What is meant by production possibility curve illustrate the central problems of what to produce and how to produce using the curve?

Barbara has 6 nickels, 8 dimes and 5 quarters in her purse

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

We know that the number of dimes is three less than the sum of the numbers of nickels and quarters, so:

d = n + q - 3

2.35$ is equal to 235 cents and nickels are worth 5 cents each, dimes 10 cents each, and quarters are 25 cents each. So the values of her coins are:

5n = value of the nickels

10d = value of the dimes

25q = value of the quarters

5n + 10d + 25q = 235

Solving the equations we have:

n +d + q = 19                 (1)

d = n + q - 3                  (2)

5n + 10d + 25q = 235  (3)

By ordering the variables in the (2) equation we have:

d = n + q - 3

d - n - q = - 3

- n + d - q = -3

n      + d      + q =      19            (1)

- n    + d       - q =      -3            (2)

5n + 10d + 25q =   235            (3)

Substitute (d) for n + q - 3  in (1) and (2) equations.

n + n + q - 3 + q = 19

2n  + 2q = 22

2(n+q) = 22

n+q = 22/2

n  + q  = 11        (4)

In (2) equation:

5n + 10(n + q - 3) + 25q = 235

5n + 10n + 10q - 30 + 25q = 235

15n + 35q = 265  (5)

We now have two equations in two unknowns instead of 3 unknowns:

n +    q =   11         (4)

15n + 35q = 265  (5)

Multiply (4) equation by -15 and add:

-15n  - 15q  = -165

15n  +35q  =  265

         20q  = 100

q = 100/20

q = 5

Substitute for (q) in (4)

n + 5 = 11

n = 11-5

n = 6

Substitute (q) and (n) value in (1)

n +d + q = 19  

6 + d + 5 = 19

d = 19 - 6 - 5

d = 8

Therefore, Barbara has 6 nickels, 8 dimes and 5 quarters

Learn more about equation at: brainly.com/question/2972832 and brainly.com/question/27815607

#SPJ4

Skydiver took 15√3 seconds to freefall 1200 feet.

What is arithmetic?

Mathematical arithmetic is the study of the properties of the standard operations on numbers, such as addition, subtraction, multiplication, division, exponentiation, and root extraction.

Here, we have

Given: A skydiver falls at a rate of t = 0.75√x seconds to freefall x feet.

x = 1200 feet

Now, we put the value of x in t = 0.75√x and we get

t = 0.75×√1200

t = 0.75× 20√3

t = 15√3

Hence, Skydiver took 15√3 seconds to freefall 1200 feet.

To learn more about the arithmetic from the given link

https://brainly.com/question/25896797

#SPJ1

The required way to find  the solution set of a system of equations is described.

system of equations, simultaneous equations Algebraic equations involving two or more must be solved cooperatively (i.e., the solution must satisfy all the equations in the system). For a system to have a single solution, the number of equations must equal the number of unknowns.

Then we will get the required variables in this system.

To know more about Solution set visit:

brainly.com/question/11988499

#SPJ4

The exponent expression [tex]\rm \left (\frac{1}{n} \right)^{-\frac{2}{3}}[/tex] will be equivalent to the exponent expression [tex]\rm \left (n \right)^{\frac{2}{3}}[/tex].

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The exponent expression is given below.

[tex]\rm \rightarrow \left (\dfrac{1}{n} \right)^{-\frac{2}{3}}[/tex]

We know that a⁻ⁿ = 1/aⁿ.

Simplify the exponent expression, then we have

[tex]\rm \rightarrow \left (\dfrac{1}{n} \right)^{-\frac{2}{3}}\\\\\rm \rightarrow \left (n ^{-1} \right)^{-\frac{2}{3}}\\\\\rm \rightarrow \left ( n \right)^{-1\times -\frac{2}{3}}\\\\ \rightarrow \left ( n \right)^{\frac{2}{3}}[/tex]

The exponent expression [tex]\rm \left (\frac{1}{n} \right)^{-\frac{2}{3}}[/tex] will be equivalent to the exponent expression [tex]\rm \left (n \right)^{\frac{2}{3}}[/tex].

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1

The correct question is attached below.

The measure of segment UY from the given triangle WUY is 90 units.

The midpoint theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the length of the third side.

Given that, VX is a midsegment of ΔUWY.

UY=13p-1 and VX=20p-95.

Since, VX is a midsegment of a triangle, we have

VX= 1/2 (UY)

20p-95 =1/2 ×(13p-1)

40p-190=13p-1

27p=189

p=189/27

p=7

So, UY=13p-1

UY=13(7)-1

UY=90 units

Therefore, the measure of segment UY is 90 units.

