According to this graph of supply and demand schedules, the **current cost **of the good is:

A **demand schedule** in economics is a table that displays the quantity demanded of an item or service at various price points. On a graph where the X-axis is quantity and the Y-axis is price, a demand schedule can be represented as a continuous demand curve.

A demand schedule, also known as a **tabular representation **or statement, displays the various quantities of goods that are wanted at various price points throughout a given time period. The precise quantity of goods and services that will be purchased at each price will be shown on a demand schedule.

The complete question is : Which statement best describes the current price for the good shown in this graph of supply and demand schedules? A. The current price should be raised to reflect lower supply. B. The current price reflects the point where supply and demand are balanced. C. The current price should be lowered to reflect higher supply. D. The current price should be lowered to reflect lower demand.

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At 8 a.m., the hobbit left Beorn's and headed towards the Misty Mountains at 3 mph. 2

hours later, Gandalf left Beorn's and headed in the same direction. If Gandalf was 5 miles

ahead at noon, what was his speed?

**Answer:**

8.5 mph

**Step-by-step explanation:**

First find how far Hobbit traveled in 4 hrs (8AM - Noon)

3 mph x 4 hr = 12 miles

Now find Gandalf's speed:

Galdalf traveled the same 12 miles that Hobbit did PLUS 5 more miles in 2 hours (10AM -Noon) for a total of 17 miles

Speed = 17 mi / 2 hr = 8.5 mph

If g(x) = - 4x^2 - 3x + 2, determine g(-2).

Show your work.

**Answer:**

g(-2) = -8

**Step-by-step explanation:**

If [tex]g(x) = - 4 x^2 - 3x +2[/tex], determine g(-2):

[tex]g(-2) = - 4 (-2)^2 - 3(-2) +2\\g(-2) = - 4 (4) - (-6)+2\\g(-2) = -16 + 6 + 2 \\[/tex]

**g(-2) = -8**

Will mark brainliest the first answer with explanation!!!

Consider a game in which each play costs one nickel (5¢). During each play, the game dispenses a coin to the player to keep. The game machine contains equal numbers of pennies (1¢), nickels, dimes (10¢), and quarters (25¢). The nickels that the player inserts do not go into the same pool of "reward" coins. What is the expected profit, in cents, for a player who plays five games in a row?

The **expected profit,** in cents, for a player who plays** five games** in a row, is given as follows:

26.25 cents.

How to obtain the expected profit?The **distribution **that models the **profit **of a player for a **single game** is given as follows:

The **expected value **of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability, hence:

E(X) = -4 x 0.25 + 0 x 0.25 + 5 x 0.25 + 20 x 0.25 = 5.25 cents.

For **five games**, the expected value is obtained as the multiplication of the expected value of a single game by five, hence:

5E(X) = 5 x 5.25 = 26.25 cents.

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What are 2 examples of arithmetic sequences in real life?

Stacking chairs and sitting around table are **examples** of arithmetic sequence in real life

**What is simple arithmetic?**

The **foundational subject** in mathematics is arithmetic, which covers operations with numbers. These include multiplication, division, addition, and subtraction. One of the key areas of mathematics, arithmetic serves as the cornerstone for students studying the topic of mathematics.

**How is arithmetic sequence used in daily life?**

There are numerous applications for arithmetic sequences in daily life. The clock, for instance, demonstrates properties of an arithmetic sequence. The standard deviation of a clock's time is 1. Other examples of arithmetic sequences can be seen in daily life, such as our age.

Among these there are many other examples of arithmetic sequence is real life like fencing and perimeter examples.

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consider the following hypothesis test: h0: ha: m $ 20 m , 20 a sample of 50 provided a sample mean of 19.4. the population standard deviation is 2. a. compute the value of the test statistic. b. what is the p-value? c. using a 5 .05, what is your conclusion? d. what is the rejection rule using the critical value? what is your conclusion?

As a result, the test is significant and we can draw this conclusion that the **population **mean is less than 20.

