In 1912, the RMS Titanic, a British passenger ship, sank in the North Atlantic Ocean after colliding with an iceberg. Historians do not know the exact passenger list, so the death toll is estimated. Here is data from the 2201 passengers on board, by cabin class. First Class Second Class Third Class Crew Row Totals Died 122 167 528 673 1490 Survived 203 118 178 212 711 Col Totals 325 285 706 885 2201 Source: Wikipedia, RMS Titanic (2015) If we randomly select a passenger who survived the Titanic, what is the probability that this passenger is in a second class cabin?

The probability that all six cells are able to replicate is approximately 0.0051, while the probability that at least one cell is not capable of replication is approximately 0.9949.

To solve this problem, we need to use the concept of probability and combinations.

There are 37 - 12 = 25 cells capable of replication. Out of these, we need to select 6 cells. The probability of selecting a cell capable of replication is 25/37 for the first selection, multiplied by 24/36 for the second selection, and so on, until 20/32 for the sixth selection. So, the probability is:

P(all 6 cells able to replicate) = (25/37) * (24/36) * (23/35) * (22/34) * (21/33) * (20/32) ≈ 0.0051

The probability that at least one cell is not capable of replication is equal to 1 minus the probability that all six cells are able to replicate. So, the probability is:

P(at least one cell not able to replicate) = 1 - P(all 6 cells able to replicate) ≈ 0.9949

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Answer:

The equation for this line, in slope-intercept form, is given by:

[tex]y = - 9[/tex]

Step-by-step explanation:

The equation of a line in the slope-intercept form has the following format:

[tex]y = ax + b[/tex]

In which a is the slope of the line and b is the y intercept.

Solution:

The line has the same y-intercept as [tex]y + 1 = 4 (x - 2)[/tex].

So, we have to find the y-intercept of this equation

[tex]y + 1 = 4 (x - 2)[/tex]

[tex]y = 4x - 8 - 1[/tex]

[tex]y = 4x - 9[/tex]

This equation, has the y-intercept = -9. Since this line has the same intercept, we have that [tex]b=-9[/tex].

Fow now, the equation of this line is

[tex]y = ax - 9[/tex]

The line contains the point [tex](9,-9)[/tex]

This means that when [tex]x = 9, y = -9[/tex]. We replace this in the equation and find a

[tex]y = ax - 9[/tex]

[tex]-9 = 9a - 9[/tex]

[tex]9a = 0[/tex]

[tex]a = \frac{0}{9}[/tex]

[tex]a = 0[/tex]

The equation for this line, in slope-intercept form, is given by:

[tex]y = - 9[/tex]

Answer:

[tex]m=-\frac{4}{7}[/tex]

[tex]b=\frac{3}{7}[/tex]

Step-by-step explanation:

Slope intercept form of a line is

[tex]y=mx+b[/tex]             ... (1)

where, m is slope and b is y-intercept.

The given equation is

[tex]4x+7y+4=7[/tex]

We need to find the slope intercept form of given line.

Subtract 4 from both sides.

[tex]4x+7y=7-4[/tex]

[tex]4x+7y=3[/tex]

Subtract 4x from both sides.

[tex]7y=3-4x[/tex]

Divide both sides by 7.

[tex]y=\frac{3-4x}{7}[/tex]

[tex]y=\frac{3}{7}-\frac{4}{7}x[/tex]

Arrange the terms.

[tex]y=-\frac{4}{7}x+\frac{3}{7}[/tex]           .... (2)

Form (1) and (2) we get

[tex]m=-\frac{4}{7}[/tex]

[tex]b=\frac{3}{7}[/tex]

Therefore, the slope of the line is -4/7 and y-intercept is 3/7.

Answer:

The solution of the system of linear equations is [tex]x=3, y=4, z=1[/tex]

Step-by-step explanation:

We have the system of linear equations:

[tex]2x+3y-6z=12\\x-2y+3z=-2\\3x+y=13[/tex]

Gauss-Jordan elimination method is the process of performing row operations to transform any matrix into reduced row-echelon form.

