A barge is carrying 342,000 pounds of concrete blocks. How much weight is this in tons?

Only one of the following functions is a solution of the differential equation y′′−9y′+18y=0.

The second-order homogeneous linear differential equation is given as:y'' - 9y' + 18y = 0This differential equation is a linear homogeneous equation. We will have two roots of the characteristic equation: r1 = 3, r2 = 6So, the general solution to the differential equation is given as:y = c1e3x + c2e6xwhere c1 and c2 are arbitrary constants.a. y(x) = e6x is a solution because it is a part of the general solution of the differential equation.y(x) = e−x, y(x) = 0, y(x) = 6x, y(x) = 3x, y(x) = ex are not solutions because they don't satisfy the differential equation. Hence, the correct options are:a. y(x) = e6xTherefore, only one of the following functions is a solution of the differential equation y′′−9y′+18y=0.

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2(x+4)

hope this helps!!!

Answer:

Step-by-step explanation:

Given that

Find the surface area of the cylinder!

Equation =

(2 × 3.14 × 10) × (10 + 7) =

62.8 × 17 ≈

The surface area of the cylinder ≈ 1067.6 square metres

_________________

#Indonesian - kexcvi

Answer:

Use this formula to calculate for the surface area of cylinder.

Step-by-step explanation:

A=2π r h+2 π r^2.

use r = 10 m and h = 7 m

2 (3.14) (10) 7 + 2 (3.14) 10 ^2. = 439.6 + 628 = 1067.6

round to the nearest hundredths = 1068

The coordinates of points A and B, we cannot provide the exact values of AC and CB or verify the required ratio. Please provide the coordinates of points A and B, and we can calculate and verify the distances accordingly.

To verify that point C divides the line AB in the required ratio, we can calculate the distances AC and CB using the distance formula.

The distance formula is given by:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Let's assume the coordinates of point A are (x1, y1) and the coordinates of point B are (x2, y2). The coordinates of point C are given as (4, -2).

To calculate the distance AC, we substitute the coordinates of points A and C into the distance formula:

AC = √((x2 - x1)^2 + (y2 - y1)^2)

= √((4 - x1)^2 + (-2 - y1)^2)

Similarly, to calculate the distance CB, we substitute the coordinates of points C and B into the distance formula:

CB = √((x2 - x1)^2 + (y2 - y1)^2)

= √((x2 - 4)^2 + (y2 + 2)^2)

By calculating AC and CB, we can determine if they are in the required ratio.

However, without knowing the specific coordinates of points A and B, we cannot provide the exact values of AC and CB or verify the required ratio. Please provide the coordinates of points A and B, and we can calculate and verify the distances accordingly.

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The next time all three lights will flash at the same time will be in 210 seconds, or 3 minutes and 30 seconds.

To find the time at which all three lights will flash at the same time, we need to find the LCM (Least Common Multiple) of the given times.

Prime factorizing each time, we get:

6 = 2 x 3

15 = 3 x 5

21 = 3 x 7

To find the LCM, we take the highest power of each prime factor that appears in any of the numbers:

2 x 3 x 5 x 7 = 210

Therefore, the next time all three lights will flash at the same time will be in 210 seconds, or 3 minutes and 30 seconds.

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The volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

The given vectors are:

A = [-4, 3, 2] cm, B = [2,1,3] cm and C= [1, 1, 4] cm

In order to calculate the volume of parallelepiped, we will use vector triple product equation:

Volume = A . (BXC)|, where BXC represents the cross product of vectors B and C.

Step-by-step solution:

We have, A = [-4, 3, 2] cm

B = [2,1,3] cm

C = [1, 1, 4] cm

Now, let's find BXC, using the cross product of vectors B and C.

BXC = | i    j     k|                    2      1     3                            1      1     4        | i    j     k |  = -i + 5j - 3k

Where, i, j, and k are the unit vectors along the x, y, and z-axes, respectively.

