a. The lengths of two sides of a triangle are 8 and 10 , and the measure of the angle between them is 40°. What is the approximate length of the third side?

Answer: fourth answer

Step-by-step explanation:

you cant factor it

Answer:

Maybe in June? Mainly the government needs money to send out the security checks

Step-by-step explanation:

Answer:

Not sure what the question is but if you're looking for who runs the most in a second I can give you that

Emily: 11 feet per second

Will: 9.66 feet per second

Stephanie: 13.27 feet per second

Liz: 8.98 feet per second

Based off this info, Stephanie runs the fastest per second

To find the largest set of un-average numbers whose elements are less than or equal to n, we can start with {1,3} and repeatedly add the largest possible element that satisfies the un-average condition. The resulting set is the largest set of un-average numbers whose elements are less than or equal to n.

Let S be a set of un-average numbers with elements less than or equal to n. For any two distinct elements a and b in S, their average (a+b)/2 must not be in S. This means that the elements of S must be at least 2 apart. Therefore, we can start with the set {1,3} and add elements to it as long as each new element is at least 2 greater than the previous one.

Let S' be the set obtained by starting with {1,3} and adding as many elements as possible using the above rule. Clearly, n must be greater than or equal to the largest element of S'. We can find S' by starting with {1,3} and repeatedly adding the largest possible element that satisfies the un-average condition:

{1,3}

{1,3,6}

{1,3,6,10}

{1,3,6,10,15}

{1,3,6,10,15,21}

{1,3,6,10,15,21,28}

...

Each new element in the sequence is obtained by adding the smallest possible integer that is at least 2 greater than the previous one and that does not form an average with any of the previous elements. We can see that the largest element in S' that is less than or equal to n is the largest element in the above sequence that is less than or equal to n.

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The maximum number of chairs that can be made will be the minimum of 12, 15, and 11. That exists, 11 chairs can be made, limited by the number of available legs.

The study of probabilities, which are determined by the ratio of favorable occurrences to probable cases, is known as probability.

The maximum number of chairs that can be made will be the minimum of the number of parts divided by the number of parts required for each chair, as calculated across the various types of parts required.

seats: 12 available, used 1 per chair: 12/1 = 12 chairs possible

backs: 15 available, used 1 per chair: 15/1 = 15 chairs possible

legs: 44 available, used 4 per chair: 44/4 = 11 chairs possible

The maximum number of chairs that can be made will be the minimum of 12, 15, and 11. That exists, 11 chairs can be made, limited by the number of available legs.

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Answer: 1

Step-by-step explanation:

Find (d + c)(3) The x value is 3 so you plug in 3 for the x's in the equation

d(x) = 2x − 4

d(3) = 2(3) - 4

d(3) = 2

c(x) = 2x − 7

c(3) = 2(3) - 7

c(3) = -1

Now you plug in the value of d and c into your original equation which is (d+c)(3)

(2 + (-1)) = 1

This means (d+c)(3) = 1

The total surface area painted is 644.16 square inches.

Let the radius of the cylindrical rod be r. The circumference of the base is given as 12π, which can be converted to the diameter as:

diameter = circumference / π = 12π / π = 12 inches.

So, the radius of the cylindrical rod is half of that. That is 6 inches.

The area of one base of the cylindrical rod can be calculated as π \(r^2\), which is:

π * \(6^2\) = 3.14 * 36 = 113.04 square inches.

The surface area of one-half of the cylindrical rod can be calculated by:

2 * π * r * l + 2 * π * \(r^2\), where l is the length of the rod.

Since the length of the rod is 4 inches, the surface area of one-half of the cylindrical rod can be calculated by:

2 * π * 6 * 4 + 2 * 113.04 = 96 + 226.08 = 322.08 square inches.

Given that two equally sized pieces are cut, the total surface area painted would be 2 * 322.08 = 644.16 square inches.

Therefore, the total surface area painted is 644.16 square inches.

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Answer:

10

Step-by-step explanation:

x x y

5x2

10

The linearly independent solution of the non-homogeneous equation is y = y-c + y-p, y = c1×(x²(-1/2)cos(x)) + c2×(x²(-1/2)sin(x)) + (8/35)×x²(3/2) + (2/35)×x²(-1/2) where c1 and c2 are arbitrary constants.

The associated homogeneous equation is: x²2y'' + xy' + (x²2 - 1/4)y = 0

The complementary solution can be found by assuming y has the form y-c = c1y1 + c2y2, where c1 and c2 are constants, and y1 and y2 are the given linearly independent solutions.

y-c = c1×(x²(-1/2)cos(x)) + c2×(x²(-1/2)sin(x))

Now, the particular solution, denoted as y-p, of the non-homogeneous equation.

y-p has the form:

y-p = Ax²(3/2) + Bx²(-1/2)

where A and B are constants to be determined.

