the first part of the problem asks them to calculate the work done on the gas when the gas goes from the initial state to the final state shown. here is part of their dialogue: nora: the gas is compressed because the volume decreases. that means that there is work done on the gas, and the work is positive. bob: ok. that's right because we're using the first law with q w. we need to use that area thing to find the work. nora: yeah. we want the area under the line between the dots. bob: that line shows the process, right? nora: yup, that's the one. so the area is one-half times base times height. it's the area of that triangle. bob: but you have to add the area of that skinny rectangle below it, don't you? nora: i don't think so. that bottom dot for the final state tells you where the bottom of the area is. bob: why don't we ever agree? tell you what. we'll each try our own way and let webassign tell us who's right. nora: hmmm... i hope i get the big, green check mark!

Patient needs to 500,000 unit of penicillin, then according to capsule availability we shall provide the 2 capsules of 200,000 unit and 1 capsule of 100,000 unit.

The doctor orders 500,000 unit of penicillin for the patient. the capsule available are 200,000 unit and 100,000 units.

we have to find out the number of capsules required for 500,000 unit,

let's see,

we have 200,000 unit of penicillin and 100,000 units of penicillin available,

patient need of 500,000 unit of penicillin,

so we shall provide the 2 capsule of 200,000 units of penicillin and 1 capsule of penicillin 100,000 unit to the patient,

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The price of the share of stock in fossil oil refineries after the three-for-one split is $50.

A stock split is an event in the stock market when the company declares split of stock into multiple parts to decrease the cost per share and make it easier to purchase.

Given,

          The selling price of a stock in fossil fuel before split = $150

          After one year the stock split into three parts

         ∴ Probable prices per share = Price before split/3

                                                         = $150/3

                                                         = $50

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Exponential growth is a type of growth that occurs when the rate of increase is proportional to the current amount.

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A constant is fixed, which is arbitrary since you don't know what that fixed number is the arbitrary denotes that no particular value has been ascribed.

The order of a differential equation is equal to the number of arbitrary constants in its general solution.

The highest-order derivative that a differential equation has is used to define the equation's order. The highest-order derivative of a differential equation is defined as its degree, which is expressed as a power. The formula:

c1=a1+ib1

and  c2=a2+ib2

the solution will be

y(x)=(a1+ib1+a2+ib2)cos(ax)+i(a1+ib1−a2−ib2)sin(ax)

If and only if

a2=a1

and  b2=−b1

will be the solution real because of complex conjugates using this property.

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Full question

Can arbitrary constants in solutions to 2nd-order linear differential equations be complex?

Answer:

$963.00

Step-by-step explanation:

.9(3x150) + .95(2x200) + 250

.9(450) + .95(400) + 250

405 + 308 + 250 = 963

If we are taking 10% off, that is like leaving 90% (.9) on.

If we are taking 5% off, that is like leaving 95% ( .95) on.

No discount for the watch because she only bought one.

To find the value of f(g(-4)), we need to first substitute -4 into the definition of g(x) and then substitute the result into the definition of f(x).

First we substitute -4 into g(x):

g(-4) = 2(-4)^2 + 4(-4) - 8

g(-4) = 2(16) + (-16) - 8

g(-4) = 32 - 16 - 8

g(-4) = 8

Now we substitute 8 into f(x):

f(g(-4)) = f(8) = 2(8) - 4 = 16 - 4 = 12

So the value of f(g(-4)) is 12.

Answer:

28

Step-by-step explanation:

The expression: f(g(-4)) just means calculate the value of g at x = -4 and then calculate what f is equal to at that value g is equal to, so we have to first calculate g(-4) which we can do by substituting in -4 as x.

g(-4) = 2(-4)^2 + 4(-4) - 8

g(-4) = 2(16) - 8 - 8

g(-4) = 32 - 16

g(-4) = 16

Now from here we can substitute 16 as g(-4) in the expression f(g(-4)) which means we want to evaluate g(16) which we can do by substituting in 16 as x.

f(16) = 2(16) - 4

f(16) = 32 - 4

f(16) = 28

So that means f(g(-4)) = 28

Data aggregation involves creating a unified collection of data that originally came from multiple sources.