The volume of the parallelepiped is given by:

Volume = A . (BXC)|

Therefore, we have: Volume = A . (BXC)

\(Volume = [-4, 3, 2] . (-1, 5, -3)\\Volume = (-4 \times -1) + (3 \times 5) + (2 \times -3)\\Volume = 4 + 15 - 6\\Volume = 13\)

Therefore, the volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

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The United States has the comparative advantage in producing footballs, while Canada has the absolute advantage in producing lumber. If the two countries specialize and trade, the United States produces 1000 footballs and Canada produces 8 tons of lumber.

(a)US Production Possibility Frontier:

Football (1000)  |  0  |  200  |  400  |  600  |  800  |  1000

Lumber (10)     | 10  |  8   |   6   |   4   |   2   |    0

Canadian Production Possibility Frontier:

Football (400)  |  0  |  100  |  200  |  300  |  400

Lumber (8)      | 8   |  7   |   6   |   5   |   4

(b) In autarky, if the United States wants to consume 500 footballs, it can consume at most 4 tons of lumber. This point is labeled A in the diagram. Similarly, if Canada wants to consume 1 ton of lumber, it can consume at most 300 footballs. This point is labeled C in the diagram.

(c) Canada has the absolute advantage in lumber production.

(d) The United States has the comparative advantage in lumber production.

(e) If each country specializes in the good in which it has the comparative advantage and there is trade, the United States produces 1000 footballs and Canada produces 8 tons of lumber.

(f) Yes, it is possible for the United States to consume 500 footballs and 7 tons of lumber. This point is labeled B in the diagram. It is not possible for Canada to consume 500 footballs and 1 ton of lumber at the same time. This point is labeled D in the diagram.

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Answer:

Source:

Answer:

4 spaces to the right

Step-by-step explanation:

hope this helps!

Answer:

6x + 1

Step-by-step explanation:

Add up like terms

4x + 2x + 1
= 6x + 1

Answer: 90

Step-by-step explanation: mAB =180° as it is a straight angle

x=180-120= 60°

so,The number should be less than 180 but more than 60, be divisible by 30 and be a 2 digit no.

nos. divisible by 30 between 60 and 180 are 90,120 and 150

But there is only one of these that are 2 digit i. e. 90

Therefore, the no. is 90

PLEASE RATE 5 STARS AND VOTE AS BRAINLIEST:) (^o^)(^o^)(^o^)(^o^)(^o^)(^o^)(^o^)(^o^)(^o^)(^o^)(^o^)(^o^)

We can use the transformation y = (x - a) / (b - a) to generate a random variable y that is linear in x and uniformly distributed over (0, 1).

To find a random variable y that is linear in x and uniformly distributed over (0, 1), we can use the following transformation:
y = (x - a) / (b - a)
This transformation maps the interval (a, b) to the interval (0, 1) and ensures that the distribution of y is uniform.
To see why this is the case, we can use the formula for the probability density function (pdf) of a uniform distribution:
f(x) = 1 / (b - a)
This means that the probability of x being between any two values c and d is proportional to the length of the interval (d - c) and is given by:
P(c < x < d) = (d - c) / (b - a)
Now, let's find the pdf of y using the transformation above:
F(y) = P(y < Y) = P((x - a) / (b - a) < y) = P(x < (b - a) * y + a)
We can differentiate this to get the pdf of y:
f(y) = dF(y) / dy = f(x) / (b - a) = 1 / (b - a)
This shows that the distribution of y is indeed uniform over (0, 1).

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If $10 can purchase 4 bunches of purple grapes, then how much can 25 purchase

Mathematically,

$10 is equivalent to 4 bunches

$25 is equivalent to x bunches since we don't know the number of bunches $25 can buy

10 dollars = 4 bunches

25 dollars = x bunches

The proportion is given below by introducing cross multiplication to the above expression

Given:

The equation is:

\(3x-2y=18\)

To find:

The slope intercept form of the given equation.

Solution:

Slope intercept form of a line is:

\(y=mx+b\)

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

We have,

\(3x-2y=18\)

It is not in the slope intercept form.

We need to isolate variable y to get the slope intercept form.

The given equation can be rewritten as:

\(-2y=-3x+18\)

\(y=\dfrac{-3x+18}{-2}\)

\(y=\dfrac{-3x}{-2}+\dfrac{18}{-2}\)

\(y=\dfrac{3}{2}x-9\)

Therefore, the slope intercept form of the given equation is \(y=\dfrac{3}{2}x-9\).