A test statistic is a** statistic** used for testing statistical hypotheses. A test statistic, which is a tally of a data** set **that can be used to conduct the test and boils the data down to a single figure, is a common way to characterize a hypothesis test.

a) Here, the test statistic is calculated as:

Z= [tex]\frac{p'-p}{\sqrt{(p(1-p)/n} }[/tex]

Z=[tex]\frac{19.4-20}{\sqrt{(20(1-20)/50} }[/tex]

Z= -2.12

Therefore -2.12 is the required test statistic value here.

b) Given that this is a one-tailed test, the following p-value was calculated using standard normal tables: p = P(Z -2.12) = 0.0169

The necessary p-value in this case is therefore 0.0169.

c) The test is significant in this case, and the null hypothesis can be rejected because the p-value is 0.0169 0.05, which is the level of significance. This means that there is enough data to conclude that the mean is less than 20.

d) For a significance level of 0.05, we have the following data from normal standard tables:

P(Z < -1.645) = 0.05

Therefore, the following is the rejection criteria in this case: Reject H0 if Z -1.645.

We can reject the null hypothesis here and draw the same conclusion as in the previous section because the test statistic value is -2.12 -1.645. As a result, the test is significant and we can draw this conclusion that the population mean is less than 20.

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What are the 6 angle types?

**Angles **are 6 types.

**1.Acute Angle:** An acute angle is any angle that is less than 90 degrees and is between 0 degrees and 90 degrees.

**2.Obtuse Angle: **Opposite of an acute angle is an obtuse angle. In other terms, an obtuse angle is one that is larger than 90 degrees and less than 180 degrees. It is the angle that is between 90 degrees and 180 degrees.

**3. Right Angle:** A right angle is always 90 degrees in length. Acute angles are those that are less than 90 degrees, whereas obtuse angles are those that are higher than 90 degrees.

**4. Straight Angle:** A straight angle has a measured angle of 180 degrees. Since the angle between its arms is 180 degrees, you can see that it is simply a straight line.

**5.Reflex angle:** The arms make an acute angle because this measurement is less than 90 degrees. What about the angle on the opposite side, though? What is the name of the larger angle that complements the acute angle? It is referred to as a reflex angle.

A** reflex angle** is any angle having a dimension higher than 180 degrees but less than 360 degrees (which corresponds to 0 degrees).

**6.Complete Rotation**: Entire rotation or full angle refers to an angle with a value of 360 degrees. When one of the arms extends completely, it is created.

**Angles** are 6 types.

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Make a sketch if you need to and solve this problem using similar triangles. A telephone pole has a shadow of 16 ft. When a person 5 ft. Tall has a shadow of 6 ft. How tall is the pole? write answer as a fraction. X = ft.

The **height **of the poll is** 40/3 **and **13.3ft.**

Let us assume that the Height of an object is h.

Let us assume that the shadow of an object is y.

(As the shadow is always proportional to height .)

Thus y∝h

**y = kh**

As given

when a person 5 ft. tall has a shadow of 6 ft.

h = 5 ft and y = 6 ft

Put in y = kh

**6 = 5k**

[tex]k=\frac{6}{5}[/tex]

As given

A telephone pole has a shadow of 16 ft.

Let us assume that the height of the pole is x.

h = x and y = 16 ft

**16 = hk ** compare the value of k

[tex]k=\frac{16}{x} \\\\\frac{6}{5} =\frac{16}{x} \\\\x=\frac{16*5}{6} \\\\x=\frac{80}{6} \\\\x=\frac{40}{3} ft[/tex]

0r

**x=13.3ft**

Therefore, The height of the poll is 13.3ft

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Devon is considering taking out a 75000 loan for a 15 year period. How many monthly payments he has to make for the life of the loan?

**Devon's monthly** **payment **will be about 416.6

To make for the life of the loan.

What is **interest** ?

Interest is the price you pay to borrow money or the cost you charge to **lend** money. Interest is most often reflected as an annual** percentage** of the amount of a loan. The three types of interest include simple (regular) interest, **accrued interest**, and **compounding interest**.

Have given,

He considered to take lone about 75,000 for a 15 year period,

In 1 year he will be paid [tex]\frac{75,000}{15}[/tex] = 5000

Then in 1 month he will be paid [tex]\frac{5000}{12}[/tex] = 416.6

Devon's monthly **payment** will be about 416.6

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Find the characteristic polynomial and the eigenvalues of the matrix. 6 3 3 6 The characteristic polynomial is □ (Type an expression using λ as the variable. Type an exact answer, using radicals as needed.) Select the correct choice below and, if necessary, fill in the answer box within your choice 0 A. The real eigenvalue(s) of the matrix is/are (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed. Type each answer only once.) B. The matrix has no real eigenvalues.

The **characteristic polynomial** is P(λ) = λ² - 12λ + 27.

The real **eigenvalues** of the matrix are 3, 9. Answer A.