The first step is to transform the system of linear equations into the matrix form. A system of linear equations can be represented in matrix form (Ax=b) using a coefficient matrix (A), a variable matrix (x), and a constant matrix(b).

From the system of linear equations that we have, the coefficient matrix is

[tex]\left[\begin{array}{ccc}2&3&-6\\1&-2&3\\3&1&0\end{array}\right][/tex]

the variable matrix is

[tex]\left[\begin{array}{c}x&y&z\end{array}\right][/tex]

and the constant matrix is

[tex]\left[\begin{array}{c}12&-2&13\end{array}\right][/tex]

We also need the augmented matrix, this matrix is the result of joining the columns of the coefficient matrix and the constant matrix divided by a vertical bar, so

[tex]\left[\begin{array}{ccc|c}2&3&-6&12\\1&-2&3&-2\\3&1&0&13\end{array}\right][/tex]

To transform the augmented matrix to reduced row-echelon form we need to follow these row operations:

[tex]\left[\begin{array}{ccc|c}1&3/2&-3&6\\1&-2&3&-2\\3&1&0&13\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&-7/2&6&-8\\3&1&0&13\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&-7/2&6&-8\\0&-7/2&9&-5\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&-7/2&9&-5\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&0&3&3\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&0&1&1\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&0&4\\0&0&1&1\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc|c}1&3/2&0&9\\0&1&0&4\\0&0&1&1\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc|c}1&0&0&3\\0&1&0&4\\0&0&1&1\end{array}\right][/tex]

From the reduced row echelon form we have that

[tex]x=3\\y=4\\z=1[/tex]

Since every column in the coefficient part of the matrix has a leading entry that means our system has a unique solution.

Answer:

The radius is a line segment that starts at the center of the circle and ends at a point on the circle.

Step-by-step explanation:

The radius is half of the diameter. The diameter is one line going across the whole, through the midpoint. The radius starts at the midpoint and that's why it's only half of the diameter.

Answer: The radius is a line segment that starts at the center of the circle and ends at a point on the circle.

Step-by-step explanation:

Let's check all the options.

The radius is a line segment joining two distinct points on the circle. → Wrong.

Reason :- Radius joins center and any point on circle not any two points.

The radius is the boundary of a circle. → Wrong.

Reason :- Circumference is the boundary of circle ,

Formula for circumference C= 2π r , where r is radius .

The radius is a line segment that starts at one point on the circle, passes through the center of the circle, and ends at another point on the circle.→ Wrong.

Reason :- Its diameter that starts at one point on the circle, passes through the center of the circle, and ends at another point on the circle and it is twice of radius.

So , the best answer that defines the radius of a circle is The radius is a line segment that starts at the center of the circle and ends at a point on the circle.

Answer:

Qualitative and Neither

Step-by-step explanation:

Quantitative data is such a data which can be measured or calculated i.e. which is defined only in terms of numbers. In simple words we can say that numeric data is the Quantitative data.

On the other hand, qualitative data describes the characteristics, attribute or quality of the objects. This type of data is not measured or calculated.

The data which we are dealing with is "Kind of pizza". The kind/flavor of pizza is an attribute or characteristic of pizza. So from here it is clear that the data is Qualitative. Though numbers are assigned  to different flavors, these numbers are just for identification of the flavor on the order form.

The terms discrete and continuous can only be used when the data is Quantitative. Qualitative data cannot be referred to as discrete or continuous data, even if some numbers are assigned to data.

Therefore, the answers are: Qualitative and Neither

Answer:

5

Step-by-step explanation:

-7x-3x+2= -8x-8;

-10x+2= -8x-8;

-10x+2+8x= -8;

-10x+8x= -8-2;

-2x= -10;

x=(-10)/(-2);

x=5.