(a) To find the values of z for which the matrix does not have an inverse, we can set up the determinant of the matrix and solve for z when the determinant is equal to zero.

The given matrix is:

|x3  x|

|9   1|

The determinant of a 2x2 matrix can be found using the formula ad - bc. Applying this formula to the given matrix, we have:

Det = (x3)(1) - (9)(x) = x3 - 9x

For the matrix to have an inverse, the determinant must be non-zero. Therefore, we solve the equation x3 - 9x = 0:

x(x2 - 9) = 0

This equation has two solutions: x = 0 and x2 - 9 = 0. Solving x2 - 9 = 0, we find x = ±3.

So, the values of x for which the matrix has no inverse are x = 0 and x = ±3.

(b) (i) To find the size of the acute angle between the vectors (3,0) and (5,5), we can use the dot product formula:

u · v = |u| |v| cos θ

where u and v are the given vectors, |u| and |v| are their magnitudes, and θ is the angle between them.

Calculating the dot product:

(3,0) · (5,5) = 3(5) + 0(5) = 15

The magnitudes of the vectors are:

|u| = sqrt(3^2 + 0^2) = 3

|v| = sqrt(5^2 + 5^2) = 5 sqrt(2)

Substituting these values into the dot product formula:

15 = 3(5 sqrt(2)) cos θ

Simplifying:

cos θ = 15 / (3(5 sqrt(2))) = 1 / (sqrt(2))

To find the acute angle θ, we take the inverse cosine of 1 / (sqrt(2)):

θ = arccos(1 / (sqrt(2)))

(ii) If the vector (-k, 3) is orthogonal to (5,5), it means their dot product is zero:

(-k, 3) · (5,5) = (-k)(5) + 3(5) = -5k + 15 = 0

Solving for k:

-5k = -15

k = 3

So, the value of k is 3.

(c) Let J be the linear transformation from R2 to R2 that reflects points in the horizontal axis and then scales them by a factor of 2. The matrix of J can be found by multiplying the reflection matrix and the scaling matrix.

The reflection matrix in the horizontal axis is:

|1  0|

|0 -1|

The scaling matrix by a factor of 2 is:

|2  0|

|0  2|

Multiplying these two matrices:

J = |1  0| * |2  0| = |2  0|

   |0 -1|   |0  2|   |0 -2|

So, the matrix of J is:

|2  0|

|0 -2|

Therefore, y = 2 and z = -2.

(d) The volume of a parallelepiped can be found by taking the dot product of two adjacent sides and then taking the absolute value of the result.

The adjacent sides of the parallelepiped P are (0,3,0)

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The fraction of the money that Sam receives is \(\frac{7}{16}\) of the money they share.

To solve this problem, we need to first understand what the ratio 7:9 means. It means that for every 7 parts that Sam receives, Adam receives 9 parts.
Let's say the sum of money they are sharing is $100. To find out how much Sam receives, we need to divide the total amount into 16 parts (7 + 9).
Each part would then be worth $6.25 ($100 ÷ 16).
To find out how much Sam receives, we need to multiply the number of parts he receives by the value of each part.
Sam receives 7 parts out of 16, so his share would be 7 x $6.25 = $43.75.
To express this as a fraction, we can put Sam's share over the total amount:
\(\frac{43.75}{100}\)
We can simplify this fraction by dividing both the numerator and denominator by 25:
\(\frac{1.75}{4}\)
Therefore, the fraction of the money that Sam receives is \(\frac{1.75}{4}\) or \(\frac{7}{16}\).
In summary, Sam receives \(\frac{7}{16}\) of the money they share, which is equivalent to $43.75 if the total amount they are sharing is $100.

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The temperature inside the building will reach 14∘C about 1 hour after noon.

