Use synthetic division to find the result when 4x^3+14x^2+13x+11 is divided by x+2. If there is a remainder, express the result in the form q(x) + r(x)/b(x).

Answer:

0.25

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

To solve this expression, we need to remember that division should be done before multiplication or addition/subtraction.

So we first simplify the expression by dividing 1/2 by 6:

1/2 ÷ 6 = 1/2 × 1/6

Next, we multiply the two fractions by multiplying their numerators and denominators:

1/2 × 1/6 = (1 × 1)/(2 × 6) = 1/12

Therefore, the value of the expression 1/2 ÷ 6 is equal to 1/12.

30% percent of the students passed both Mathematics and English.

A rate, number, or amount in each hundred is known as a percentage

Let's use a Venn diagram to represent the information given in the problem. Let M be the set of students who passed Mathematics, E be the set of students who passed English, and F be the set of students who failed both.

We know that there are 40 students in the class, and 90% passed Mathematics, so the number of students who passed Mathematics is 0.9 × 40 = 36. Similarly, 75% passed English, so the number of students who passed English is 0.75 × 40 = 30.

We also know that 2 students failed both Mathematics and English, so we can label the F section with 2.

where the number in each section represents the number of students who passed the respective exam.

To find the percentage of students who passed both examinations (i.e., the intersection of M and E), we need to add the number of students in the M and E intersection to the F section, then subtract that from the total number of students (40), and finally divide by 40 to get the percentage. That is:

percentage of students who passed both exams = (M ∩ E + F) / 40 × 100%

= (28 + 2) / 40 × 100%

= 30%

Therefore, 30% of the students passed both Mathematics and English.

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Yes, there is a chance that the bottled water you are drinking is just tap water packaged in a bottle. According to a study by the Natural Resources Defense Council, 25% of bottled water is just tap water that has been packaged in a bottle. [Scientific American, July 2003]

Bottled water is drinking water that has been packaged in bottles or containers for sale. Bottled water can come from a variety of sources, such as municipal supplies, springs, wells, and other sources. In some cases, bottled water is treated or purified to remove impurities and contaminants. However, not all bottled water is purified or treated, and some may be just tap water that has been packaged in a bottle.

Purified water is water that has been treated to remove impurities and contaminants. Purified water can come from any source, including municipal supplies, wells, and other sources. Purification methods may include filtration, reverse osmosis, distillation, or other methods. Purified water is commonly used in medical and industrial applications, as well as in homes for drinking and cooking.

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The solid has a surface area of about 401.92 cm2.

A three-dimensional shape's surface area is the sum of all of its faces. The surface area of a shape can be calculated by finding the area of each face and combining them.

The surface areas of the cylinder and the hemisphere must be added to determine the solid's surface area.

The cylinder's surface area is equal to 2rh + 2r2, where r is the cylinder's radius and h is its height.

The hemisphere's surface area is equal to 2r2, where r is the hemisphere's radius.

As the cylinder's and hemisphere's radiuses are equal, we can sum their two surface areas as follows:

The solid's surface area is equal to 2rh plus 2r2 plus 2r2.

= 2πrh + 4πr²

Solid's surface area is equal to 2(4)(8) + 4(4)(2).

= 64π + 64π

= 128π

≈ 401.92 cm²

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Side BC is the hypotenuse of the right triangle ABC. Against A: The side that is opposed to angle A is side BC. Adjacent A: Side AB is the side that faces angle A. The side that is in opposition to angle C is side AB.

The opposite side of any right-angled triangle, ABC, is referred to as the hypotenuse. Here, we adhere to the tradition that the side opposite angle A is designated with the letter a. Both sides opposing B and C are given the letters b and c, respectively.

When a and b if the lengths of the legs of a right triangle are and the hypotenuse's length is c, then the sum of the squares of the legs' lengths equals the square of the hypotenuse's length.

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The volume of the rectangular prism is approximately 0.2996 cubic meters.

Six rectangular faces that are congruent and parallel to one another make up the three-dimensional solid known as a rectangular prism. A rectangular cuboid is another name for it.