Answer:

8771408311 steps ( approx )

Step-by-step explanation:

Given,

The radius of the earth,

[tex]r=6.38\times 10^6[/tex]

So, the circumference of the earth,

[tex]S=2\pi (r)[/tex]

[tex]=2\times \frac{22}{7}\times (6.38\times 10^8)[/tex]

[tex]=4.0102857143\times 10^9\text{ meters}[/tex]

∵ 1 meter = 39.3701 inches

[tex]\implies S =1.578853496\times 10^{11}\text{ inches }[/tex]

Also, the length of one step = 18 inches

Hence, the total number of steps =  [tex]\frac{1.578853496\times 10^{11}}{18}[/tex]

[tex]= 8.7714083111\times 10^9[/tex]

[tex]\approx 8771408311[/tex]

Answer:

Jamal received 2,880 votes

Step-by-step explanation:

In the election,

Jamal received 40% of all votes

Tran received 100% - 40% = 60% that is 4,320 votes

Let x be the number of votes Jamal received. Then

x - 40%

4,320 - 60%

Write a proportion:

[tex]\dfrac{x}{4,320}=\dfrac{40}{60}\\ \\\text{Cross multiply}\\ \\60\cdot x=40\cdot 4,320\\ \\x=\dfrac{40\cdot 4,320}{60}=\dfrac{2\cdot 4,320}{3}=\dfrac{2\cdot 1,440}{1}=2,880[/tex]

The sum of 7.25 L and 875 cL, reduced to milliliters, is 16,000 mL as per the concept of addition.

To add 7.25 L and 875 cL, we need to convert the centiliters to liters before performing the addition.

1. Convert 875 cL to liters:

Since there are 100 centiliters in a liter, we divide 875 by 100 to get the equivalent in liters:

875 cL ÷ 100 = 8.75 L

2. Now that both quantities are in liters, we can add them together:

7.25 L + 8.75 L = 16 L

3. Finally, to convert the result to milliliters, we multiply by 1000 since there are 1000 milliliters in a liter:

16 L × 1000 = 16,000 mL

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Final answer:

To add 7.25 L and 875 cL and reduce the result to milliliters, convert 875 cL to liters to get 8.75 L, then add it to 7.25 L to total 16 L. Finally, convert 16 L to milliliters by multiplying by 1,000, resulting in 16,000 mL.

Explanation:

To add 7.25 L and 875 cL and reduce the result to milliliters, you first need to understand the conversion between liters, centiliters, and milliliters. Remember, there are 1000 milliliters (mL) in a liter (L) and 10 milliliters in a centiliter (cL).

First, let's convert 875 cL to liters to simplify the addition. Since there are 10 mL in a cL, and 1000 mL in a L, you would convert as follows:

875 cL = 875 / 10 = 87.5 mL

However, we need to recognize the proper conversion to liters in the step above. Correctly, it should state: 875 cL = 8.75 L (since 100 cL = 1 L).

Once we have both measurements in liters, we can easily add them:

7.25 L + 8.75 L = 16.0 L

To convert the total liters to milliliters, multiply by 1,000 (since there are 1,000 mL in 1 L).

16.0 L × 1,000 = 16,000 mL

Answer:

-½

Step-by-step explanation:

Simplify \frac{25}{100}

100

25

to \frac{1}{4}

4

1

.

-\sqrt{\frac{1}{4}}−√

4

1

2 Simplify \sqrt{\frac{1}{4}}√

4

1

to \frac{\sqrt{1}}{\sqrt{4}}

√

4

√

1

.

-\frac{\sqrt{1}}{\sqrt{4}}−

√

4

√

1

3 Simplify \sqrt{1}√

1

to 11.

-\frac{1}{\sqrt{4}}−

√

4

1

4 Since 2\times 2=42×2=4, the square root of 44 is 22.

-\frac{1}{2}−

2

1

Done

Decimal Form: -0.5

Answer: D.)

Step-by-step explanation:

The first step would be to reduce the fraction in the square root, so divide both the numerator and denominator by 25 to get 1/4.

Then calculate the root, any root of one equals one so that stays as is. The exponential form of 4 would be 2^2.