It is the process of combining data from multiple sources into one file, report or summary. Data aggregation can be done using a variety of methods, such as mathematical formulas, grouping, filtering and sorting. For example, a mathematical formula can be used to calculate the average of a set of numbers. Grouping data can be used to divide data into categories and subcategories, such as by country or by product. Filtering data involves removing unnecessary or unwanted data, such as outliers or irrelevant information. Finally, sorting data can be used to organize data in a specific order, such as alphabetically or numerically. Data aggregation is a useful tool for making sense of large datasets and providing greater insight into the data.

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The unknown angle in the parallel lines is a follows;

m∠5 = 75 degrees

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, vertically opposite angles etc.

Therefore, let's use the angle relationships to find the m∠5 in the parallel lines.

The angle m∠1 and m∠5 are corresponding angles.

Corresponding angles are congruent.

Therefore,

m∠1 = m∠5 = 75 degrees.

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Without the equation of the graph of the region R, it is not possible to determine the volume of the solid defined by a region R, an isosceles right triangle cross-section, and a line y=k.

The question describes a solid where the base is a region R in the first quadrant, bounded by the graph of y, the x-axis, and the line y = k.

It is also mentioned that each cross section perpendicular to the y-axis is an isosceles right triangle with the right angle on the x-axis and one leg in the XY-plane.

However, the equation of the graph of the region R is not given, which makes it impossible to determine the range of y over which the solid is defined and therefore, calculate the volume of the solid. It's very important to have the equation of the graph of the region R to find the volume of the solid.

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The question is -

Let R be the region In the first quadrant bounded by the "graph of y the !-axis, and the line y The region R Is the base of a solid For the solid, each cross section perpendicular [tex]t_0[/tex] to the y-axis Is an isosceles right triangle with the right angle on the !-axis and one leg in the 1y-plane What is Ithe volume of the solid?

The average of two numbers, A and B, is calculated by adding them together and then dividing by two. In this case, A = 21, B = 20, X = 19, and Y = 20. When we calculate (A + B) / 2, we get 20.00.

1. Add A and B together: 21 + 20 = 41

2. Divide the sum by 2: 41 ÷ 2 = 20.50

3. Round the answer to two decimal places: 20.50 → 20.00

The average of two numbers, A and B, is calculated by adding them together and then dividing by two. This formula is expressed as (A + B) / 2. In this problem, we were given the values A = 21, B = 20, X = 19, and Y = 20. To solve for the average, we first need to add A and B together and get 41. Then we divide this sum by two and get 20.50. To get the final answer, we need to round this value to two decimal places, which results in the answer 20.00. This answer indicates that the average of 21 and 20 is 20.00.

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No, you are not given enough information to prove that the quadrilateral is a parallelogram.

In order to prove that the quadrilateral is a parallelogram, we must have four points to calculate the lengths of the sides and angles. We need to verify that the opposite sides of the quadrilateral are equal in length and that the opposite angles are equal. We can use the formula for the area of a parallelogram: A = b*h, where b is the length of the base and h is the height of the parallelogram. We can also use the formula for the sum of the angles of a quadrilateral: A1 + A2 + A3 + A4 = 360 degrees. Without having the four points, we cannot calculate the lengths of the sides or angles, so we cannot prove that the quadrilateral is a parallelogram.

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Answer:

22.386

Step-by-step explanation:

The simplest choice is a linear transformation, for example, the one given by the

matrix [tex]\left[\begin{array}{ccc}-1/2&1&0\\-1/2&0&1\end{array}\right][/tex]

When you represent a three-dimensional object graphically in the plane con paper, the blackboard, or a computer screen), you have to transform spatial coordinates,

[tex]$\mathrm{x} 1$ & \\[/tex]

[tex]$\mathrm{x} 2$[/tex] & into plane coordinates

[tex]$\mathrm{x} 3$[/tex]& [tex]$\mathrm{y} 1$[/tex]& [tex]$\mid$ \\[/tex]

[tex]$\mathrm{x}$[/tex] &[tex]$\mathrm{y} 2$[/tex] &

The simplest choice is a linear transformation, for example, the one given by the

matrix [tex]\left[\begin{array}{ccc}-1/2&1&0\\-1/2&0&1\end{array}\right][/tex]

The complete question is,

When you represent a three-dimensional object graphically in the plane (on paper, the blackboard, or a computer screen), you have to transform spatial coordinates | x 1 | | x 2 | into plane coordinates | y 1 |. | x 3 | | y 2 | The simplest choice is a linear transformation, for example, the one given by the matrix | -1/2 1 0 0 | 1 |.