By multiplying the prism's length, width, and height, one may get the volume of a rectangular prism, which is the volume of the interior space of the prism.

Given that, area of the square base is 7 1/2 sq. m.

The side of the square base is thus,

√(7 1/2) ≈ 2.7386 m

The volume of the rectangular prism is given as:

Volume = length x width x height

Volume ≈ 2.7386 x 2.7386 x 1/5 m

Volume ≈ 0.2996 cubic meters.

Hence, the volume of the rectangular prism is approximately 0.2996 cubic meters.

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Answer:

x = [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

[tex]\frac{x+1}{3}[/tex] - [tex]\frac{x-1}{2}[/tex] = [tex]\frac{1+2x}{3}[/tex]

multiply through by 6 ( the LCM of 2 and 3 ) to clear the fractions

2(x + 1) - 3(x - 1) = 2(1 + 2x) ← distribute parenthesis on both sides

2x + 2 - 3x + 3 = 2 + 4x

- x + 5 = 2 + 4x ( subtract 4x from both sides )

- 5x + 5 = 2 ( subtract 5 from both sides )

- 5x = - 3 ( divide both sides by - 5 )

x = [tex]\frac{-3}{-5}[/tex] = [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

remember, the sum of all angles in a triangle is always 180°.

the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

with a, b, c being the sides, and A, B, C being the three corresponding opposite angles.

so, the angle at Q is

180 = 48 + 48 + angle Q = 96 + angle Q

84° = angle Q

5mm/sin(48) = PR/sin(84)

PR = 5×sin(84)/sin(48) = 6.691306064... mm

The length of PR is approximately 10.33 mm.

what is isosceles triangle ?

An isosceles triangle is a triangle with at least two sides that have equal length, and thus two corresponding angles that are also equal in measure. The third side and angle of an isosceles triangle may or may not be of different length or measure. The two sides that are equal in length are called the legs, and the third side is called the base. The angle opposite the base is called the vertex angle, while the angles adjacent to the legs are called the base angles. In an isosceles triangle, the two base angles are equal in measure.

Since the sum of the angles in a triangle is 180 degrees, we can find the measure of angle PQR as follows:

PQR = 180 - QPR - QRP

PQR = 180 - 48 - 48

PQR = 84 degrees

Since angles QRP and QPR have the same measure, we know that sides OP and OR have equal length (they are opposite those angles). Therefore, triangle POR is an isosceles triangle.

To find the length of PR, we can use the Law of Cosines:

PR^2 = OP^2 + OR^2 - 2(OP)(OR)cos(POR)

Since OP and OR are equal in length, we can simplify this equation to:

PR^2 = 2(OP^2) - 2(OP^2)cos(POR)

We know that POR is 180 - PQR = 96 degrees. We also know that OP = OR, and that QP = 5 mm. Using the Law of Cosines, we can find the length of OP:

OP^2 = QP^2 + OR^2 - 2(QP)(OR)cos(QPR)

OP^2 = 5^2 + OR^2 - 2(5)(OR)cos(48)

OP^2 = OR^2 - 5ORcos(48) + 25

Since OP = OR, we can substitute OP for OR in the above equation:

OP^2 = OP^2 - 5OPcos(48) + 25

5OPcos(48) = 25

OP = 25/(5cos(48))

OP ≈ 6.25 mm

Now we can substitute this value into the equation we derived earlier to find PR:

PR^2 = 2(OP^2) - 2(OP^2)cos(POR)

PR^2 = 2(6.25^2) - 2(6.25^2)cos(96)

PR ≈ 10.33 mm

Therefore, the length of PR is approximately 10.33 mm.  

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The inequality that shows the remaining distance Rina must climb to reach the peak is 0 < d < P

Let's assume that the distance from Rina's current position to the peak of the mountain is "P" feet and the distance from her current position to the base camp is "B" feet.

Then, the remaining distance, "d", that she must climb to reach the peak can be calculated as follows

d = P - B

Since Rina has not yet reached the base camp, the distance she has traveled so far is less than the distance to the base camp, which means:

B > 0

Substituting this inequality in the equation for "d", we get

d = P - B < P

Therefore, the inequality that shows the remaining distance Rina must climb to reach the peak is:

0 < d < P

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Based on the image given, the height of the parallelogram can be expressed as 2 units.

