both values to base 10 as follows;

(5 * 6^2) + (5 * 6^1) + (0 * 6^0) = 180 + 30 + 0 = 210 ten

(5 * 6^1) + (0 * 6^0) = 30 + 0 = 30 ten

Then we carry out the division in base ten; 210 ten/30 ten = 7 ten

We convert back to base six to obtain 11 six

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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.

According to the graph we have:

1. If the lines A and B cut by the secant D are parallel, then the collateral angles are supplementary, i.e. add up to 180°. In this case:

2. Solve for x:

Answer: x = 24

3. Angle 6 corresponds to angle 3x + 7 so they are equal. So:

Where: x = 24

Substitute the value:

Answer: <6 = 79°

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

A brief definition of a triangle according to Euclidean geometry is shown below:

Closed figure consisting in three non-colinear, all of them coplanar, points named vertices and three line segments associated to each pair of points named sides.

To understand what a triangle is, we need to understand some basic concepts of the Euclidean geometry. There are three undefined terms, that is, fundamental elements that cannot be defined but are described in terms of its attributes. Those terms are point, line and plane. The atributes of each element are described below:

A line can be formed by knowing the location of two distinct points on a plane. Lines can be continuous lines (endless), line segments (lines with finite length) or semirrays (lines with only one endpoint).

Let suppose that we have three points not collinear to each other, then we construct line segments for each pair of collinear points. Then, we create a triangle, whose brief definition is shown below:

Closed figure consisting in three non-colinear, all of them coplanar, points named vertices and three line segments associated to each pair of points named sides.

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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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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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The interest that will be earned when the city is issuing bonds to raise money for a building project is $670.

It should be noted that the formula for the calculation is the interest is given as:

Interest = Principal × Rate × Time / 100

where P = $6700

R = 2%

Time = 5 years

Interest = Principal × Rate × Time / 100

Interest = (6700 × 2 × 5) / 100

= 670

The interest is $670.

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The equation D show the multiplication property of inequality if n+4 =11

What is inequality ?

inequality, When two numbers or algebraic expressions are stated to be greater than, greater than or equal to, less than, or less than or equal to each other in order. Inequalities can be stated as either statements of fact in the form of theorems, which are solved using methods similar to those used to solve equations, or as questions. For instance, the triangle inequality states that the length of the remaining side is greater than or equal to the sum of the lengths of any two sides of a triangle. Many of these inequalities, including the Cauchy-Schwarz inequality, are used in the proofs of many of mathematical analysis' most significant theorems.

Sol-

If n+4 =11

Then by applying the product rule -

(n+4)×2 =11×2

So the correct option is D.

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Answer:

The answer would be £36

Step-by-step explanation:

12+12+12=36

Let us prepare an inequality statement to answer the question.

There is a one-time fee of $85 and a fee of $23 per guest. If x represents the number of guests, the amount spent will be:

If the amount spent cannot exceed $1750, we have the inequality statement to be:

We can solve as follows:

Since we cannot have a fraction of a person, the answer will be 72.

her maximum number of guests is 72.

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.