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Answer: D. The distance from A to C

Step-by-step explanation:

This formula can be used to find the distance between two points on a three-dimensional coordinate system:

D(x, y, z) = [tex]\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} + (z_{2} - z_{1})^{2} }[/tex]

If you apply the formula for all options, you will find the distance from A to C is equal to [tex]\sqrt{5}[/tex]. The other distances are:

A. [tex]\sqrt{17}[/tex]

B. [tex]\sqrt{45}[/tex]

C. [tex]\sqrt{44}[/tex]

So, the answer is D.

An Interval is all the numbers between two given numbers. 95% confidence level would result in a wider confidence interval.

What is interval in math?

Given data :

confidence interval = ( -11.98, -4.52)

-11.98≤x≤-4.52, [-11.98,-4.52], and {x∈ℝ|-11.98≤x≤-4.52} all mean that x is between -11.98 and -4.52 and could be either endpoint.

95% confidence level would result in a wider confidence interval. Increasing the confidence level increases the length of the confidence interval.

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The two situations that describe the volume:

A. the amount of shampoo in a bottle.

B. the amount of soap in a bar of soap.

The space occupied by an object in three-dimensional space is called the volume of an object. In simple words, space is taken by an object.

Four phrases are given.

A. the amount of shampoo in a bottle.

This describes the volume.

B. the amount of soap in a bar of soap.

This also describes the volume.

c. the amount of border around a chalkboard.

This describes the perimeter.

D. the amount of wrapping paper covering a gift

This describes the surface area.

Therefore, A and B describe the volume.

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The complete Question:

Choose all the examples that describe volume.

A. the amount of shampoo in a bottle

B. the amount of soap in a bar of soap

c. the amount of border around a chalkboard

D. the amount of wrapping paper covering a gift

The class interval [15-19] has the greatest frequency, and the class interval [10-14] has the least frequency

From the question, we have the following parameters that can be used in our computation:

10. 9. 5. 19. 17

13. 2. 0. 4. 10

1. 16. 9. 7. 3

15. 17. 18. 16. 6

Using a class of 5, we have the following class intervals

0 - 4, 5 - 9, 10 - 14 and 15 - 19

When the frequencies of each class are counted, we have the following table

Interval Midpoint Frequency R/F        C/F

0 - 4 2           5                 5/20 5

5 - 9 7           5                 5/20 10

10 - 14 12           3                 3/20 13

15 - 19 17            7                 7/20 20

using the above as a guide, we have the following:

The class interval [15-19] has the greatest frequency 7

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The holding pulse is nonzero only for[tex]0 \leq t \leq T[/tex], the autocorrelation of X(t) is given by\begin{align}

[tex]R_{xx}(t,t+\tau) =[/tex]

[tex]\begin{cases}\sigma_v^2 \sum_{n=-\infty}^{\infty}\sum_{m=-\infty}^{\infty}h(t-nT)h(t+\tau-mT) & 0 \leq \tau \leq T \\0 & \text{otherwise}.\end{cases}\end{align}[/tex]

The autocorrelation of X(t) is defined as[tex]R_{xx}(t,t+\tau) = E[X(t)X(t+\tau)][/tex]where E[.] is the expectation operator. Since V(nT) has zero mean and is statistically independent, we can write

[tex]R_{xx}(t,t+\tau) &= E[X(t)X(t+\tau)]\\ &= E\left[\sum_{n=-\infty}^{\infty}V(nT)h(t-nT)\sum_{m=-\infty}^{\infty}V(mT)h(t+\tau-mT)\right]\\&= \sum_{n=-\infty}^{\infty}\sum_{m=-\infty}^{\infty}E[V(nT)V(mT)]h(t-nT)h(t+\tau-mT)\\&= \sigma_v^2 \sum_{n=-\infty}^{\infty}\sum_{m=-\infty}^{\infty}h(t-nT)h(t+\tau-mT)\end{align}[/tex]