Then reduce the index of the radical and exponent with 2 and you get answer D

Answer:

B. 5 rolls

Step-by-step explanation:

The areas of the room, not including the ceiling, are discriminated as follows:

Longer walls: [tex](12.5\times8)\times2=200ft^2[/tex] (6 inches equals one foot)

Shorter walls: [tex](10.5\times8)\times2 = 168ft ^ 2[/tex] (6 inches equals one foot)

Window area: [tex](4\times3)\times2 = 24ft ^ 2[/tex]

Door area: [tex](7\times3) = 21ft ^ 2[/tex]

Area that will be effectively covered:

Total area to wallpaper: [tex]200 + 168 -24 -21 = 323ft ^ 2[/tex]

Amount of paper needed: [tex]323\times1.1 = 355.3ft ^ 2[/tex]

[tex]30in = 24in + 6in = 2ft + 0.5ft = 2.5ft.[/tex] That is, the area of ​​a roll of paper is [tex]2.5\times30 = 75ft ^ 2[/tex]

Number of rolls needed:

[tex]\frac{355.3}{75} = 4.73[/tex] rolls

Answer:

Correct answer is B. 5Rolls

Step-by-step explanation:

12 inches is 1 feet

6 inches is 6/12 feet= 0,5 feet.

12 inches is 1 foot

30 inches is 30/12 feet=2,5feet.

2. Second,you have to calculate the total surface where you will wallpaper.

So you have to calculate the dimension of 2 different rectangles and substract the surfaces that you don't have to wallppaper (door and windows).

[tex]Area rectangle 1 =10.5feet*8feet=84ft^{2} \\Area rectangle2=12.5feet*8feet=100ft^{2}\\Total Area of walls=(Area rectangle 1 *2) + (Area rectangle2*2)\\Total Area of walls=(84ft^{2} *2)+(100ft^{2})\\\\Total Area of walls=368ft^{2}[/tex]

3. Now we have to calculate the area to substract from the total area, since you will not wallpaper the door and windows:

[tex]Windows=4feet*3feet*2=24ft^{2}  \\Door=7feet*3feet=21ft^{2}[/tex]

4. Total area to wallpaper is Total surface of the room minus door and windows surface:

[tex]wallpaperArea=368ft^{2} -45ft^{2}\\wallpaperArea=323ft^{2}[/tex]

5. Now you have to add 10% waste to the calculated surface:

[tex]323ft^{2} +(323*0.10)=355.3ft^{2}[/tex]

6. So, you have the real area that will wallpaper considering 10% waste, it is 326.23 square feet. To calculate how many rolls you will need, you have to calculate the surface that each roll covers and then divide total surface by roll surface.

[tex]Roll surface=2,5feet*30feet=75feet^{2}[/tex]

[tex]Rolls needed=355.3ft^{2}/75ft^{2}=4.73[/tex]

7. As the number of rolls is not integer you have to round, then the answer is you will need 5 rolls of wallpaper.

Answer:

Step-by-step explanation:

Given that the solution of a certain differential equation is of the form

[tex]y(t) = ae^{7t} +be^{11t}[/tex]

Use the initial conditions

i) y(0) =1

[tex]1=a(1)+b(1)\\a+b=1[/tex] ... I

ii) y'(0) = 4

Find derivative of y first and then substitute

[tex]y'(t) = 7ae^{7t} +11be^{11t}\\y'(0) =7a+11b \\7a+11b =4 ...II[/tex]

Now using I and II we solve for a and b

Substitute b = 1-a in II

[tex]7a+11(1-a) = 4\\-4a+11 =4\\-4a =-7\\a = 1.75 \\b = -0.75[/tex]

Hence solution is

[tex]y(t) = 1.75e^{7t} -0.75e^{11t}[/tex]

Answer:

y(t) = a exp(3t) + b exp(4t) conditions, y(0) = 3 y'(0) = 3 y(0) = a exp(3 x 0) + b exp(4 x 0) = a exp(0) + b exp(0) = (a x 1) + (b x 1) = a + b y'(0) = 0 so the linear equation is, a + b = 3

Step-by-step explanation:

Answer:

[tex]\text{Density}=\frac{0.556\text{ Grams}}{\text{ cm}^3}[/tex]

Step-by-step explanation:

We are asked to find the density of a cylinder whose volume is 1000.0 cubic cm and mass is 556 grams.