Learn more about the midpoint theorem here:

https://brainly.com/question/28667736.

#SPJ1

Answer:

  6⁸ = 1679616

Step-by-step explanation:

You want to simplify the expression (6²)⁴.

The applicable rule of exponents is ...

  (a^b)^c = a^(bc)

Here, this means ...

  [tex](6^2)^4=6^{2\times4}=\boxed{6^8=1679616}[/tex]

__

Additional comment

Your calculator is good at evaluating numerical expressions.

<95141404393>

Consequently, the total number of days required to exit the well is 28.

It represents the taxonomical name, which assures that every creature has a single name made up of the genus and species.

Example :

A frog plunged 30 meters down a well while looking for water. Very erratically, it emerged from the well. It was able to advance 3 m each day, but the next night it fell 2 m. The time it took to exit the well was how many days?

Well depth is 30 m.

If a frog was able to advance 3 metres per day but fell 2 metres the following night,

The frog can climb one metre in a single day and 27 metres in 27 days.

It climbs 3 metres on the 28th day and exits the well.

Consequently, the total number of days required to exit the well is 28.

The Complete Question.

To Learn more About   total number of days   refer To:

https://brainly.com/question/408099

#SPJ1

-1 is the negative integer.

Now, According to the question:

Let's know:

What are Integers?

Integers are the collection of whole numbers and negative numbers. Similar to whole numbers, integers also does not include the fractional part. Thus, we can say, integers are numbers that can be positive, negative or zero, but cannot be a fraction. We can perform all the arithmetic operations, like addition, subtraction, multiplication and division, on integers.

The word integer originated from the Latin word “Integer” which means whole or intact. Integers is a special set of numbers comprising zero, positive numbers and negative numbers.

Examples of Integers: – 1, -12, 6, 15.

So, According to the above statement is:

-1 is the negative integer.

Learn more about Integers at:

https://brainly.com/question/15276410

#SPJ4

The equation that could be used to find how many students are in the class is → {2x + 8 = 3x - 11}.

Given is that the teacher were to distribute sheets of paper so that each student got two sheets, there would be 8 sheets remaining. However, if three sheets were given to each student, the teacher would be 11 sheets short

Let the number of sheets be {y} and the number of students be {x}. We can write -

y = 2x + 8

y = 3x - 11

Equating both -

2x + 8 = 3x - 11

Therefore, the equation that could be used to find how many students are in the class is → {2x + 8 = 3x - 11}.

To solve more questions on algebraic expressions, visit the link below -

brainly.com/question/1041084

#SPJ1

The value of sinB using trigonometry ratio is 8/17 (optionB)

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Sin(tetha) = opposite/ hypotenuse

cos ( tetha) = adjascent/ hypotenuse

tan (tetha) = opposite/adjascent

In the triangle 8 is the opposite to angle B and 15 is the adjacent to angle B and 17 is the hypotenuse.

sinB = opposite/ hypotenuse

sinB = 8/17

therefore the value of sinB = 8/17

learn more about trigonometry ratio from

https://brainly.com/question/24349828

#SPJ1

Using the sine ratio, sin B is calculated as: B. 8/17.

The sine ratio is a formula of the trigonometry ratios that is used to solve a right triangle. It is given as:

sin ∅ = length of opposite side / length of hypotenuse.

Given the following:

Length of opposite side = 8

Hypotenuse length = 17

Reference angle (∅) = B

Substitute the values into the sine ratio formula:

sin B = 8/17

Therefore, the value of sin B is expressed as: B. 8/17.

Learn more about the sine ratio on:

https://brainly.com/question/2920412

#SPJ1

An example of an extraneous solution in math is solving the equation 1/(x−2) + 1/(x+2) = 4/(x−2)(x+2) for x.

An extraneous solution is a root of a transformed equation that is not the root of the original equation because it was excluded from the domain of the original equation.

Solve the equation 1/(x−2) + 1/(x+2) = 4/(x−2)(x+2) for x

1/(x−2) + 1/(x+2) = 4/(x−2)(x+2)

(x−2)(x+2)/(x−2) + (x−2)(x+2)/(x+2) = 4(x−2)(x+2)/(x−2)(x+2)

(x−2) + (x+2) = 4

2x = 4

x = 2

But 2 is excluded from the domain of the original equation because it would make the denominator of one of the fractions zero--and division by zero is not allowed. Therefore, it cannot be the root of the original equation. So, 2 is an extraneous solution. So, the equation has no solutions.