Since the holding pulse is nonzero only for[tex]0 \leq t \leq T[/tex], the autocorrelation of X(t) is given by\begin{align}

[tex]R_{xx}(t,t+\tau) =[/tex]

[tex]\begin{cases}\sigma_v^2 \sum_{n=-\infty}^{\infty}\sum_{m=-\infty}^{\infty}h(t-nT)h(t+\tau-mT) & 0 \leq \tau \leq T \\0 & \text{otherwise}.\end{cases}\end{align}[/tex]

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The ordered pair that is included in the solution to this system of inequalities is: B. (−6, −3)

In order to determine the ordered pair is included in the solution to this system of linear inequalities, we would first of all translate the word problem into an algebraic equation as follows;

y is greater than or equal to two-thirds times x plus 1 ⇒ y ≥ 2x/3 + 1.

y is less than negative one-fourth times x plus 2 ⇒ y < -x/4 + 2.

Next, we would use an online graphing calculator to graphically solve the system of linear inequalities. Therefore, the required solution for the given system of linear inequalities is the shaded area below the solid line, which is given by the ordered pair (−6, −3).

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Answer:

Step-by-step explanation:bmmmv m

Answer:C. Approx. Normal

Step-by-step explanation:

The total amount paid with a monthly payment of $100 for a credit of $756.25 at an annual rate of 24.5% is $871.69.

The periodic payment is the amount the car owner pays monthly to offset the balance on the credit card for purchasing new brakes.

The periodic payment is determined using an online finance calculator as follows:

N (# of periods) = 1 year

I/Y (Interest per year) = 24.5%

PV (Present Value) = $756.25

PMT (Monthly Payment) = $100

Results:

Sum of all periodic payments = $871.69

Total Interest = $115.44

Thus the total payment made by the car owner is $871.69 with an interest of $115.44.

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Answer:

$830.52

Step-by-step explanation:

I got it right on the test :)

Have great day

All terms should be shifted to the left and set to zero. After that, make each factor equal to zero. [tex]C=\frac{P}{1+M}$$[/tex]

P=C+M C

As C + M C = P, rewrite the equation.

C+M C=P

Add C to the equation on both sides. .MC=P−C

Simplify M C = P C by dividing each term by C.

Divide each phrase into [tex]$M C|=| \boldsymbol{P}-\boldsymbol{C}$[/tex] by C

[tex]\frac{M C}{C C} \equiv \frac{P}{C}+\frac{-C}{C}$$[/tex]

C's common factor should be cancelled.

[tex]$M=\frac{P}{C}+\frac{-C}{C}$[/tex]

M=PC−1

An equation that is mostly made up of letters is said to be literal. Literal equations include those found in formulas. Each variable acts as a "literal" representation of an essential element of the overall relationship that the equation expresses. For instance, P = 2L + 2W is a formula for expressing a rectangle's perimeter.

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The Scale Factor is 0.75, or 3/4

Scale factor is a ratio of two related lengths, areas, volumes, or other quantities. It is used to describe how a figure is enlarged or reduced in size. For example, when a figure is enlarged, the scale factor is greater than one, and when a figure is reduced, the scale factor is less than one. Scale factors can be used to calculate the lengths of sides and areas of figures when one side or area is known.


The Scale Factor is calculated by dividing the coordinates of point A' (9, 3) by the coordinates of point A (12, 4). Therefore, the Scale Factor is 0.75, or 3/4.

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Answer:

h = 6 m

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)

where h is the perpendicular height between the bases b₁ and b₂

given A = 51 , b₁ = 10 and b₂ = 7 , then

[tex]\frac{1}{2}[/tex] h (10 + 7) = 51 ( multiply both sides by 2 to clear the fraction )

17h = 102 ( divide both sides by 17 )

h = 6 m

Find the height of the trapezoid.

if the area of the trapezoid is [tex]51m^{2}[/tex] and parallel sides are [tex]7m[/tex] and [tex]10m[/tex].