The given information is: the time constant for the building is 3hr and the temperature inside the building will reach 14∘C about hr after noon. A first-order differential equation is used to solve this problem, and the formula for solving the first-order differential equation is given by; dy/dt + y/τ = k, where, y is the temperature inside the building, τ is the time constant for the building, and k is the constant value. dT/dt + T/3 = k ----(1)Given, T = 14 ∘C, τ = 3 hrs Therefore, substituting the given values in the equation (1),14/3 = k. Substitute k in the equation (1),dT/dt + T/3 = 14/3Multiplying by 3 on both sides we get,3(dT/dt) + T = 14Taking Laplace transform,3L(dT/dt) + L(T) = 14L(Take note of initial conditions, and L(0) = T0 )Since the initial temperature is not given, we assume it to be zero. Therefore, L(0) = T0 = 0, and solving for L(T),L(T) = 14/ (s + 3) Applying the inverse Laplace transformation, T = 14(1 - e^(-3t)) Therefore, after noon hour, i.e., after 1 pm, the temperature inside the building will reach 14 ∘C. This can be confirmed by putting             t = 1 in the equation above which yields T = 14(1 - e^-3) ≈ 13.4 C.

The temperature inside the building will reach 14∘C about 1 hour after noon.

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Answer: 300 tomatoes.

Step-by-step explanation: 150/0.50 is 300, meaning John and Jamie must have sold 300 tomatoes to get a profit of $150. (However, practically speaking, that's impossible, nobody can sell 300 tomatoes, and if you do, it takes months, and that's not worth $150, trust me.)

Answer:

It would end up being 300

Answer:

positive

Step-by-step explanation:

the reasoning behind this is because when you do powers you multiply the number by itself. If you multiply -2x-2 then it turns into a positive number and will stay a positve number

have a great day :D

The two triangles are similar If they have the same shape, but their sizes are different.

Similar triangles are triangles that have the same shape, but their sizes may be same or different. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. The similarity of triangles are denoted by ‘~’ symbol

AA (or AAA) or Angle-Angle Similarity

If any two angles of a triangle are equal to any two angles of another triangle, then those two triangles are similar to each other.

SAS or Side-Angle-Side Similarity

If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed between those two sides in both the triangle are equal, then two triangles are said to be similar.

SSS or Side-Side-Side Similarity

If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.

Therefore, two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

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To test whether there is evidence of a linear relationship between the given data (x and y values), we can perform a hypothesis test.

Step 1: State the null hypothesis (H0) and the alternative hypothesis (H1).
H0: There is no linear relationship between x and y (i.e., the correlation coefficient, r, is equal to 0)
H1: There is a linear relationship between x and y (i.e., the correlation coefficient, r, is not equal to 0)
Step 2: Calculate the correlation coefficient, r, using the given data. You can do this using a statistical calculator or software.
Step 3: Determine the critical value for the correlation coefficient at a chosen significance level (e.g., 0.05).
Step 4: Compare the calculated correlation coefficient, r, to the critical value. If |r| is greater than the critical value, reject the null hypothesis (H0) in favor of the alternative hypothesis (H1), indicating evidence of a linear relationship. If |r| is less than or equal to the critical value, fail to reject the null hypothesis (H0), suggesting there is not enough evidence to support a linear relationship.
By following these steps, you can test the hypothesis and determine if there is evidence of a linear relationship between the given data points.

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Based on the given data, we can determine that there are 75 students in the class.

Let's use the principle of inclusion-exclusion to calculate the total number of students in the class.

Total number of students = Number of chess players + Number of Go players + Number of backgammon players - (Number of chess and Go players + Number of chess and backgammon players + Number of Go and backgammon players) + Number of students playing all three games

Using the given data:

Number of chess players = 50

Number of Go players = 40

Number of backgammon players = 35

Number of chess and Go players = 20

Number of chess and backgammon players = 15

Number of Go and backgammon players = 10

Number of students playing all three games = 5

Substituting these values into the equation:

Total number of students = 50 + 40 + 35 - (20 + 15 + 10) + 5 = 75

Therefore, there are 75 students in the class.

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Answer:

x=2

Step-by-step explanation:

Add 4 to both sides:

-2=-4+x​

-2+4=-4+4+x​

2=x

Answer:

\(x = 2\)

Step-by-step explanation:

First we must add 4 to both sides.

\(-2 = -4 + x\)

+4      +4

-4 + 4 = 0

-2 +4 = 2

Isolating a variable means that it is alone on its side of the eqation.