The full question is in the attachment. The characteristic polynomial from a **matrix** is P(λ) = |A - λI|

Matrix A is 2× 2 matrixI = the identity matrix

[tex]I \:=\: \left(\begin{array}{cc}1&0\\0&1\end{array}\right)[/tex]λ = the eigen value when P(λ) = 0

A - λ

[tex]A \:-\: \lambda I \:=\: \left(\begin{array}{cc}6&3\\3&6\end{array}\right) \:-\: \lambda \left(\begin{array}{cc}1&0\\0&1\end{array}\right)[/tex]

[tex]A \:-\: \lambda I \:=\: \left(\begin{array}{cc}6&3\\3&6\end{array}\right) \:-\: \left(\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right)[/tex]

[tex]A \:-\: \lambda I \:=\: \left(\begin{array}{cc}6 \:-\: \lambda&3\\3&6 \:-\: \lambda\end{array}\right)[/tex]

If matrix P [tex]\left(\begin{array}{cc}a&b\\c&d\end{array}\right)[/tex] than **determinant** of matrix P = |P| = ad - bc

P(λ) = |A - λI

P(λ) = (6 - λ) (6 - λ) - (3 × 3)

P(λ) = 36 - 12λ + λ² - 9

P(λ) = λ² - 12λ + 27

The eigenvalues

P(λ) = 0

λ² - 12λ + 27 = 0

(λ - 3) (λ - 9) = 0

λ - 3 = 0 or λ - 9 = 0

λ₁ = 3 λ₂ = 9

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What is an example of perpendicular equations?

An example of **perpendicular** equations are:

f(x)=2x+4

g(x)=[tex]\frac{-1}{2}\\[/tex]x+2

A **straight line** passing through a point is called a perpendicular line. It forms a 90-degree **angle** with a specific place where the line passes. The need for determining the perpendicular line is **coordinates** and a line equation.

Think about a line with the equation ax + by + c = 0 and the coordinates (x1, y1). The slope should be a/b. Let m1 and m2 represent the **slopes** of two lines; their product will be -1 if the lines are perpendicular to one another.

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

m = Δy/Δx = dy/dx = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line may be shown as

tan θ = Δy/Δx

A line's slope often indicates the steepness and direction of the line.

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Think about a line with the equation ax + by + c = 0 and the coordinates (x1, y1). The slope should be a/b. Let m1 and m2 represent the slopes of two lines; their product will be -1 if the lines are perpendicular to one another.

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

m = Δy/Δx = dy/dx = change in y/change in x

where "m" represents a line's slope.

Snooty had to solve the following

equation for x:

x² = 64

Someone told Snooty there are actually

2 solutions! This confused Snooty. Can

you explain to Snooty why there are 2

solutions for x in this equation?

Type a response

0.

**Answer:**

8, -8

**Step-by-step explanation:**

There are 2 answers for the solution because x² = 64 can equal 8, and -8. It can equal 8 because 8 x 8 = 64. It can also equal -8 because -8 x -8 is a positive 64.

Is 3xÂ² a polynomial?

The expression given in question is not a **polynomial **because it could not satisfy the criteria for polynomial.

The **algebraic** expression that contains two or more terms having different power of the same variables along with subtraction, addition or multiplication sign is termed as polynomial.

such as x² - 4x+7

In the above expression, there are different power of same variable x,

or x³+ 3x²+x-5

The terms are separated by either addition or subtraction sign.

What is the degree of a polynomial?We know that a polynomial expression contains different terms in where there is different power of same variables. The highest power is called the degree of polynomial.

As example, 4x³+2x²-3x+2

we have highest power 3 so this is called 3-degree polynomial.

What are the criteria of polynomial?We stated earlier that an expression can be said a polynomial whenever two or more terms which contain numbers and variables along with addition or subtraction operator. From the question we have a term 3xA² that contain a number and two variable x and A. There is no addition or subtraction sign. So, the term could not satisfy the criteria for polynomial. It is called monomial.

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Which congruence theorem can be used to prove â–³ ABC â‰… â–³ DEF?

The **ASA criterion** might be the most appropriate, as it states that two triangles are congruent if two angles and the included side are congruent.

To use a **congruence** criterion in the given situation, you will need to determine which criterion is most appropriate based on the information provided. There are several congruence criteria that can be used to determine whether two triangles are congruent, including the Side-Side-Side (SSS) criterion, the Side-Angle-Side (SAS) criterion, the Angle-Side-Angle (ASA) criterion, and the Angle-Angle-Side (AAS) criterion.