[tex]\text{Density}=\frac{\text{Mass}}{\text{Volume}}[/tex]

Substitute the given values:

[tex]\text{Density}=\frac{556\text{ Grams}}{1000.0\text{ cm}^3}[/tex]

[tex]\text{Density}=\frac{0.556\text{ Grams}}{\text{ cm}^3}[/tex]

Therefore, the density of the metallic cylinder is 0.556 grams per cubic centimeter.

Answer:

option C the 69 businesses that returned the questionnaire.

Step-by-step explanation:

It is given in the question that only 69 businesses out of all 282 randomly chosen businesses have returned the questionnaire mailed by the committee.

Therefore,

The data available for the study by the committee is of only 69 businesses that have replied to the committee. So the study is based on this population of 69 businesses only.

Hence, option c is the correct answer.

Answer:

The linear problem is to maximize [tex]Z = C_ {1} X_ {1} + C_ {2}X_ {2} = 60X_ {1} + 50X_ {2}[/tex], s.a.

subject to

[tex]\frac {1} {5} X_ {1} + \frac {1} {4} X_ {2} \leq 20\\\\\frac {1} {3} X_ {1} + \frac {1} {6} X_ {2} \leq 24\\\\X_ {2} \geq 2\\\\X_ {1}, X_ {2} \geq 0[/tex]

Step-by-step explanation:

Let the decision variables be:

[tex] X_ {1} [/tex]: number of units of product 1 to produce.

[tex] X_ {2} [/tex]: number of units of product 2 to produce.

Let the contributions be:

[tex]C_ {1} = 60\\\\C_ {2} = 50[/tex]

The objective function is:

[tex]Z = C_{1} X_{1}+ C_{2}X_{2} = 60X_ {1} + 50X_ {2}[/tex]

The restrictions are:

[tex]\frac {1} {5} X_ {1} + \frac {1} {4} X_ {2} \leq 20\\\\\frac {1} {3} X_ {1} + \frac {1} {6} X_ {2} \leq 24\\\\X_ {2} \geq 2\\\\X_ {1}, X{2} \geq 2\\\\[/tex]

The linear problem is to maximize [tex]Z = C_ {1} X_ {1} + C_ {2}X_ {2} = 60X_ {1} + 50X_ {2}[/tex], s.a.

subject to

[tex]\frac {1} {5} X_ {1} + \frac {1} {4} X_ {2} \leq 20\\\\\frac {1} {3} X_ {1} + \frac {1} {6} X_ {2} \leq 24\\\\X_ {2} \geq 2\\\\X_ {1}, X_ {2} \geq 0[/tex]

Answer:

Step-by-step explanation:

As per the given question,

In a manufacturing operation, a part is produced by machining, polishing, and painting.

Number of machine tools = 3

Number of polishing tools = 4

Number of painting tools = 3

Now,

For finding the different routing consisting of machining, followed by polishing, and followed by painting, we have to simply multiply the number of machine tools, polishing tools and painting tools.

Therefore,

The different routing (consisting of machining, followed by polishing, and followed by painting) for a part are possible = 3 × 4 × 3 = 36.

Hence, the required answer is 36.

Number of ways a process can be done is the count of total distinguished ways that process can be done. The count of different routings possible for a part is 36

Suppose that a process A can be done in 'a' different ways.
And there is a process following A, call it B, can be done in 'b' different ways. Then, the process A then B can be done in a×b different ways.

This is called rule of product in combinatorics.

Since there are 3 processes to be done subsequently(machining, polishing, then painting), and each of them can be done in 3, 4, and 3 ways respectively, thus,

Total number of routings possible for a part is [tex]3 \times 4 \times 3 = 36[/tex] ways.