To know more about extraneous solution, here

https://brainly.com/question/28887790

#SPJ4

The difference between log x + 1 and log (x + 1) is that their solution is respectively;

1) (log x) + 1

2) log (x + 1) = log(x/1)

There are different rules of logarithm such as;

1) Product rule;

Log (M * N) = Log M + Log N

2) Quotient rule;

Log (M/N) = Log M - Log N

3) Power rule;

Log Mⁿ = NLog M

Now, we want to find the difference between log x + 1 and log (x + 1) .

Thus;

log x + 1 can also be expressed as;

(log x) + 1

Meanwhile using product rule of logarithm, we get that;

log (x + 1) = log(x/1)

Read more about logarithmic problems at; https://brainly.com/question/237323

#SPJ1

The required value of z in the given system of equations is 4. Option D is correct.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
3x + 5y - z = 15 - - - - (1)

x + 2y = 8 - - - - -(2)

x - 3y + 2z = - 9 - - - - (3)

multiply equation 1 by 2 and add with equation 3,
6x + x + 10y -3y -2z + 2z = 30 - 9
7x + 7y = 21
x + y = 3 - - - -(4)

Subtract equation 4 from 2
y = 5
Now, from equation 4
x + 5 = 3
x = -2

From equation 1
3(-2) + 5(5) - z = 15
-6 + 25 - z = 15
z = 10 - 6
z = 4

Thus, The required value of z in the given system of equations is 4. Option D is correct.

Learn more about simultaneous equations here:

https://brainly.com/question/16763389

#SPJ1

Step-by-step explanation:

I don't see any defined inequality here in the text.

but I can tell you what's in the picture. and how the correct inequality would look like.

the function, for which we need to define the range (all valid y-values) is moving between y = 2 and y = -2, including these 2 values.

the inequality shown is

-9 < y < -4

the values -4 and -9 are not included (indicated by the dotted lines).

so, we need to change that to

-2 <= y <= 2

please consider the "<=" signs, as both values have to be included, because the function is clearly also producing -2 and +2 values.

FYI

it would also be correct to write

2 >= y >= -2

The graph for [tex]y=5\sqrt{x}-2x[/tex] has been attached below. The solution has been obtained using graphing the function.

What is graphing of a function?

Drawing the graph of an applicable function is the process of graphing a function. While graphing simple functions like direct, quadratic,etc. is fairly easy, complex functions like rational, logarithmic,etc. bear some complexity and an understanding of certain fine ideas. Every point on the curve will satisfy the function equation if the curve represents the function.

We are given [tex]y=5\sqrt{x}-2x[/tex]

The range is given as [0,12]

The graph obtained has been attached below.

It is observed that graph of the function is increasing gradually and then decreasing.

Hence, the graph of the function is increasing gradually and then decreasing.

Learn more about graphing function from the given link

https://brainly.com/question/17089414

#SPJ1

The expression for the solution is 6x² - 18x - 4x + 12

We have different methods of solving quadratic equation, they include;

From the information given, we the quadratic equation;

6x² - 22x + 12 = 0

Let's solve the quadratic equation by using the factorization method, we have;

Multiply the coefficient of x² by the constant

Then find the pair factors of the product that adds up to -22, we get;

-18 and -4

Substitute the values into the formula to determine the expression, we have;

6x² - 18x - 4x + 12 =0

group in pairs

(6x² - 18x) - (4x + 12)  = 0

Hence, the expression is (6x² - 18x) - (4x + 12)

Learn about quadratic equation on:

https://brainly.com/question/1214333

#SPJ1

Answer:

x = 15 , y = -5

Step-by-step explanation:

refer to attachment for answer

Hope this helps!

-Rishabh

Simply multiply the number of moles by 24 to obtain the volume of gas in dm3 at standard pressure and temperature.

According to the chemical formula 2 C2H6 + 7 O2 → 4 CO2 + 6 H2O + 3120 kJ, the full combustion of ethane releases 1559.7 kJ/mol, or 51.9 kJ/g, of heat along with carbon dioxide and water. Amorphous carbon and carbon monoxide can be produced when combustion doesn't involve too much oxygen.

Exothermic reactions, such as the combustion of hydrocarbons, provide heat energy. To find the volume of gas in dm3 at room temperature and pressure, simply multiply the number of moles by 24.

The typical scenario is that you are following a recipe that, for instance, calls for a 0.5 molar solution of NaOH. As you are aware, "0.5 M" refers to 0.5 moles per liter.

Therefore, the correct answer is option B 24 dm³.

To learn more about ethane refer to:

https://brainly.com/question/18486242

#SPJ1

Answer: To reduce the fraction to lowest terms, we need to divide both the numerator and denominator by their greatest common factor.