In this case, the ASA criterion might be the most appropriate, as it states that two** triangles** are congruent if two angles and the included side are congruent. Given that ∠A=∠C=90∘ and AE=CB, you can use the ASA criterion to conclude that triangles AEB and CED are congruent.

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The question is -

Which congruence theorem can be used to prove EB = BD, AE = CB, ∠ A = ∠ C = 90°?

ralph records the time it takes for each of his classmates to run around the track one time. as he analyzes the data on the graph, he locates the mean and median time. which component of data analysis is ralph utilizing?

The component of **data analysis** that Ralph is utilizing is the overall spread of the **data**. That is **option ****D****.**

**Data analysis** is defined as the method a researcher uses to collect, clean, sort, and process raw data in a way that it's representation can be understood by the reader.

The **mean** of a data set is defined as the addition of all the data set which is then **divided** by the number of the data set.

The **median** of a data set is the number that falls at the middle of the set after being arranged in an **ascending** or **descending** order.

Therefore, to find the mean and median of a data set will depend on the spread out of the data.

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**Complete question:**

Ralph records the time it takes for each of his classmates to run around the track one time. As he analyzes the data on the graph, he notices very little variation between his classmates' times.

Which component of data analysis is Ralph observing?

A. An outlier in the data set

B. The overall shape of the data

C. The center of the data set

D. The overall spread of the data

**Answer:**

The overall spread of the data.

**Step-by-step explanation:**

Got it right on the test.

What are the 2 formulas for volume?

**Answer:**

length x width x height or probably like area x height

**Step-by-step explanation:**

Evaluate x/y for x=1/6 and y=1/3.

1/18

1/2

1/9

9

**Answer:**

soln:

x/y=1/6/1/3

=1/6×3/1

=1/2

Therefore x/y = 1/2

When two angles and a non-included side of one triangle are congruent to the corresponding pieces of another triangle?

The correct **answer **is option b) AAS

According to the AAS congruence theorem, if two angles and the non-included side of one triangle are congruent with the corresponding components of another triangle, then the two triangles are congruent.

Therefore, option B is the correct answer.

"AAS congruence" theorem an be used to prove that the triangles are congruent .

The complete question is:

Two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle. Which congruence theorem can be used to prove that the triangles are congruent?

a) SSS

b) AAS

c) SAS

d) HL

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How do you find the total from 1 to 100?

The **total number **from 1 to 100 is found by **addition**

What is addition in math ?

Combining things and counting them as one big group is done through **addition**.

In math, addition is the process of adding two or more integers together.

Addends are the numbers that are added, and the outcome of the operation, or the final response, is referred to as the sum.

In the problem the **addends **are the numbers 1 2 3 4 5 6 .......97 98 99 100

The applying the **addition operation **the sum is calculated to be 5050. **calculator **will make the operation easier

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find and sketch the domain of the function. f(x, y, z) = ln(144 − 9x2 − 16y2 − z2)

The** domain** of the function f(x, y, z) = ln(144 − 9x² − 16y² − z²) is x ∈ (-4, 4), y ∈ (-3, 3) and z ∈ (-12, 12). It forms an ellipsoid.

**Domain** of a function is the set of all values possible for the input parameters for real output parameter or output parameter in given range.

f(x, y, z) = ln(144 − 9x² − 16y² − z²)

For f(x, y, z) to be real, 144 − 9x² − 16y² − z² should be** greater than 0**. So,

144 − 9x² − 16y² − z² > 0

9x² + 16y² + z² < 144

x²/ 4² + y²/ 3² + z²/ 12² < 1

So the domain is an **ellipsoid**.

Therefore x ∈ (-4, 4)

y ∈ (-3, 3)

z ∈ (-12, 12)

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How many solutions does the pair of equations y 0 and y =- 5 have class 10?

If there were two **equation**, one on top of the other, there would be **infinitely **many solutions. but here no solution

If there were two lines that **intersected **at one point, there would be one solution.

y=0 and y=-5 don't have any **solutions**. When you ask if a pair of equations have a solution, that means there is an intersection of the equations. The 2 **equations **will meet somewhere, and that is the solution. To find the solution, you set the equations equal to each other.

0≠-5

It is obvious that 0 and -5 are not equal to each other. Therefore, there is no solution. Also, y=0 and y=-5 are **horizontal **lines that are parallel to each other. They will never meet, which means there will be no intersection. No intersection means no solutions

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Is cleaning the measuring instrument not necessary?