Parallelograms are two-dimensional figures that include four sides as rectangles. However, in parallelograms, the opposite sides are parallel and the vertical or horizontal sides are diagonal. Due to this, the height in a parallelogram can be determined by measuring the distance between the top and bottom lines. Based on this principle, the height of the parallelogram would be 2.

Note: Below I attach the missing image in this question:

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The exponential probability distribution is employed with a random variable that is continuous in nature.

What do you mean by exponential probability distribution ?

In the field of probability, a probability distribution refers to a mathematical function that gives the probabilities of various possible outcomes of an experiment. The exponential probability distribution is a probability distribution that models the time between events in a Poisson process, where events occur continuously and independently at a constant average rate. It is a continuous probability distribution, meaning that the random variable takes on values within a continuous range, as opposed to a discrete probability distribution, where the random variable takes on only a finite or countable set of values.

Explanation of the correct answer :
The exponential probability distribution is defined by a single parameter, [tex]\lambda[/tex] which represents the average rate of occurrence of events in the Poisson process.

The probability density function (pdf) of the exponential distribution is given by [tex]f(x) = \lambda e^{(-\lambda x)}[/tex], where x is the time between events. The cumulative distribution function (cdf) is given by [tex]F(x) = 1 - e^{-\lambda x}[/tex].

The exponential probability distribution is used in many applications, such as queuing theory, reliability theory, and finance. For example, it can be used to model the time between customer arrivals in a queue, the time between machine failures in a manufacturing process, or the time until default on a bond.

In summary, the exponential probability distribution is a continuous probability distribution that is used with a continuous random variable, specifically to model the time between events in a Poisson process.
Hence, option B is correct.

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There are a total of 27 combinations that give a sum of 10 when rolling three dice.

We have,

The possible outcomes in the sample space for rolling three dice:

S = {(1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 1, 4), (1, 1, 5), (1, 1, 6),

(1, 2, 1), (1, 2, 2), (1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 2, 6),

(1, 3, 1), (1, 3, 2), (1, 3, 3), (1, 3, 4), (1, 3, 5), (1, 3, 6),

(1, 4, 1), (1, 4, 2), (1, 4, 3), (1, 4, 4), (1, 4, 5), (1, 4, 6),

(1, 5, 1), (1, 5, 2), (1, 5, 3), (1, 5, 4), (1, 5, 5), (1, 5, 6),

(1, 6, 1), (1, 6, 2), (1, 6, 3), (1, 6, 4), (1, 6, 5), (1, 6, 6),

(2, 1, 1), (2, 1, 2), (2, 1, 3), (2, 1, 4), (2, 1, 5), (2, 1, 6),

(2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 2, 4), (2, 2, 5), (2, 2, 6),

(2, 3, 1), (2, 3, 2), (2, 3, 3), (2, 3, 4), (2, 3, 5), (2, 3, 6),

(2, 4, 1), (2, 4, 2), (2, 4, 3), (2, 4, 4), (2, 4, 5), (2, 4, 6),

(2, 5, 1), (2, 5, 2), (2, 5, 3), (2, 5, 4), (2, 5, 5), (2, 5, 6),

(2, 6, 1), (2, 6, 2), (2, 6, 3), (2, 6, 4), (2, 6, 5), (2, 6, 6),

(3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 1, 4), (3, 1, 5), (3, 1, 6),

(3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 2, 4), (3, 2, 5), (3, 2, 6),

