3. How many terms of the arithmetic sequence 2, 8, 14, 20, are required to give a sum of
660?

Answer:

A

Step-by-step explanation:

umm so for some reason I cant submit my answer unless theres 20 characters. :)

The distance from the base of the ramp to the base of the sofa is approximately 32.97 inches.

we can use the Pythagorean theorem. Let's denote the distance from the base of the ramp to the base of the sofa as 'x'.

According to the information given, the length of the ramp is 42 inches, and the height from the top of the seat cushion to the floor is 26 inches.

Using the Pythagorean theorem, we have the equation:

x² + 26²  = 42²

Simplifying:

x² + 676 = 1764

Subtracting 676 from both sides:

x² = 1088

Taking the square root of both sides:

x ≈ 32.97 inches

Therefore, the distance from the base of the ramp to the base of the sofa is approximately 32.97 inches.

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The reduced cost matrix for travelling salesperson problem in the given instance is shown below. The Travelling Salesperson Problem (TSP) is a classical combinatorial optimization issue that belongs to the category of NP-Hard problems.

This problem can be resolved using a branch and bound algorithm or by using dynamic programming.The reduced cost matrix for the given travelling salesperson problem instance The computation of the reduced cost matrix for travelling salesperson problem involves two steps: Identify the smallest element of each row and subtract the value from all the values in the row.

Identify the smallest element of each column and subtract the value from all the values in the column.In the given instance, the smallest element of each row is highlighted in bold. Therefore, after performing Step 1 the matrix becomes the matrix becomes Hence, the reduced cost matrix for the travelling salesperson problem is obtained.

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Answer:

(2, - 3 )

Step-by-step explanation:

Given the 2 equations

y = - 3x + 3 → (2)

y = - 9x + 15 → (2)

Substitute y = - 3x + 3 into (2)

- 3x + 3 = - 9x + 15 ( add 9x to both sides )

6x + 3 = 15 ( subtract 3 from both sides )

6x = 12 ( divide both sides by 6 )

x = 2

Substitute x = 2 into either of the 2 equations and solve for y

Substituting into (1)

y = - 3(2) + 3 = - 6 + 3 = - 3

solution is (2, - 3 )

41x - 164 = 271

x = 35

Answer:

x= 35

Step-by-step explanation:

1271 + 164 = 1435

1435/41 = 35

The functions that are solutions of the differential equation y''?4y'+4y=e^t are: (B) y=e^(2t)+te^t & (E) y=e^(2t)+e^t.The given differential equation is, y''+4y'+4y=e^t ...(1)

We have to find the solutions of the differential equation. Let's solve the differential equation:(1) => r²+4r+4=0Now, solve the quadratic equation using the quadratic formula: r= (-(4)+√((4)²-4(1)(4))) / 2(1)= -2 (repeated)So, the solution of the corresponding homogeneous equation is:(2) yh= (c₁+c₂t)e^(-2t) ---------------(2)Now, we have to find a particular solution of the non-homogeneous differential equation (1).

Let, yp= Ae^t. Now, yp'= Ae^t, yp''= Ae^t. Substitute yp and its derivatives in the equation (1):yp''+4yp'+4yp= e^tAe^t+4Ae^t+4Ae^t= e^t9Ae^t= e^tA= 1/9Therefore, the particular solution is,(3) yp= e^t/9 ------------(3)

Hence, the general solution of the given differential equation is,(4) y= yh+yp= (c₁+c₂t)e^(-2t) + e^t/9Now, substitute the initial conditions in the general solution to get the constants c₁ and c₂:Let, y(0)=0 and y'(0)=0, then,c₁= -1/9 and c₂= 5/9Finally, the solution of the differential equation y''?4y'+4y=e^t is,(5) y= -(1/9)e^(-2t) + (5/9)te^(-2t) + e^t/9 =(e^(2t)+te^(2t))/9+ e^t ...

(Ans)The options that represent the functions that are solutions of the differential equation y''?4y'+4y=e^t are: (B) y=e^(2t)+te^t & (E) y=e^(2t)+e^t.

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Answer:

segment a would be 2.5, b would be 2.5, and c would be 3.5 i believe

Step-by-step explanation:

to get a midpoint, you measure the distance between the two endpoints, then divide that answer by 2.

Answer:

1. 30

2. 10

3. -10

30, 10, and -10

60 - 30 - 30

50 - 40 = 10

40 - 50 = -10

The average density of the rod is  0.704 kg/m.

For given question,

We have been given the linear density in a rod 5 m long is 10 / x + 4 kg/m, where x is measured in meters from one end of the rod.

We need to find the

The length of rod is, L = 5 m.