It is necessary to clean the measuring instrument the moving parts of the measuring device may be harmed if **airborne dust** or dirt gets inside of it. Additionally, if any foreign objects are present between the measurement target and the measuring device, **precise** measurements may be affected.

A measuring instrument is a tool used to quantify anything** tangible**. The act of obtaining and comparing physical amounts of actual objects and occurrences is known as measuring in the physical sciences, **quality** control, and engineering. Vernier calipers, micrometers, dial gauges, gauges of various types, bubble levels, protractors, and rulers are some of the primary goods that fall under the category of measurement instruments. These equipment are employed in the production process and for quality assurance.

It is necessary to clean the measuring instrument the moving parts of the measuring device may be harmed if airborne dust or dirt gets inside of it.

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find an equation of the tangent line to the curve at the given point. y = 4ex cos(x), (0, 4)

The **equation **of the **tangent **line to the curve at the given **point**, y = 4ex cos(x), (0, 4) as **calculated **is y' = 0.

In order to find the equation we will have to **differentiate **y = 4ex cos(x)

On differentiating we get the **differential **as ,

y' = - 4eˣsin(x)

given the value of x as 0 and y as 4

y' = -4e⁰sin(0)

= 0 because sin( 0 ) = 0

Therefore ,the required equation is , y' = 0.

**Differentiation **is a technique which is used to find the derivative of a function . Differentiation is a mathematical procedure it determines the rate of change of a function based on one of its variables.

Other than differentiation **calculus **also has a branch known as **integration**.

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a normal population has a mean of 59.8 and a standard deviation of 18.0. a sample of 10 will be taken. find the probability that the sample mean will be greater than 59.8. a) calculate the z score. (round your answer to 2 decimals.) b) find the probability that the sample mean will be greater than 59.8. (round your answer to 4 decimals.)

The **z-score **is 0 and the **probability **that the **sample mean **will be greater than 59.8 is 0.5000

From the question, the given parameters about the distribution are

The z-score

The **z-score **of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (59.8 - 59.8)/18.0

Evaluate

z = 0

The probability

The probability that the **sample mean **will be greater than 59.8 is then calculated as:

P(x > 59.8) = P(z > 0)

From the **z table** of probabilities, we have;

P(x > 59.8) = 0.5

Hence, the probability is 0.5000

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Given the arithmetic sequence:

5, 9, 13,...

Part A: What is the common difference AND how do you find it?

Part B: What are the 4th and 5th terms of this sequence?

Part A: The **common difference** is 4.

Part B: The **4th term **is 17 and the **5th term** is 21 of this sequence.

**What do you mean by arithmetic sequence?**

The difference between each term in an **arithmetic sequence** is a constant. To put it another way, we just add the same value repeatedly, indefinitely.

**According to the given question,**

We have the given information:

The **arithmetic sequence:**

5, 9, 13,...

Now, we need to find the common difference and we will find it in this way,

The common difference is the difference between two consecutive terms in a sequence. To find it, we just need to do simple subtraction.

d = t2 - t1

= 9-5 = 4

So, the **common difference is 4**.

Then, we need to find the 4th and 5th terms of this sequence,

t4 = t3 + d

= 13+4

= 17

t5 = t4 + d

=17 + 4

=21

Therefore, the **4th term is 17 **and the **5th term is 21**.

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The common difference of this **arithmetic sequence** is 4 and 4th, 5th term of this arithmetic sequence is 17 and 21.

Each phrase in an arithmetic sequence increases by adding or subtracting a specific constant, k. Each word in a **geometric** **sequence** is raised by either multiplying by or dividing by a certain constant, k.

Part A:

The constant difference between consecutive terms of an arithmetic sequence is called the common difference and its is denoted by d.

Therefore, the common difference (d) is equal to 9 - 5 = 4.

The 4th and 5th terms of this sequence are

Part B:

Using Arithmetic progression formula,

**aₙ = a + (n- 1)d**

where

n = nth term

a (first term = 5

d = common difference = 4

**4th term of the sequence**

a₄ = a + (n- 1)d

a₄ = 5 + (4 - 1)4

a₄ = 17

**5th term of the sequence**

a₅ = a + (n- 1)d

a₅ = 5 + (5 - 1)4

a₅ = 21

Hence the **4th and 5th term **of this arithmetic sequence is 17 and 21.