(3, 3, 1), (3, 3, 2), (3, 3, 3), (3, 3, 4), (3, 3, 5), (3, 3, 6),

(3, 4, 1), (3, 4, 2), (3, 4, 3), (3, 4, 4), (3, 4, 5), (3, 4, 6),

(3, 5, 1), (3, 5, 2), (3, 5, 3), (3, 5, 4), (3, 5, 5), (3, 5, 6),

(3, 6, 1), (3, 6, 2), (3, 6, 3), (3, 6, 4), (3, 6, 5), (3, 6, 6),

(4, 1, 1), (4, 1, 2), (4, 1, 3), (4, 1, 4), (4, 1, 5), (4, 1, 6),

(4, 2, 1), (4, 2, 2), (4, 2, 3), (4, 2, 4), (4, 2, 5), (4, 2, 6),

(4, 3, 1), (4, 3, 2), (4, 3, 3), (4, 3, 4), (4, 3, 5), (4, 3, 6),

(4, 4, 1), (4, 4, 2), (4, 4, 3), (4, 4, 4), (4, 4, 5), (4, 4, 6),

(4, 5, 1), (4, 5, 2), (4, 5, 3), (4, 5, 4), (4, 5, 5), (4, 5, 6),

(4, 6, 1), (4, 6, 2), (4, 6, 3), (4, 6, 4), (4, 6, 5), (4, 6, 6),

(5, 1, 1), (5, 1, 2), (5, 1, 3), (5, 1, 4), (5, 1, 5), (5, 1, 6),

(5, 2, 1), (5, 2, 2), (5, 2, 3), (5, 2, 4), (5, 2, 5), (5, 2, 6),

(5, 3, 1), (5, 3, 2), (5, 3, 3), (5, 3, 4), (5, 3, 5), (5, 3, 6),

(5, 4, 1), (5, 4, 2), (5, 4, 3), (5, 4, 4), (5, 4, 5), (5, 4, 6),

(5, 5, 1), (5, 5, 2), (5, 5, 3), (5, 5, 4), (5, 5, 5), (5, 5, 6),

(5, 6, 1), (5, 6, 2), (5, 6, 3), (5, 6, 4), (5, 6, 5), (5, 6, 6),

(6, 1, 1), (6, 1, 2), (6, 1, 3), (6, 1, 4), (6, 1, 5), (6, 1, 6),

(6, 2, 1), (6, 2, 2), (6, 2, 3), (6, 2, 4), (6, 2, 5), (6, 2, 6),

(6, 3, 1), (6, 3, 2), (6, 3, 3), (6, 3, 4), (6, 3, 5), (6, 3, 6),

(6, 4, 1), (6, 4, 2), (6, 4, 3), (6, 4, 4), (6, 4, 5), (6, 4, 6),

(6, 5, 1), (6, 5, 2), (6, 5, 3), (6, 5, 4), (6, 5, 5), (6, 5, 6),

(6, 6, 1), (6, 6, 2), (6, 6, 3), (6, 6, 4), (6, 6, 5), (6, 6, 6)}

Now,

The combination where the sum is 10 is 27.

ie.

{(1, 3, 6), (1, 4, 5), (1, 5, 4), (1, 6, 3), ........, (6, 1, 3), (6, 2, 2,), (6, 3, 1)}

Thus,

There are 27 ways of combination where the sum is 10.

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The correct statement regarding where the graph of h(x) = x³ has positive signal is given as follows:

x > 0.

The graph of a function is positive in the regions where the function values are greater than zero, and negative in the regions where the function values are less than zero.

The comparisons to zero are given as follows:

Hence, considering the function defined by the rule y = x³, the graph of the function is classified as positive or negative as follows:

The function is h(x) = x³, and it's graph is given by the image presented at the end of the answer.

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The appropriate domain for the number of miles travelled by the taxi is found as: [0, 25]

In a two-variable linear equation, x and y have a linear connection, meaning that the value of any one of the variables, y, relies upon that value of the other, x.

Cost for first mile of  taxi service  = $2.00

Additional cost = $1.20 per mile.

Peak distance = 25 miles.

a = number of miles traveled by taxi.

y = total cost of the taxi ride

The linear equation forms:

y = $1.20a + $2.00

When a = 0; y = $2.00

a = 25 ; y = $1.20*25 + $2.00 = 32

Thus, the appropriate domain for the number of miles travelled by the taxi is found as: [0, 25]

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Answer:

0.4

Step-by-step explanation:

Subtract 2.4m on each side

-1.2 = -3.0m

divide by -3.0

you get 0.4

the answer to the problem that you need to is 1024

Answer:

To determine which test Elena got a higher ratio of correctly spelled words to total words, we need to calculate the ratio of correctly spelled words to total words for each test and compare them.