In this case, the greatest common factor between the numerator and denominator is x^2y.

So we can divide the numerator and denominator by x^2y to get:

(4x^(4)y^(3))/(-8x^(2)y) = (4x^2y^2)/(-8) = -(1/2) x^2y^2

So the fraction reduced to lowest terms is -(1/2) x^2y^2, which corresponds with option B.

Step-by-step explanation:

(2,-4), (-2, 3), (-3, 4), (-5, 0) is the transformation for the coordinates of the vertices of the given pairs of quadrilaterals.

In order to represent a quadrilateral visually, four line segments' ends are connected to form a closed geometric object. Each intersection point of every two line segments of a quadrilateral is referred to as a quadrilateral vertex because the ends of the four line segments cross at four separate places.

Triangle area equals 2 1

[x 1 (y 2 y 3 )+x 2 (y 3 y 1 )+x 3 (y 1 y 2 )]

Quadrilateral ABCD's area is equal to the sum of its sides, ACD and ABC.

(2,-4), (-2, 3), (-3, 4), (-5, 0) is the transformation for the coordinates of the vertices of the given pairs of quadrilaterals.

To learn more about coordinates refer to:

https://brainly.com/question/24394007

#SPJ1

Answer:

area=262.5

Step-by-step explanation:

15x10=150

15x15=225

225÷2=112.5

150+112.5=262.5

Some players make very low salaries, and these outliers pull the average down. Option A is the correct option.

What is average of a data?

Averages are used to condense a large number of data points into a single value. It is a visual representation of all the data set's available numbers. By adding up all the data values and dividing them by the total number of data points, the average is calculated. To determine the average age of the students in a class, the ages of all the students are taken into account and an average is calculated.

Given that the average salary of Chicago Bulls players was $5,950,435.

The median salary was only $1,669,178.

A data set's median value is the point where 50% of the data points have values that are lower or equal to it, and 50% of the data points have values that are higher or equal to it.

Since the median represents the mid-value of the data. The salary of some players may be very low. Thus median is less than the average salary.

To learn more about the median, click on the below link:

https://brainly.com/question/13168193

#SPJ1

The kind of system and equation that has many solutions is a linear system of equations with infinitely many solutions.

Equation is an expression that states the equality of two things. It is usually written using mathematical symbols, and it typically contains an equals sign (=). An equation is used to describe a relationship between two or more variables, such as the relationship between the circumference of a circle and its radius, or the relationship between a certain amount of money and the amount of interest it will generate. Equations are used to solve problems in mathematics, chemistry, physics, engineering, and other disciplines.

This means that any combination of values for the unknowns that satisfies the equation will provide a solution. A linear system of equations can be written in the form of ax + by = c, where a, b, and c are all real numbers, and x and y are the unknown variables. When the equation has infinitely many solutions, it means that for any given value of a, b, and c, there is an infinite number of possible values for the unknowns x and y. This can be seen by looking at the graph of the equation, which will be a straight line that passes through the origin, and the line will have an infinite number of points on it.

To know more about equation click-
https://brainly.com/question/2972832
#SPJ4

Step-by-step explanation:

the volume of the cube at the beginning is

edge³ = 16³ = 4096 cm³

after 1 minute it is 4101 cm³

that means the edge is then

cubic root(4101) = 16.00650777... cm

the surface area of a cube is

6×edge²

at the beginning it was

6×16² = 1536 cm²

after 1 minute (and the increased volume) it is

6×16.00650777...² = 1,537.249746... cm²

at that moment the surface area is increasing at

1.249745825... cm²/ minute

Answer:

24x - 1/4

Step-by-step explanation:

Answer: 3.76

Step-by-step explanation:

6.26 - 2.5 = 3.76

Answer:

3.76

Step-by-step explanation:

Answer:

27.6%

Step-by-step explanation:

See the attached worksheet. Find the total number of marbles (29) and then take the green marbles and divide by the total and multiply by 100%.  (8/29)*(100%) = 27.6% to the nearest tenth.

Carlos have to travel 105 miles to reach the destination.

The path followed by an object to travel a predetermined distance at a predetermined speed from one place to another is called the distance traveled. As was previously said, the distance formula combines distance, speed, and time.

As per the details share in the above question are as bellow,

The details provided are as follow,

Carlos is traveling by automobile for more than 240 miles.

Carlos has traveled 135 miles so far.

How far must Carlos still travel?

We have to use subtraction method to determine the distance remaining.

Now subtract the total distance by the distance traveled,

Substitute the value in above we get,

=240-135

=105 miles

To know more about distance visit :

https://brainly.com/question/2854969

#SPJ4