The linear density of rod is, ρ = 10/( x + 4) kg/m

To find the average density we need to integrate the linear density from x₁ = 0 to x₂ = 5,  

The expression for the average density is given as,

⇒ ρ'

\(=\int\limits^5_0 {\rho} \, dx\\\\=\int\limits^5_0 {\frac{m}{L} } \, dx\\\\=\int\limits^5_0 {\frac{10}{5(x+4)} }\, dx\\\\=\int\limits^5_0 {\frac{2}{x+4} }\, dx\)                        ......................(1)

Using u = x + 4  

du = dx

u₁ = x₁ + 4

u₁ = 0 + 4

u₁ = 4

and

u₂ = x₂ + 4

u₂ = 5 + 4

u₂ = 9

By entering the values above into (1), we have:

⇒ ρ'

\(=2\int\limits^9_4 {\frac{1}{u} } \, du\\\\ = 2[(log~u)]_4^{9}\\\\=2[(log~9-log~4)]\\\\=2\times[0.352]\)

= 0.704

Thus, we can conclude that the average density of the rod is  0.704 kg/m.

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Answer:

45726.82

Step-by-step explanation:

Yes

The area of a parallelogram is 45726.82 square units.

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.

Given that, b= 202.6 units and h= 225.7 units

We know that, the area of a parallelogram is Base×Height

= 202.6×225.7

= 45726.82 square units

Therefore, the area of a parallelogram is 45726.82 square units.

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Answer:

8km  5mi

Step-by-step explanation:

20x400=8000meters a km = to 1000meters

8000/1000=8km

A mile is a kilometer/ 1.6  8/1.6=5 miles

Sanford ran approximately 8 kilometers and about 4.97 miles.

Given that a coach made someone run 20 laps on a 400 m track.

We need to find the number of mile he ran as well as number of kilometers he ran.

To find out how many kilometers Sanford ran, we can use the fact that 1 kilometer is equal to 1000 meters.

Similarly, to find out how many miles he ran, we'll use the conversion factor of 1 mile being equal to approximately 1609.34 meters.

Let's calculate it:

1 lap = 400 meters

20 laps = 20 x 400 = 8000 meters

Kilometers:

8000 meters ÷ 1000 meters/kilometer = 8 kilometers

Miles:

8000 meters ÷ 1609.34 meters/mile ≈ 4.97 miles

So, Sanford ran approximately 8 kilometers and about 4.97 miles.

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Based on the calculated values, we  can say about the percentage of students using the company's tablets in public school districts that relative to the mean, there are some school districts where many more students are using the tablets.

What can we say about the percentage of students using the company's tablets in public school districts?Based on the calculated values, relative to the mean, there are some school districts where many more students are using the tablets. Therefore, we cannot say that the use of tablets is similar for all school districts or that it is very low or high for all school districts.

However, we can say that there are some school districts where much fewer students are using the tablets.The percentage of students using the company's tablets in public school districts depends on various factors such as the district's size, demographic, socioeconomic status, and technological infrastructure. Therefore, the usage rate can vary greatly between different school districts. Some districts might have higher tablet usage rates than the mean, while others might have lower usage rates than the mean.

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The equation representing a line that is perpendicular to y=2/3x−5 and passes through the point (6,12) is y = -3x/2 +24

Equation of line perpendicular to another line is defined by the slope of the lines. If the slope is m, then the relationship between the slopes are

m = -1/m'

The equation of the line given y = 2/3x − 5

slope , m = 2/3

slope of the perpendicular line, m' = -1/m

m' = -3/2

The line passes through point (6,12)

y - 6 = -3/2(x-12

y - 6 = -3x/2 + 18

y = -3x/2 + 18 + 6

y = -3x/2 + 24

The equation of the perpendicular line required is y = -3x/2 +24

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Although horror book sales appear to be only 50% of fantasy sales, but they are actually only about 8% smaller, that is, option a.

Here, we are given a graph as shown in the figure below.

Just by looking at the graph it appears that that horror books are 50% of fantasy book sales.

From the graph we have the following data-

Number of horror books sold = 55

Number of fantasy books sold = 60

Number of extra fantasy books than horror books = 60 - 55

= 5

Thus, in percentage terms horror books will be - (5/60) % smaller than fantasy books

= 8.33%

Therefore, although horror book sales appear to be only 50% of fantasy sales, but they are actually only about 8% smaller, that is, option a.

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Your question was incomplete. Check for the missing graph below.

Answer:

what should i answer?

Step-by-step explanation:

The length of the support wire is approximately 54 feet. To find the length of the support wire, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the telephone pole forms the height of a right triangle, and the distance from the base to the anchor point forms the base.