For last week's test, the ratio of correctly spelled words to total words is:

16/20 = 0.8

For this week's test, the ratio of correctly spelled words to total words is:

13/15 ≈ 0.867

Since 0.867 is greater than 0.8, Elena got a higher ratio of correctly spelled words to total words on this week's test. Therefore, the new studying method appears to be working better for Elena. However, it is important to note that a single comparison is not sufficient to draw a definitive conclusion about the effectiveness of the studying method, and it would be beneficial for Elena to continue tracking her performance over a longer period of time.

The T(U) is a subspace of W.

Since U is a subspace of V, the zero vector of V, 0v, is in U. Since T is linear, T(0v) = 0w, where 0w is the zero vector of W. So 0w is in T(U). Therefore, T(U) is a subspace of W.

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In the following question, among the given options, the statement is said to be, The pooled estimate of the standard deviation for the data given is √(54.14^2/10 + 24.26^2/10) = 22.74.

According to the rule for examining standard deviations in ANOVA from Chapter 12 (page 560), the within-group standard deviation should be no more than twice the size of the between-group standard deviation. In this case, the between-group standard deviation is 44.85 and the within-group standard deviation (22.74) is less than twice the size of the between-group standard deviation, so it is reasonable to use a pooled standard deviation for the analysis of these data.

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Answer:

58.24

Step-by-step explanation:

1456 ÷ 25 = 58.24

Answer:

sixty nine hundredths

Step-by-step explanation:

three tenths can be expressed in decimal as 3/10

thirty nine hundredths can be expressed in decimal as 39/100

Therefore the sum of three tenths plus thirty nine hundredths equals

3/10 +39/100

We first find the l.c.m of the two fractions equals 100 so we have 100 as the denominator

then 100 divided by 10  multiplied by 3 +100 divided by 100 multiplied by 39 as illustrated below gives the answer

3/10 +39/100

=30+39/100

=69/100= sixty nine hundredths

Answer

Initial velocity = 32 ft/s

Initial height = 24 ft.

Explanation

The function gives us the function that models the height, h, in feet for the ball as a function of time, t, in seconds.

h(t) = -16t (t - 2) + 24

We are then asked to find the initial velocity and the initial height of the ball.

This means we find the velocity and the height of the ball at t = 0

Velocity is given as the first derivative of the height function

v = (dh/dt)

h(t) = -16t (t - 2) + 24

h(t) = -16t² + 32t + 24

v = (dh/dt) = -32t + 32

When t = 0

v = -32t + 32 = -32 (0) + 32 = 0 + 32 = 32 ft/s

Initial velocity = 32 ft/s

For the initial height, t = 0

h(t) = -16t (t - 2) + 24

h(t) = -16t² + 32t + 24

h(0) = -16(0²) + 32(0) + 24

h(0) = 0 + 0 + 24

h(0) = 24 ft

Initial height = 24 ft.

Answer:

The initial velocity of the ball is 32 feet per second.

The initial height of the ball is 24 feet.

Step-by-step explanation:

Velocity is the rate of change of distance with respect to time.

Therefore, to find the equation for velocity, differentiate the height function with respect to time.

[tex]\begin{aligned} h(t) &= -16t(t - 2) + 24\\&= -16t^2+32t+24\\\\\implies v=h'(t)&=-32t+32\end{aligned}[/tex]

The initial velocity of the ball is its velocity when t = 0.

Therefore, at time t = 0, the velocity is:

[tex]\begin{aligned}\implies v=h'(0)&=-32(0)+32\\&=32\sf\;ft\;s^{-1}\end{aligned}[/tex]

Therefore, the initial velocity of the ball is 32 feet per second.

The initial height of the ball is the height when t = 0.

Therefore, at time t = 0, the height of the ball is:

[tex]\begin{aligned} \implies h(0) &= -16(0)(0 - 2) + 24\\&= 0+24\\&=24\sf\;ft\end{aligned}[/tex]

Therefore, the initial height of the ball is 24 feet.