The first and second derivatives of y-p:

y-p' = A×(3/2)x²(1/2) - (1/2)Bx²(-3/2)

y-p'' = A(3/4)×x²(-1/2) + (3/4)Bx²(-5/2)

Substituting these into the non-homogeneous equation:

x²2y_-p'' + xy-p' + (x²2 - 1/4)×y-p = x²(3/2)

x²2×(A×(3/4)x²(-1/2) + (3/4)Bx²(-5/2)) + x(A×(3/2)x²(1/2) - (1/2)Bx²(-3/2)) + (x^2 - 1/4)(Ax²(3/2) + Bx²(-1/2)) = x²(3/2)

Simplifying and collecting like terms:

(3A/4)x²(3/2) + (3B/4)x²-1/2) + (3A/2)x²(3/2) - (1/2)Bx²(3/2) + (A - (1/4))x²(5/2) + (B/4)x²(1/2) - (A/4)x²(-1/2) + Bx²(-3/2) = x²(3/2)

Matching the coefficients of like powers of x:

[(3A/4) + (3A/2) - (1/2)B]x²(3/2) + [(3B/4) + (B/4)]x²(-1/2) + [(A - (1/4))]x²(5/2) + [(-A/4) + B]x²(-1/2) + [B/4]x²(-3/2) = x²(3/2)

Equating the coefficients of x²(3/2) on both sides:

(3A/4) + (3A/2) - (1/2)B = 1

(9A/4) - (1/2)B = 1

Equating the coefficients of x²(-1/2) on both sides:

[(3B/4) + (B/4)] - (A/4) = 0

(4B/4) - (A/4) = 0

Simplifying the equations:

(9A - 2B) = 4

4B - A = 0

Solving these equations simultaneously ,A = 8/35 and B = 2/35.

Therefore, the particular solution is: y-p = (8/35)×x²(3/2) + (2/35)×x²(-1/2)

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Answer:x = 5.333333333

Step-by-step explanation:

Answer:

144

Step-by-step explanation:

Using the rule of radicals

\(\sqrt{a}\) × \(\sqrt{b}\) ⇔ \(\sqrt{ab}\)

Given

4\(\sqrt{2}\) × 6\(\sqrt{18}\)

= 4 × 6 × \(\sqrt{2}\) × \(\sqrt{18}\)

= 24 × \(\sqrt{36}\)

= 24 × 6

= 144

The answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.

In this scenario, P(Z ≤ b) represents the cumulative probability of a standard normal distribution up to the value of b. To find the corresponding value of b, we need to find the z-score that corresponds to a cumulative probability of 0.0311.

By looking up the z-table or using a statistical calculator, we can find that the z-score corresponding to a cumulative probability of 0.0311 is approximately -1.865.

Therefore, the answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.

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Answer:

y = 10x + 20

Step-by-step explanation:

The slope is rise over run.

It looks to be about:

10/1 = $10 per hour

And if we extend the line, the y-intercept will be around 20.

So, the equation for this line is:

y = 10x + 20

The total surface area of the given pyramid is 304 sq units.

A pyramid is three dimensional shape. A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex.

Every face of the pyramid is triangular  except the base. The base is square shaped. So we will use the formula of area of triangle to find the area of each face of the pyramid. And we will use the formula of area of square to find the base area of the pyramid.

The area of triangle is = (1/2)×base×height

The are of square = (side)²

Given that the length and breadth of base is = 8 units

So, the area of base is = 8²=64 sq units.

Also the height of the each triangular face is 15 units.

So, the area of each face is = (1/2)×8×15

=4×15

=60 sq units.

So, the total area of four triangular faces of the pyramid = 4×60

=240 sq units.

Hence, the surface area of the pyramid = Area of four traingular faces + Area of square base

=240+64

=304sq units

Thus , The required surface area of the pyramid is = 304 sq units

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I'm sure the answer is B if it's not B it's A trust

The constant of proportionality in terms of dollars per hour is A 40.

The constant of proportionality is used to illustrate the constant relationship between the variables.

In this case, a 3 hour lesson costs $120.00 and the cost of a lesson is proportional to the duration, in hours, of the lesson.

The constant will be the division of the values. This will be:

= $120 / 3

= $40

The correct option is A

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Number of students should be sampled to be within 0.5 drink of population mean with 95% probability is 617 students.