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what is the relationship between the servings of blueberries and the number of calories? Answer in a complete sentence

i will give brainless to some that answers right and fast

**Answer:**

Each blueberries serving contain 21 calories or the slope of this is 21

**Step-by-step explanation:**

**The slope is rise/run**

We see that when the x increase by 1, the y increase by 21, so the slope is 21.

f(x) = -3 |x-1| +5; Find f(3)

**Answer: f(3) = -1**

**Step-by-step explanation:**

f(x) = -3 |x-1| +5

f(3), we just need to put 3 in for both the x

f(3) = -3 |3-1| +5

f(3) = -9 + 3 +5

f(3) = -1

The function V(x)=x3−6x2 repreent the volume (in cubic inche) of the box hown. The function W(x)=V(12x) repreent the volume (in cubic inche) when x i meaured in feet. Write a rule for W. Then find W(2)

The rule for **transformed function** W(x ) = V(12x) is, W(x) = 1728 x³ - 864 x² and the **value** of **W(2)** is 10368 in³.

Transforming a function means that the **curve** representing the graph "moves left, right, up and down" or "stretches " or "mirrors". For example, the graph of the function f(x) = x² + 3 can be obtained by simply shifting the graph of g(x) = x² up by 3 units. We have , function of **Volume of box** in cubic inches, V(x) = x³- 6 x² --(1)

also, an another function, W(x) = V(12x) repreent the volume (in cubic feet ) when x is meaured in inches. Now , understand the problem,

We are a function V whose inputs are in inches and whose **outputs** are in **cubic inches** . We are provide an another function W whose inputs are in inches and whose outputs are in **cubic** **feet**., W(x) = V(12x) makes sense because there are 12 inche in 1 feet. We are asked to write a rule for W and interpret the output for an input. Write the transformed function W(x) ,

W(x) = V(12x)

=> W(x) = (12x)³ - 6 (12x)²

=> W(x) = 1728 x³- 6× 144 x²

=> W(x) = 1728 x³ - 864 x²

Now, calculate W(2)

W(2) = 1728 (2)³ - 864 (2)²

=> W(2) = 13824 - 3456

=> W(2) = 10368 in³

When x is 2 feet , the volume of the is 8100 cubic inches.

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**Complete ****question****:**

The function V(x)=x3−6x2 repreent the volume (in cubic inche) of the box hown. The function W(x)=V(12x) repreent the volume (in cubic feet) when x i meaured in inches. Write a rule for W. Then find W(2)

How to teach area Grade 5?

On the basis of their sides, we may similarly **determine the areas** of various shapes like rectangles, parallelograms, triangles, and any polygon.

The space the thing occupies is known as the area. Any shape can call this **area **home. We solely take into account the side's length when calculating the square's area. A square's area is equal to the sum of its squared sides since all of its sides are **equal**.

Similar to triangles, we can determine the area of any polygon based on its sides, as well as the areas of other forms like rectangles, parallelograms, and triangles. The radius of the surface, or the separation of the outer line from the axis for **curved surface objects**, is used to compute the area of the surface.

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URGENT!

in how many ways can 7 books be arranged in a shelf if three particular books must stay together?

**Answer:**

5040 ways

**Step-by-step explanation:**

We need to place 3 particular books so that they are always together.

let 3 books are **one** books

we have 5 books

these can be arranged in ⁵P5 = 5! = 12O

total books = 3 × 2 = 6

Required no. of books are 120×6 = 720.

A canoe travels 4 miles per hour downstream and 2 miles per hour upstream.

Let x represent the canoe's speed with no water current (still water) and y

represent the speed of the water current, in miles per hour. Then the situation

can be represented by this system of equations:

Choose the two correct options.

x + y = 4

x - y = 2

A. The speed of the water current is 1 mile per hour.

B. The speed of the canoe in still water is 3 miles per hour.

C. The speed of the canoe in still water is 1 mile per hour.

D. The speed of the water current is 3 miles per hour.

**Answer:**

A, B

**Step-by-step explanation:**

Given the system of equations, we should first solve for x and y so we can answer this question:

equation 1: x + y = 4, equation 2: x - y = 2 ⇒ *add both equations together*

x + y + x - y = 4 + 2 ⇒ *combine like terms*

2x + 0y = 6 ⇒ *divide both sides by 2*

x = 3 ⇒ *plug into the x + y = 4 equation to solve for y*

3 + y = 4 ⇒ *subtract 3 from both sides*

y = 4 - 3 = 1

Since we know y is the speed of the water current and x is the canoe's still water speed, we know that the water current's speed is 1 mph and the canoe's still water speed is 3 mph

This corresponds with** choices A **and **B**

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