If the set of expressions represents measures of the sides of a triangle x, 4, 6 , the range of possible measures of x is 2 < x < 10.

To determine the range of possible measures of X if the set of expressions represents measures of the sides of a triangle x, 4, 6, we need to use the triangle inequality theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Mathematically, this can be expressed as:

x + 4 > 6

x + 6 > 4

4 + 6 > x

Simplifying these inequalities, we get:

x > 2

x > -2

x < 10

The first two inequalities indicate that x must be greater than 2, since the sum of any two sides of a triangle must be greater than the third side. The third inequality indicates that x must be less than 10, since the longest side of a triangle cannot be greater than the sum of the other two sides.

This means that x can take any value between 2 and 10, but not including 2 or 10, in order for the set of expressions to represent the measures of the sides of a triangle.

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Answer:

x=15

Step-by-step explanation:

use the side splitter theorem

(x-6)/x = 3/5 (cross-multiply)

3x=5(x-6) distributive property

3x=5x-30

2x = 30

x = 15

Answer:

y = -3(x - 2)^2 + 1. Explanation: x-coordinate of vertex: x = -b/(2a) = -12/-6 = 2 y-coordintae of vertex: y(2) = -12 + 24 - 11 = 1

Step-by-step explanation:

Answer:x-coordinate of vertex:

x = -b/(2a) = -12/-6 = 2

y-coordinate of vertex:

y(2) = -12 + 24 - 11 = 1

Vertex form:

y = -3(x - 2)^2 + 1

Check.

Develop y to get back to standard form:

y = -3(x^2 - 4x + 4) + 1 = -3x^2 + 12x - 11.

Step-by-step explanation:

(a) If Amir is the splitter, he can divide the cake into two equal halves, offer Brandon the first choice, who will likely choose the chocolate half worth 6.67 dollars to him, and Amir will take the vanilla half worth 3.33 dollars to him.

(b) If Brandon is the splitter, he can divide the cake into two equal halves, offer Amir the first choice, who will likely choose the chocolate half worth 5 dollars to him, and Brandon will take the vanilla half worth 5 dollars to him.

(a) If Amir is the splitter, he can divide the cake into two equal halves, one chocolate and one vanilla. He can then offer Brandon the first choice of which half he wants. Since Brandon likes chocolate four times as much as vanilla, he will likely choose the chocolate half, which is worth 6.67 dollars to him (4/5 of the total value of the cake). Amir will then take the vanilla half, which is worth 3.33 dollars to him (1/5 of the total value of the cake).

(b) If Brandon is the splitter, he can divide the cake into two equal halves, one chocolate and one vanilla. He can then offer Amir the first choice of which half he wants. Since Amir likes chocolate twice as much as vanilla, he will likely choose the chocolate half, which is worth 5 dollars to him (1/2 of the total value of the cake). Brandon will then take the vanilla half, which is worth 5 dollars to him (1/2 of the total value of the cake)

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Therefore represented by the point of intersection, which is (10, 7). All products are sold at this price and quantity, clearing the market.

A function is a mathematical concept that links an input (usually denoted by the variable x) to an output (usually denoted by the variable y or f(x)) in a well-defined way. A function can be compared to a computer that processes inputs and outputs in accordance with rules or guidelines. Each input value (also known as the domain) in a function is connected to precisely one output value (also known as the range). For instance, the linear function f(x) = 2x multiplies the input value x by two to create the output value.

given

f(x) = -0.5x + 12

The supply role is also provided by:

g(x) = 0.5x + 2

We must put these two functions equal to one another and then solve for x to determine where these two functions intersect:

-0.5x + 12 = 0.5x + 2

By multiplying both parts by 0.5, we get:

12 = x + 2

x = 10

The position at which the supply and demand functions intersect is therefore (10, f(10)) or (10, g(10)). We can enter the value x = 10 into either of the following functions to obtain the appropriate y-coordinate:

f(10) = -0.5(10) + 12 = 7

g(10) = 0.5(10) + 2 = 7

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