To determine the sample size required to estimate the population mean with a given level of precision, we can use the formula for the margin of error

Margin of error = Z × (standard deviation / sqrt(sample size))

where Z is the critical value of the standard normal distribution corresponding to the desired level of confidence. For a 95% confidence level, Z is 1.96.

We want the margin of error to be no more than 0.5 drinks, so we can set up the equation

0.5 = 1.96 × (6.3 / sqrt(sample size))

Solving for the sample size, we get

sqrt(sample size) = 1.96 × 6.3 / 0.5

sqrt(sample size) = 24.82

sample size = (24.82)^2

sample size = 617

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Answer:

D is false

A is true

B is true

C is true

Step-by-step explanation:

Answer:

I this a multiple choice answer? I found that A B and C are true.

I know this because the article Newtons laws of Universal Gravitation states that "Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces. So as two objects are separated from each other, the force of gravitational attraction between them also decreases." This makes C the best answer

Answer: 11.4

Step-by-step explanation:

You would use the distance formula.

(1−8)^2+(−2−7)^2

=(−7)^2+(−2−7)^2

=49+(−2−7)^2

=49+(−9)^2

=49+81

=130

= 11.4

​

Main Answer:The linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

Supporting Question and Answer:

How can we express a vector as a linear combination of  vectors using a system of equations?

To express a vector as a linear combination of  vectors using a system of equations, we need to find the coefficients that multiply each given vector to obtain the desired vector. This can be done by setting up a system of equations, where each equation corresponds to the components of the vectors involved.

Body of the Solution:

(a) To show that the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3, we need to demonstrate two conditions: orthogonality and linear independence.

u1 · u2 = (2)(-3) + (0)(0) + (3)(2) = -6 + 0 + 6 = 0

u1 · u3 = (2)(0) + (0)(7) + (3)(0) = 0 + 0 + 0 = 0

u2 · u3 = (-3)(0) + (0)(7) + (2)(0) = 0 + 0 + 0 = 0

Since the dot product of every pair of vectors is zero, they are orthogonal.

   2.Linear Independence: We need to show that the vectors u1, u2, and u3 are linearly independent, meaning that no vector can be written as a linear combination of the other vectors.

We can determine linear independence by forming a matrix with the vectors as its columns and performing row operations to check if the matrix can be reduced to the identity matrix.

[A | I] = [u1 | u2 | u3 | I] =

[2 -3 0 | 1 0 0]

[0 0 7 | 0 1 0]

[3 2 0 | 0 0 1]

Performing row operations:

R3 - (3/2)R1 -> R3

R1 <-> R2

[1 0 0 | -3/2 1 0]

[0 1 0 | 0 1 0]

[0 0 7 | 0 0 1]

Since we can obtain the identity matrix on the left side, the vectors u1, u2, and u3 are linearly independent.

Therefore, the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3.

(b) To write v = (1, 2, 3) as a linear combination of u1, u2, and u3, we need to find the coefficients x, y, and z such that:

v = xu1 + yu2 + z*u3

Substituting the given vectors and coefficients:

(1, 2, 3) = x(2, 0, 3) + y(-3, 0, 2) + z(0, 7, 0)

Simplifying the equation component-wise:

1 = 2x - 3y

2 = 7y

3 = 3x + 2y

From the second equation, we can solve for y:

y = 2/7

Substituting y into the first equation:

1 = 2x - 3(2/7)

1 = 2x - 6/7

7 = 14x - 6

14x = 13

x = 13/14

Substituting the found values of x and y into the third equation

3 = 3(13/14) + 2(2/7)

3 = 39/14 + 4/7

3 = 39/14 + 8/14

3 = 47/14

Therefore, we have determined the values of x, y, and z as follows:

x = 13/14

y = 2/7

z = 47/14

Thus, we can write the vector v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) as:

v = (13/14)u1 + (2/7)u2 + (47/14)u3

Therefore, v can be expressed as a linear combination of the given vectors.

Final Answer:Therefore,the linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

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The linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

To express a vector as a linear combination of  vectors using a system of equations, we need to find the coefficients that multiply each given vector to obtain the desired vector. This can be done by setting up a system of equations, where each equation corresponds to the components of the vectors involved.

Body of the Solution:

(a) To show that the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3, we need to demonstrate two conditions: orthogonality and linear independence.

Orthogonality: We need to show that each pair of vectors is orthogonal, meaning their dot product is zero.

u1 · u2 = (2)(-3) + (0)(0) + (3)(2) = -6 + 0 + 6 = 0

u1 · u3 = (2)(0) + (0)(7) + (3)(0) = 0 + 0 + 0 = 0

u2 · u3 = (-3)(0) + (0)(7) + (2)(0) = 0 + 0 + 0 = 0

Since the dot product of every pair of vectors is zero, they are orthogonal.