\(2 = x\)

x is now isolated and we also have the solution for it.

\(x = 2\)

 B = | 1 0 0 |
      | 0 1 0 |
      | 1 1 2 |

To construct a matrix whose column space contains vectors [1, 0, 1] and [0, 1, 1], and whose nullspace contains the vector [2, 1, 2], follow these steps:

1. Form the column space by arranging the given vectors as columns of the matrix A:
  A = | 1 0 |
      | 0 1 |
      | 1 1 |

2. Determine a third column vector (C) that, when added to A, will create a matrix that has the given nullspace vector. To do this, use the equation Ax = 0, where x is the nullspace vector [2, 1, 2]. Multiply the matrix A with the nullspace vector to find the third column vector:

  A * x = | 1 0 | * |2| = |2|
          | 0 1 |   |1|   |1|
          | 1 1 |   |2|   |4|

3. Subtract the nullspace vector from the product obtained in step 2 to get the third column vector (C):

  C = Ax - x = | 2 - 2 | = | 0 |
               | 1 - 1 |   | 0 |
               | 4 - 2 |   | 2 |

4. Combine the matrix A with the third column vector C to form the final matrix B:

  B = | 1 0 0 |
      | 0 1 0 |
      | 1 1 2 |

The matrix B has the required column space containing [1, 0, 1] and [0, 1, 1] and a nullspace containing [2, 1, 2].

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Answer:

\(f(g(1))=11\)

Step-by-step explanation:

So we have the two functions:

\(f(x)=2x+7\text{ and } g(x)=-3x+5\)

And we want to find f(g(1)).

So, let's find g(1) first:

\(g(x)=-3x+5\)

Substitute 1 for x:

\(g(1)=-3(1)+5\)

Simplify:

\(g(1)=-3+5\)

Add:

\(g(1)=2\)

So:

\(f(g(1))=f(2)\)

Now, substitute 2 for x in f(x):

\(f(x)=2x+7\\f(2)=2(2)+7\)

Multiply:

\(f(2)=4+7\)

Add:

\(f(2)=11\)

So:

\(f(g(1))=11\)

Answer:

40/1 you'd drive 40 miles an hour

It is TRUE that If you want to calculate the total magnification, take the power of the objective (4X, 10X, 40x) and multiply by the power of the eyepiece, usually 10X.

If you want to get the total magnification of a microscope, you need to multiply the magnification of the objective lens by the magnification of the eyepiece lens. The objective lens typically has a magnification of 4X, 10X, or 40X, and the eyepiece lens usually has a magnification of 10X. So, for example, if you are using a 10X objective lens and a 10X eyepiece lens, the total magnification would be 10 × 10 = 100X.

On the other hand, these numbers may be the total magnification for a lower powered stereomicroscope. 10X and 40X are achievable with 10X eyepieces and 1X or 4X objective lenses. Or it can be a zoom stereomicroscope with zoom set to 1X and 4X and 10X eyepieces. To get a total of 4X, you can use the 0.8X zoom setting (which is common) plus the 5X eyepiece. Or you can use the 0.5x auxiliary lens, 0.8x zoom and 10x eyepieces.

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Complete Question:

True, or False

To get the total magnification take the power of the objective (4X, 10X, 40x) and multiply by the power of the eyepiece, usually 10X.

Tensor y will have the shape (4, 1, width, 64), where width is determined by the shape of the input tensor.

Based on the given dimensions of the tensors x and y, we can determine the shape of the tensor y. Tensor x has a shape of (16, 3, 128, 96), which means it has 16 channels, 3 height pixels, 128 width pixels, and 96 depth pixels. Tensor y has a shape of (4, 1, -1, 64), which means it has 4 channels, 1 height pixel, an undetermined width, and 64 depth pixels.

The -1 in the width dimension of tensor y represents a placeholder for the unknown size of that dimension. This is a common technique used in deep learning frameworks to allow for flexibility in the size of input data. The value of the width dimension will depend on the shape of the input tensor to which tensor y is being applied.

Therefore, the shape of tensor y will be (4, 1, width, 64) where width is determined by the shape of the input tensor to which it is applied.

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