Thus, The count of different routings possible for a part is 36

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Answer:

Quality A is greater

Step-by-step explanation:

Answer:

7/10

Step-by-step explanation:

The total number of marbles is 7 + 2 + 1 = 10.  So the probability of selecting a brown marble is 7/10

During the flood season, the water rises 26.4 feet up the side of the lake.

The angle of elevation is given as 15 degrees 30 minutes,

Now, it can be converted to decimal degrees as 15.5 degrees.

Let's denote the distance up the side of the lake as x feet.

Now set up a trigonometric equation using the tangent function:

tan(15.5°) = (7.3 feet) / x

We can solve for x by rearranging the equation:

x = (7.3 feet) / tan(15.5°)

Evaluating this expression gives us:

x = (7.3 feet) / 0.277

x = 26.4 feet

Therefore, the water rises 26.4 feet up the side of the lake.

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Answer:

0

Step-by-step explanation:

total number of balls = 3+5+2= 10

Probability of getting red P(R) = 3/10

Probability of getting white P(W) = 5/10

Probability of getting black P(B) = 2/10

for each red ball drawn you win $6 and for each black ball drawn you loose $9 dollars

E(X)= 6×3/10 +0×5/10 -9×2/10= 0

E(X)= 0

The problem is a step-by-step calculation with several possible combinations of type A and type B vehicles when a total of 101 counts are registered. A systematic approach is required to find all possible whole number solutions.

This problem is an example of a diophantine problem or a linear equation in two variables. If we denote the number of type A vehicles by 'a', and the number of type B vehicles by 'b', the problem can be represented by the equation 2a + 9b = 101.

As you are looking for all possible solutions, you have to do a systematic search. You will find that:

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Answer:

2500

Step-by-step explanation:

We have to find the largest product of two numbers whose sum is 100.

Let the two numbers be x and y.

Thus, we can write x+y=100

We can calculate the value of y as:

y = 100 - x

The product of these number can be written as: (x)(y) = (x)(100-x) = 100x - x²

Let f(x) = 100x - x²

Now, the first derivative of this function with respect to x is

[tex]\frac{df(x)}{dx}[/tex] = 100-2x

Equating [tex]\frac{df(x)}{dx}[/tex] = 0, we get,

100-2x = 0

⇒ x = 50

Now, we find the second derivative of the the function f(x) with respect to x

[tex]\frac{d^2f(x)}{dx^2}[/tex] = -2

Since, [tex]\frac{d^2f(x)}{dx^2}[/tex] < 0, then by double derivative test the function have a local maxima at x = 50

This, x = 50 and y = 100-50 =50

Largest product = (50)(50) = 2500

Answer:

The inverse function of [tex]\sqrt{3]{x} - 8[/tex] is [tex](x+8)^{3}[/tex]

Step-by-step explanation:

Inverse of a function:

To find the inverse of a function [tex]y = f(x)[/tex], basically, we have to reverse r. We exchange y and x in their positions, and then we have to isolate y.

In your exercise:

[tex]y = \sqrt[3]{x} - 8[/tex]

Exchanging x and y, we have:

[tex]x = \sqrt[3]{y} - 8[/tex]

[tex]x + 8 = \sqrt[3]{y}[/tex]

Now we have to write y in function of x

[tex](x+8)^{3} = (\sqrt[3]{y})^{3}[/tex]

[tex]y = (x+8)^{3}[/tex]

So, the inverse function of [tex]\sqrt{3]{x} - 8[/tex] is [tex](x+8)^{3}[/tex]

Answer:

[tex]y(t)\ =\ C_1.e^{-2t}+C_2e^t-\ t.\dfrac{e^{-2t}}{3}-\dfrac{1}{3}[/tex]

Step-by-step explanation:

Given differential equation is,

     y"+y'-2y=1

[tex]=>\ (D^2+D-2D)y\ =\ 1[/tex]

To find the complementary function we will write,

    [tex]D^2+D-2=0[/tex]