To find the height of the trapezoid, substitute the area and parallel sides into the formula for the area of the trapezoid.

Trapezoid area formula is

[tex]L=\frac{1}{2}(number of parallel sides)(height)\\ L=\frac{1}{2} (a+b)(t)[/tex]

The next step is substitute the area and parallel sides into the formula for the area of the trapezoid.

[tex]51=\frac{1}{2}(7+10)(t)[/tex]

Complete the arithmetic operation

[tex]51=\frac{1}{2}(17)(t)\\ 51=\frac{17}{2}(t)[/tex]

Multiply each side by [tex]\frac{2}{17}[/tex]

[tex]51(\frac{2}{17}) =\frac{17}{2}(\frac{2}{17})(t)\\ 6=t[/tex]

So the height of the trapezoid is [tex]6m[/tex]

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From the given points, it was found that the slope is m= -3.

You can correlate two data from a function. An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=9x+5. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=9 and b=5.

The question gives some points of the linear function, see below.

x    y

−1  6

0   3

1   0

2  −3

From the given data you can find the slope by solving the system linear equation.

You can write a system linear equation using the points: (-1,6) and (2,-3), for example.

6=m*(-1)+b  (1)

-3=2m+b    (2)

Multiplying equation 2 by -1, you have

6=-m+b  (1)

3= -2m-b    (2)

Summing the previous equation, you have:

9=-3m

m= -9/3

m= -3

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Answer: the answer is A

Step-by-step explanation: I took the text and got it right

If the magnitude of two vectors is 10 and 6 and their dot product is 30, then the angle between the vectors is 60°.

What is a vector?

A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.

There are two ways to define a dot product: algebraically and geometrically. The sum of the products of the matching entries of the two number sequences is the definition of the dot product in algebra. Geometrically, it is the sum of the cosine of the angle formed by the two vectors and their Euclidean magnitudes.

The magnitude of the vector 1 is, |a| = 10

The magnitude of the vector 2 is, |b| = 6

The dot product of the two vectors is, a·b = 30.

The formula for dot product of vectors is -

a·b = |a| |b| cos θ

Solve the equation to get the angle -

30 = (10 × 6) cos θ

30 = 60 cos θ

cos θ = 30/60

cos θ = 1/2

θ = cos^-1 (1/2)

θ = 60°

Therefore, the angle is obtained as 60°.

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48.28 m/s is the speed .

What is the definition of a velocity simple?

The speed at which a body or object is moving determines its direction of motion. Most of the time, speed is a scalar quantity. Velocity is fundamentally a vector quantity.

                         The rate at which distance changes is what it is. It measures the displacement's rate of change.

Height, y = 52t - 1.86t²

Velocity = ∆y/∆t = 52 - 1.86 * 2t = 52- 3.72t

A. Average velocity = (v1 + v2)/2

(i) At t = 1, 2

Average velocity = (52 - 3.72*1 + 52 -3.72*2)/2 = 46.42 m/s

(ii) At t = 1,1.5

Average velocity = (52 - 3.72*1 + 52 - 3.72*1.5)/2 = 47.35 m/s

(iii) At t = 1,1.1

Average velocity = (52 - 3.72*1 + 52 -3.72*1.1)/2 = 48.09m/s

(iv) At to = 1, 1.01

Average velocity = (52 - 3.72*1 + 52 - 3.72*1.01)/2 = 48.26 m/s

(iv) At t = (1, 1.001)s

Average velocity = (52 - 3.72*1 + 52 - 3.72*1.001)/2 = 48.28 m/s

B. Speed at t = 1s

Velocity = 52 - 3.72 * 1 = 48.28 m/s

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Answer:

50

Step-by-step explanation:

140/x = 168/60

x = 60*140/168 = 50

Answer:

50

Step-by-step explanation:

168/60=2.8

140/2.8=50

To find the x-intercept of the graph of the equation 2x - 4y = 9, we need to find the value of x when y = 0.

We can solve for x as follows:

2x - 4y = 9

2x - 4(0) = 9 (substitute y = 0)

2x = 9

x = 9/2

Therefore, the x-intercept of the graph of the equation 2x - 4y = 9 is (9/2, 0).