  2.Linear Independence: We need to show that the vectors u1, u2, and u3 are linearly independent, meaning that no vector can be written as a linear combination of the other vectors.

We can determine linear independence by forming a matrix with the vectors as its columns and performing row operations to check if the matrix can be reduced to the identity matrix.

[A | I] = [u1 | u2 | u3 | I] =

[2 -3 0 | 1 0 0]

[0 0 7 | 0 1 0]

[3 2 0 | 0 0 1]

Performing row operations:

R3 - (3/2)R1 -> R3

R1 <-> R2

[1 0 0 | -3/2 1 0]

[0 1 0 | 0 1 0]

[0 0 7 | 0 0 1]

Since we can obtain the identity matrix on the left side, the vectors u1, u2, and u3 are linearly independent.

Therefore, the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3.

(b) To write v = (1, 2, 3) as a linear combination of u1, u2, and u3, we need to find the coefficients x, y, and z such that:

v = xu1 + yu2 + z*u3

Substituting the given vectors and coefficients:

(1, 2, 3) = x(2, 0, 3) + y(-3, 0, 2) + z(0, 7, 0)

Simplifying the equation component-wise:

1 = 2x - 3y

2 = 7y

3 = 3x + 2y

From the second equation, we can solve for y:

y = 2/7

Substituting y into the first equation:

1 = 2x - 3(2/7)

1 = 2x - 6/7

7 = 14x - 6

14x = 13

x = 13/14

Substituting the found values of x and y into the third equation

3 = 3(13/14) + 2(2/7)

3 = 39/14 + 4/7

3 = 39/14 + 8/14

3 = 47/14

Therefore, we have determined the values of x, y, and z as follows:

x = 13/14

y = 2/7

z = 47/14

Thus, we can write the vector v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) as:

v = (13/14)u1 + (2/7)u2 + (47/14)u3

Therefore, v can be expressed as a linear combination of the given vectors.

Therefore, the linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

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Answer:

Any combination of angles the sum of which = 180 degrees.

answer is 2 acute 1 right

The solution of the system of equations is (2, 1).

Here we have the system of equations:

y = 2x - 3

y = -x + 3

To solve the system of equations graphically, we need to graph both of these lines in the same coordinate axis and then find the point where the lines intersect.

That point will be the solution of the system.

On the image at the end you can see the graph of the system of equations, there we can see that the solution is (2, 1).

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Total number of students that likes both dog and Cat = 194 students.

Total number of students = 335 students

Therefore,

percentage = 58%

Answer:

Genevieve's garden is 12 square feet and thus, has a smaller area than Esmeralda's

Step-by-step explanation:

Given:

Esmeralda's garden = 25 square feet

Genevieve's garden = 4 square yards

Convert Genevieve's units (yards) to feet

Yards to feet

1 yard = 3 feet

4 yards = 4 * 3 feet

4 yards = 12 feet

Genevieve's garden = 12 square feet

Genevieve's garden is 12 square feet and thus, has a smaller area than Esmeralda's

Answer:

The answer is: Genevieve's garden is 36 square feet, and thus, has a larger area than Esmeralda's

Step-by-step explanation:

The calculated value of x in the pentagon is 121

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

The pentagon (see attachment)

The sum of angles in a pentagon is

Sum = 180 * (n - 2)

Where

n = 5

So, we have

Sum = 180 * (5 - 2)

Evaluate

Sum =  540

Algebraically, we have

x + 87 + 92 + 105 + 135 = 540

So, we have

x + 419 = 540

Subtract 419 from both sides

x = 121

Hence, the value of x is 121

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In a graph, if there are exactly two vertices with an odd degree (an odd number of edges connected to them), any Eulerian trail (a path that visits every edge exactly once) must start at one of these vertices and end at the other. This property holds true for all graphs that meet the given condition.

An Eulerian trail is a path in a graph that visits each edge exactly once. In a connected graph, all vertices must have an even degree for an Eulerian trail to exist. However, if there are exactly two vertices with an odd degree, an Eulerian trail can still be formed, but it must start at one of the odd-degree vertices and end at the other.
The reason behind this is that every time we enter and leave a vertex, the degree of that vertex changes by two. Starting at an odd-degree vertex ensures that when we reach the end of the trail, the other odd-degree vertex is the only remaining vertex with an odd degree. By connecting the last edge to that vertex, we balance the degrees of all vertices, satisfying the condition for an Eulerian trail.
Therefore, if a graph has exactly two vertices of odd degree, it is guaranteed that all Eulerian trails in that graph will start at one of the odd-degree vertices and end at the other.

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