We can find the length of the support wire, which is the hypotenuse.

Using the Pythagorean theorem, we have:
Length of support wire = √(30^2 + 45^2)
Length of support wire = √(900 + 2025)
Length of support wire = √2925
Length of support wire ≈ 54 feet

Therefore, the length of the support wire is approximately 54 feet.

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The equations ordered from the least to greatest is

y = (-3/4)x + 2

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

3x - 4y = 7

y = 12(x - 19) + 5

From the question, we are to order the equations from least to greatest by the value of the slope

The given equations are

y = (-3/4)x + 2

3x - 4y = 7

y = 12(x - 19) + 5

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

To determine the slopes of the line, we will compare the equations to the general form of the equation of a line

The general form of the equation of a line is

y = mx + b

Where m is the slope

and b is the y-intercept

By comparison,

m = -3/4

∴ Slope = -3/4

First, rearrange

3x - 7 = 4y

4y = 3x - 7

y = (3/4)x - 7/4

By comparison,

m = 3/4

∴ Slope = 3/4

First, simplify

y = 12x - 228 + 5

y = 12x - 223

By comparison,

m = 12

∴ Slope = 12

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

First, simplify

y - 3= (1/2)x - 2

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

y = (1/2)x + 1

By comparison,

m = 1/2

∴ Slope = 1/2

Now,

The slopes ordered from the least to greatest is

-3/4 < 1/2 < 3/4 < 12

Thus,

The equations ordered from the least to greatest is

y = (-3/4)x + 2

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

3x - 4y = 7

y = 12(x - 19) + 5

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Answer: yes

Step-by-step explanation:

12    3

4     1

to get to 3 from 12 you divide by 4 and to get from 4 to 1 you also divided by 4

The given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

To show continuity, we need to verify that the partial derivatives of ψ and φ with respect to x and y are equal. Let's calculate these partial derivatives:

∂ψ/∂x = 2y

∂ψ/∂y = 2x

∂φ/∂x = 2x

∂φ/∂y = -2y

From the above calculations, we can see that the partial derivatives of ψ and φ with respect to x and y are equal. Therefore, the condition for continuity, which requires the equality of partial derivatives, is satisfied.

To show irrotational flow, we need to verify that the curl of the velocity vector is zero. The velocity vector can be obtained from the stream function ψ and velocity potential φ as follows:

V = ∇φ x ∇ψ

Taking the curl of V:

∇ x V = ∇ x (∇φ x ∇ψ)

Using vector calculus identities and simplifying the expression, we find:

∇ x V = 0

Since the curl of the velocity vector is zero, the condition for irrotational flow is satisfied.

Therefore, based on the calculations and verifications, we can conclude that the given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

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Answer:

Ask your Teacher

Step-by-step explanation:

Answer:

slope(m)=2

Step-by-step explanation:

Answer:94.5

Step-by-step explanation:

Answer:

Hi! The answer to your question is \(y=3x-10\)

Step-by-step explanation:

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Answer:

y = 3x - 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (3, - 1) and (x₂, y₂ ) = (5, 5)

m = \(\frac{5+1}{5-3}\) = \(\frac{6}{2}\) = 3 , then

y = 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (5, 5 ) , then

5 = 15 + c ⇒ c = 5 - 15 = - 10

y = 3x - 10 ← equation of line

Answer:

3x = 3

Step-by-step explanation:

Since for 3x = 3, we can plug in the 1.

It becomes:

3(1) = 3

3 = 3

Thus, 3x =3 would be true if x = 1.

The conditional pdfs are as follows:

fy(y|X=2)=dΦ(y-2)dyfy(y|X=−2)=dΦ(y+2)dyAnswer:fy(y|X=2)=dΦ(y−2)dyfy(y|X=−2)=dΦ(y+2)dy

Given:

A binary transmission system transmits a signal X of value -2[V] to send a "O" and 2[V] to send a "1".Let Y = X + N be the received signal, where N is a random variable with normal standard distribution that represents an additive noise.To Determine:We need to find the conditional pdfs fy(y|X = 2) and fy(y|X = -2)We know that,The standard Normal Distribution formula is given byf(x)=1/√2πe−x22f(x) = \frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}f(x)=2π​1​e−2x2​A binary transmission system transmits a signal X of value -2[V] to send a "O" and 2[V] to send a "1".Let X takes only two values +2 or -2.Therefore,P(X=+2)=P(X=-2)=0.5We need to find the conditional pdfs fy(y|X = 2) and fy(y|X = -2)We can calculate the expected values of Y,E(Y|X=2) = E(X|X=2) + E(N) = 2+0 = 2E(Y|X=-2) = E(X|X=-2) + E(N) = -2+0 = -2The conditional pdfs fy(y|X = 2) and fy(y|X = -2) are given byfy(y|X=2) = P(Y ≤ y | X = 2)fy(y|X=-2) = P(Y ≤ y | X = -2)P(Y ≤ y | X = 2) = P(X + N ≤ y | X = 2) = P(N ≤ y - X | X = 2) = ∫-∞y-2fN(x)dx∫-∞∞fN(x)dx=∫-∞y-2f(x−2)dx∫-∞∞f(x−2)dx=∫-∞y-22π​e−12(x−2)2dx∫-∞∞2π​e−12(x−2)2dxP(Y ≤ y | X = 2) = Φ(y-2)P(Y ≤ y | X = -2) = P(X + N ≤ y | X = -2) = P(N ≤ y + 2 | X = -2) = ∫-∞y+2fN(x)dx∫-∞∞fN(x)dx=∫-∞y+22π​e−12(x+2)2dx∫-∞∞2π​e−12(x+2)2dxP(Y ≤ y | X = -2) = Φ(y+2)where Φ(.) denotes the standard normal cumulative distribution function.

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The value of a binary transmission system that transmits a signal X of value -2[V] to send a "O" and 2[V] to send a "1" is called binary. A normal random variable is N that represents an additive noise in the received signal Y = X + N.

Hence, the conditional pdfs are given by:

\(f(y|X = 2) = \frac{1}{\sqrt{2\pi}}\text{exp}(-\frac{(y-2)^{2}}{2})$\)

\(f(y|X = -2) = \frac{1}{\sqrt{2\pi}}\text{exp}(-\frac{(y+2)^{2}}{2})$\)

(i) Fy(y|X = 2),

(ii) Fy(y|X = -2) are the conditional probability density functions (pdfs). The difference between "f" and "F" is that "f" represents the probability density function and "F" represents the cumulative distribution function. The conditional pdfs fy(y|X = 2),

fy(y|X = -2) can be obtained as follows:

fy(y|X = 2)

Y = 2 + N

If Y = y, then

N = y - 2.

Fy(y|X = 2) is the distribution function of N and it can be given as:

\(F(y|X = 2)=\int_{-\infty}^{y}\frac{1}{\sqrt{2\pi}}\text{exp}(-\frac{n^{2}}{2})dn\)

\(f(y|X = 2)=\frac{\partial F(y|X = 2)}{\partial y}=\frac{1}{\sqrt{2\pi}}\text{exp}(-\frac{(y-2)^{2}}{2})\end{align*}$\)

Similarly, fy(y|X = -2)

Y = -2 + N

If Y = y,

then N = y + 2.

Fy(y|X = -2) is the distribution function of N and it can be given as:

\(F(y|X = -2)=\int_{-\infty}^{y}\frac{1}{\sqrt{2\pi}}\text{exp}(-\frac{n^{2}}{2})dn\)

\(f(y|X = -2)=\frac{\partial F(y|X = -2)}{\partial y}=\frac{1}{\sqrt{2\pi}}\text{exp}(-\frac{(y+2)^{2}}{2})\end{align*}\)

Hence, the conditional pdfs are given by:

\(f(y|X = 2) = \frac{1}{\sqrt{2\pi}}\text{exp}(-\frac{(y-2)^{2}}{2})$\)

\(f(y|X = -2) = \frac{1}{\sqrt{2\pi}}\text{exp}(-\frac{(y+2)^{2}}{2})$\)

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The polar bear has a birth weight of 0.5 kilogram.

The linear equation is y = x + 0.4t

Given,

The weight gained by polar bear each week after it was born = 0.4 kg

The weight of polar bear after 3 weeks = 1.7 kilo grams

We have to write an linear equation to represent this ;

Here,

y be the weight of polar bear

x be the initial weight

t be the number of week.

So,

the equation be like;

y = x + 0.4t

Then,

1.7 = x + 0.4 x 3

x = 1.7 - 1.2 = 0.5

The polar bear has a birth weight of 0.5 kilogram.

The linear equation is y = x + 0.4t

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Answer:

2 quarts

Step-by-step explanation:

Since a stack of  wood 4 feet wide 8 feet long and 4 feet high is equal to 1 quart of wood., then dimensionally, we write it as 4 × 8 × 4.

We then need to find the number of quarts in a pie of 4 feet wide and 16 feet long and 4 feet high. We write it dimensionally as 4 × 16 × 4.

Since 1 quart = 4 × 8 × 4, then the number of quarts in 4 × 16 × 4 is

4 × 16 × 4 × 1 quart/4 × 8 × 4 = 2 × 1 quart = 2 quarts