[tex]=>\ D\ =\ \dfrac{-1+\sqrt{1^2+4\times 2\times 1}}{2\times 1}\ or\ \dfrac{-1-\sqrt{1^2+4\times 2\times 1}}{2\times 1}[/tex]

[tex]=>\ D\ =\ -2\ or\ 1[/tex]

Hence, the complementary function can be given by

[tex]y(t)\ =\ C_1e^{-2t}\ +\ C_2e^t[/tex]

Let's say,

[tex]y_1(t)\ =\ e^{-2t}\ \ =>y'_1(t)\ =\ -2e^{-2t}[/tex]

[tex]y_2(t)\ =\ e^{t}\ \ =>y'_2(t)\ =\ e^{t}[/tex]

[tex]g(t)\ =\ 1[/tex]

Wronskian can be given by,

[tex]W\ =\ y_1(t).y'_2(t)\ -\ y_2(t).y'_1(t)[/tex]

     [tex]=\ e^{-2t}.e^{t}\ -\ e^{t}.(-2e^{-2t})[/tex]

     [tex]=\ e^{-t}\ +\ 2e^{-t}[/tex]

     [tex]=\ 3.e^{-t}[/tex]

Now, the particular integral can be given by

[tex]y_p(t)=\ -y_1(t)\int\dfrac{y_2(t).g(t)}{W}dt\ +\  y_2(t)\int\dfrac{y_1(t).g(t)}{W}dt[/tex]

        [tex]=\ -e^{-2t}\int\dfrac{e^t.1}{3.e^{-t}}+e^t\int\dfrac{e^{-2t}.1}{3.e^{-t}}dt[/tex]

       [tex]=\ -e^{-2t}\int\dfrac{1}{3}dt+\dfrac{e^t}{3}\int e^{-t}dt[/tex]

       [tex]=\ \dfrac{-e^{-2t}}{3}.t\ -\ \dfrac{e^t}{3}.e^{-t}[/tex]

        [tex]=\ -t.\dfrac{e^{-2t}}{3}-\dfrac{1}{3}[/tex]

Hence, the complete solution can be given by

[tex]y(t)\ =\ C_1.e^{-2t}+C_2e^t-\ t.\dfrac{e^{-2t}}{3}-\dfrac{1}{3}[/tex]

Answer:

x=2

Step-by-step explanation:

−3(4−x)+3x=3(10−5x)

(−3)(4)+(−3)(−x)+3x=(3)(10)+(3)(−5x)

−12+3x+3x=30+−15x

(3x+3x)+(−12)=−15x+30

6x+−12=−15x+30

6x−12=−15x+30

6x−12+15x=−15x+30+15x

21x−12=30

Step 3: Add 12 to both sides.

21x−12+12=30+12

21x=42

Answer:

The value of x is [tex]\frac{(3c+b)}{3-c}[/tex].

Step-by-step explanation:

The given equation is

[tex]cx+b=3(x-c)[/tex]

Using distributive property we get

[tex]cx+b=3(x)+3(-c)[/tex]

[tex]cx+b=3x-3c[/tex]

To solve the above equation isolate variable terms.

Subtract 3x and b from both sides.

[tex]cx-3x=-3c-b[/tex]

Taking out common factors.

[tex]x(c-3)=-(3c+b)[/tex]

Divide both sides by (c-3).

[tex]x=-\frac{(3c+b)}{c-3}[/tex]

[tex]x=\frac{(3c+b)}{3-c}[/tex]

Therefore the value of x is [tex]\frac{(3c+b)}{3-c}[/tex].

Answer:

14. Quadrant IV

13. Quadrant II

12. Quadrant III

11. Quadrant I

15. -17

16. -1

17. 7

Step-by-step explanation:

Answer:

The first two coins are quarters, and the one on the right is a nickle.

the two quarters [0.25+0.25] is 0.50 cents. Add the nickle [0.5] and you have 0.55 cents!

ex:     0.25+0.25+0.5

             0.50+0.5

                 =0.55 (cents)

Step-by-step explanation: