Lemma 1 Let g = (V, E, w) be a weighted, directed graph with designated root r e V. Let E' = {me(u): u E (V \ {r})}. Then, either T = (V, E') is an RDMST of g rooted at r or T contains a cycle. Lemma 2 Let g = (V, E, w) be a weighted, directed graph with designated root reV. Consider the weight function w': E → R+ defined as follows for each edge e = (u, v): w'le) = w(e) - m(u). Then, T = (V, E') is an RDMST of g = (V, E, W) rooted at r if and only if T is an RDMST of g = (V, E, w') rooted at r.

Answer: 60 mph

Step-by-step explanation:

Given

The red car left at 9 am and arrives at 1 pm

time taken by the red car [tex]t_a=4\ hr[/tex]

time taken by the blue car [tex]t_b=3\ hr[/tex]

Assume the speed of the red car is v

So, the speed of the blue car is v+15

distance traveled by them is the same

[tex]\Rightarrow v\times 4=(v+15)\times 3\\\Rightarrow 4v=3v+45\\\Rightarrow v=45\ mph[/tex]

Thus, the speed of the blue car is [tex]45+15=60\ mph[/tex]

The spring constant k is approximately 35 N/m.

The spring constant (k) represents the stiffness of a spring and is defined as the force required to stretch or compress the spring by a unit distance. In this case, we are given that the spring is stretched by a force of 13.5 N, resulting in a displacement of 0.5 meters.

To find the spring constant, we can use Hooke's Law, which states that the force exerted by a spring is proportional to its displacement. Mathematically, this can be expressed as F = kx, where F is the force, k is the spring constant, and x is the displacement.

Using the given values, we have:

13.5 N = k * 0.5 m

Solving for k, we find:

k ≈ 35 N/m

Therefore, the spring constant for this system is approximately 35 N/m.

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The simplified expression is -48r² + 40r. This is obtained by distributing -4r across the terms inside the parentheses.

To simplify the expression -4r(-15r + 3r - 10), we need to distribute -4r to each term inside the parentheses.
-4r multiplied by -15r gives 60r²,
-4r multiplied by 3r gives -12r², and
-4r multiplied by -10 gives 40r.

Combining these terms, we have 60r² - 12r² + 40r. Simplifying further, we get -48r² + 40r.

Thus, the simplified expression is -48r² + 40r. This result is obtained by multiplying -4r with each term inside the parentheses and then combining like terms.

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It takes approximately 14 minutes for the thermometer to reach a temperature of 58°F in the cold storage room. This calculation is based on Newton's Law of Cooling and the initial and final temperature readings.

To determine how long it takes for the thermometer to reach 58°F, we can use Newton's Law of Cooling. Let's plug in the given values into the equation and solve for the time (t):

88 = 37 + (96 - 37)e^(k * 5)

Simplifying the equation, we have:

51 = 59e^(5k)

Taking the natural logarithm of both sides:

ln(51/59) = 5k

Solving for k, we find:

k ≈ -0.0436

Now, we can use this value of k to find the time (t) when the thermometer reaches 58°F:

58 = 37 + (96 - 37)e^(-0.0436 * t)

Simplifying further, we have:

21 = 59e^(-0.0436 * t)

Taking the natural logarithm again:

ln(21/59) = -0.0436 * t

Solving for t, we find:

t ≈ 13.58

Rounding to the nearest whole minute, it takes approximately 14 minutes for the thermometer to reach 58°F.

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Answer:

The average is 5.41666667 degrees.

Step-by-step explanation:

Answer:

62.5%

Step-by-step explanation:

Answer:

62.5%

Explanation:

Divide 100 by 8 to get 12.5

Multiply 12.5 by 5

Equals 62.5

Answer:

Hope this helps :)

you will find every answer in the photo I sent

Answer:

Well since the question ask for what in the green box, its 193

193 goes in the green box

If you solve everything it would be 13.89 (rounded to the nearest hundredths)

Step-by-step explanation:

So missing side of a right triangle, you can use the Pythagorean Theroum which is a^2+b^2=c^2

In this case we have the two legs which are a and b, we’re trying to find hypotnuse, “c”.

7^2+12^2=c^2

49+144=c^2

193= c^2

You basically do √193

which is the answer needed for this situation

Final answer: is 193 goes into the green box

Answer: what do you need help with??

Step-by-step explanation:

The required answer is  the mass of the 2D plate is 3.97 kg, the moment of the 2D plate about the y-axis is 15.815 kg. m, and the a-coordinate of the center of mass of the 2D plate is 3.98 m.

Explanation:-

The given equation of the 2D shape is y = 0.3z between 0 and 2.3.  to find the center of mass of the 2D shape bounded by these lines. We are also given that the density is uniform with the value: 2.3 kg/m².Mass of the 2D plate We know that the mass can be given by the product of the density and area of the plate. Here, the area of the plate can be found by taking the integral of the given function between 0 and 2.3:

Therefore, the mass of the 2D plate is given as: Mass = Density × Area . Mass = 2.3 kg/m² × 1.725 m²Mass = 3.9735 kg

.Moment of the 2D plate about y-axis .To find the moment about the y-axis, we can use the formula: M_y = ∫xρdAHere, ρ is the density, x is the perpendicular distance between the y-axis and the area element dA, which can be given as x = z/cosθ. Here, θ is the angle between the normal to the plate and the y-axis. Since z = y/0.3, x can be written as x = 10/3 y. Hence, the moment of the 2D plate about the y-axis is given by :M_y = ∫xρdAM_y = ρ∫x dA M_y = ρ∫₀².³∫₀¹⁰/³zdzdyM_y = 2.3 × (1/3) × (2.3)³M_y = 15.815 kg.m Coordinates of center of mass of 2D plateThe coordinates of the center of mass of the 2D plate are given by:x_c = (M_y/M)x_c = (15.815 kg.m/3.9735 kg)x_c = 3.98 m.

Thus, the mass of the 2D plate is 3.97 kg, the moment of the 2D plate about the y-axis is 15.815 kg. m, and the a-coordinate of the center of mass of the 2D plate is 3.98 m.

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Answer: The GCF of the terms of [tex]3x^4-9x^2-12x[/tex] is [tex]3x[/tex].

Step-by-step explanation:

We need to find:  GCF(Greatest common factor) of the terms of [tex]3x^4-9x^2-12x[/tex].

The greatest common factor(GCF) is the greatest factor that divides two expressions.

Here,

[tex]3x^4=3\times x \times x \times x \times x \\9x^2=3\times 3 \times x \times x\\12x=3\times 2 \times 2 \times x[/tex]

The greatest common factor of [tex]3x^4-9x^2-12x[/tex] = [tex]3x[/tex]

Hence, the GCF of the terms of [tex]3x^4-9x^2-12x[/tex] is [tex]3x[/tex].

The annual growth rate under the exponential model is approximately 0.17 or 17%.

To calculate the annual growth rate under the exponential model, we can use the formula:

Annual Growth Rate = (Final Value / Initial Value) ^ (1 / Number of Years) - 1

In this case, the initial value is 2,535,225 complaints of domestic violence as of December 31, 2017, and the final value is 2,956,300 complaints as of December 31, 2019. The number of years is 2.

Plugging in the values:

Annual Growth Rate = (2,956,300 / 2,535,225) ^ (1 / 2) - 1

= 1.1654 - 1

= 0.1654

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Answer:

Oh Lol i didnt even see the pic

Step-by-step explanation:

Answer:

5*2=10

10*8=80

Step-by-step explanation:

Multiply all number!!!

Answer:

1) x = 36

2) x = 127

3) x = 36

Step-by-step explanation:

1)

x + 144 = 180

x = 36

2)

15 + x + 38 = 180

x + 53 = 180

x = 127

3)

2x + 16 + 92 = 180

2x + 108 = 180

2x = 72

x = 36

Answer:

C. 37

Step-by-step explanation:

winindoutpickc

Answer:

A)94.5 cm

Step-by-step explanation:

height = 9cm

Base 1 = 5cm

Area of a Trapezoid = 1/2 × (b1 + b2)h

h = 9cm

b1 = 5cm

b2 = (9 cm + 5cm + 2cm) = 16cm.

Area of Trapezoid

= 1/2 (5 + 16) × 9

= 1/2 × 21 × 9

= 94.5 cm

Option A is the correct answer

Answer:

Sam made a mistake. The answer should have been 30.

This is what Sam should have done:

2n^2 - 20

2n^2 - 20 = 2(5)^2 - 20

= 2(25) - 20

= 50 - 20

= 30

Sam multiplied 2 and 5 when he should have done the power first.

There exists a connected undirected graph with a degree sequence of 2, 2, 3, 3, 4. This graph does not have an Euler circuit or an Euler path, but it does have a Hamiltonian circuit.

To construct a graph with the given degree sequence, we can start by connecting the vertices with the highest degree (degree 4) to each other. This ensures that each of these vertices has a degree of at least 4. Then, we can connect the vertices with degree 3 to the remaining vertices. Finally, we connect the remaining vertices with degree 2 to complete the graph.

(a) Yes, a connected undirected graph having degree sequence 2, 2, 3, 3, 4 does exist. Here is an example of such a graph:

   1

  / \

 2 - 3

  \ /

   4

    \

     5

In this graph, vertex 1 has degree 2, vertex 2 has degree 3, vertex 3 has degree 4, vertex 4 has degree 3, and vertex 5 has degree 2.

(b) (i) No, this graph does not have an Euler circuit. An undirected, connected graph has an Eulerian circuit if and only if it has 0 vertices of odd degree1. In this case, the graph has 4 vertices of odd degree (1, 2, 4, and 5), so it does not have an Euler circuit.

(ii) Yes, this graph does have an Euler path. An undirected, connected graph has an Eulerian path if and only if it has either 0 or 2 vertices of odd degree1. In this case, the graph has 4 vertices of odd degree (1, 2, 4, and 5), so it does not have an Euler circuit but it does have an Euler path.

(iii) No, this graph does not have a Hamiltonian circuit. A Hamiltonian circuit is a cycle that visits each vertex exactly once. This graph does not have a Hamiltonian circuit because there is no way to visit all the vertices exactly once and return to the starting vertex without repeating any edges or vertices.

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Japan's superconducting bullet that is being tested in Yamanashi Maglev Test Line will have an elevation of 2580 meters and actual distance of the track as 6.9 kilometers.

A. To calculate the elevation change in the steepest section of the track:

Grade = 40% (Given)

Horizontal distance = 6450 meters (Given)

Elevation change = Grade × Horizontal distance

= 40% × 6,450 meters

= 0.40 × 6,450 meters

= 2,580 meters

Therefore, the elevation change in this section of the track will be 2,580 meters.

B. To find the actual distance of the track in this section:

By using Pythagorean theorem, the horizontal distance represents the base of a right triangle, and the elevation change represents the height.

Actual distance of the track = √(Horizontal distance² + Elevation change²)

= √(6,450²  + 2,580² )

= √(41,602,500 + 6,656,400)

= √48,258,900

= 6,945 meters

= 6.9 kilometers

Therefore, the actual distance of the track in this section will be 6.9 kilometers.

C.  To determine which plane is closer to the tower:

Plane A: Altitude = 20,000 ft, Distance from tower = 5 km

Plane B: Altitude = 8,000 ft, Distance from tower = 7 km

1 ft is approximately equal to 0.0003048 km.

Altitude of Plane A in km = 20,000 ft × 0.0003048 km/ft ≈ 6.096 km

Altitude of Plane B in km = 8,000 ft × 0.0003048 km/ft ≈ 2.4384 km

On comparing the distances, we find that Plane A is closer to the tower than Plane B.

Therefore, Plane A is closer to the tower as compare to Plane B.

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The center of the sphere is (-2, 1, 0).

The radius of the sphere is √65.

The given equation is x² + y² + 2 + 4x - 2y - 62 = 0.

We can rewrite the given equation as follows:

x² + 4x + y² - 2y = 60

Completing the square of x and y, we get:

(x + 2)² - 4 + (y - 1)² - 1 = 60

(x + 2)² + (y - 1)² = 65

Now, we know that the general equation of the sphere is :

(x - a)² + (y - b)² + (z - c)² = r² where (a, b, c) is the center of the sphere, and r is the radius.

To compare the given equation with the equation of the sphere, we will have to convert it into the standard form as follows:

(x + 2)² + (y - 1)² + (0 - 0)² = √65²

The center of the sphere is (-2, 1, 0), and its radius is √65.

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Answer: $770

Step-by-step explanation:

Number of units to be purchased by Alicia:

= 200,000 / 1,000

= 200 units

Alicia is purchasing a 5-year term life insurance policy. At age 30, the cost per $1,000 unit of insurance is $3.85 for a female.

The formula for the annual premium is:

= Number of units purchased * Premium per $1,000

= 200 * 3.85

= $770

Step-by-step explanation:

all you have to do is number the line from -5 to 5 and just plot the points next to it

Yes, it can be concluded at α = 0.05 that the average size of the farms in the two counties is different.

Traditional Method:

To test the hypothesis that the average sizes of farms in Indiana County and Greene County are different, we can use a two-sample t-test. The traditional method involves the following steps:

1. Formulate the null hypothesis (H0) and the alternative hypothesis (Ha):

  H0: μ1 = μ2 (The average sizes of farms in both counties are equal)

  Ha: μ1 ≠ μ2 (The average sizes of farms in both counties are different)

2. Determine the significance level (α): α = 0.05 (given)

3. Calculate the test statistic:

  t = (x1 - x2) / sqrt((s1^2 / n1) + (s2^2 / n2))

  where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

4. Determine the degrees of freedom:

  df = n1 + n2 - 2

5. Find the critical value(s) corresponding to the chosen significance level and degrees of freedom from the t-distribution table.

6. Compare the test statistic with the critical value(s) to make a decision:

  If the absolute value of the test statistic is greater than the critical value(s), reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

P-value Method:

Alternatively, we can use the p-value method to perform the hypothesis test. The p-value is the probability of obtaining a test statistic as extreme as the observed value (or more extreme), assuming the null hypothesis is true.

1. Formulate the null hypothesis (H0) and the alternative hypothesis (Ha) as mentioned earlier.

2. Determine the significance level (α): α = 0.05 (given)

3. Calculate the test statistic as described above.

4. Calculate the p-value corresponding to the test statistic using the t-distribution.

5. Compare the p-value with the significance level:

  If the p-value is less than α, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

In this case, both the traditional method and the p-value method lead to the same conclusion. If the p-value is less than 0.05, we reject the null hypothesis and conclude that the average sizes of farms in Indiana County and Greene County are different.

Note: Since the sample sizes are relatively small (8 and 10), it is assumed that the populations are normally distributed.

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Answer:

6.4 because subtract 9.6 from 15

Answer:

answer is here

Step-by-step explanation:

https://www.mathpapa.com/algebra-calculator.html

Answer:

The answer is A.

Step-by-step explanation:

Answer:

Step-by-step explanation:

A is the correct answer on Edge

The solution to the initial value problem y" - 2y' + 10y = 0, y(0) = 0, y'(0) = 6 is y(t) = 6[tex]e^t[/tex] × sin(3t).

To solve the initial value problem y" - 2y' + 10y = 0, with initial conditions y(0) = 0 and y'(0) = 6, we can use the method of the characteristic equation. Let's solve it step by step:

Step 1: Characteristic equation

We assume the solution has the form y = [tex]e^{(rt)[/tex], where r is a constant. Substituting this into the differential equation, we get:

r² - 2r + 10 = 0

Step 2: Solve the characteristic equation

Solving the quadratic equation, we find the roots:

r = (2 ± sqrt(2² - 4(1)(10))) / 2

r = (2 ± sqrt(-36)) / 2

r = 1 ± 3i

Step 3: General solution

Since the roots are complex, the general solution of the differential equation can be written as:

y(t) = [tex]e^{(1t)[/tex] (A × cos(3t) + B × sin(3t))

Step 4: Apply initial conditions

Using the initial condition y(0) = 0, we substitute t = 0 into the general solution:

0 = A × cos(0) + B × sin(0)

0 = A

Using the initial condition y'(0) = 6, we substitute t = 0 into the derivative of the general solution:

6 = (A × 1 × cos(0) - 3B × sin(0))

6 = A

Step 5: Final solution

Now we have A = 0 and B = 6. Substituting these values into the general solution, we obtain the particular solution:

y(t) = [tex]e^t[/tex] × (0 × cos(3t) + 6 × sin(3t))

y(t) = 6[tex]e^t[/tex] × sin(3t)

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In summary, △PQS ≅ △RQS by the SAS congruence criterion, as we have a shared side, two congruent angles, and an equal side, satisfying the conditions for triangle congruence.

Proof: To show that △PQS ≅ △RQS, we can use the following information: ∠QSP ≅ ∠QSR (Right angles)

S is the midpoint of PR¯¯¯¯¯ (Given)

PQ¯¯¯¯¯ ≅ QR¯¯¯¯¯ (Given)

QS¯¯¯¯¯ bisects ∠Q (Given)

Using these conditions, we can establish the congruence of the two triangles:

Since ∠QSP and ∠QSR are right angles, we have a common angle. Additionally, we know that PQ¯¯¯¯¯ ≅ QR¯¯¯¯¯, which gives us two equal sides. Moreover, QS¯¯¯¯¯ bisects ∠Q, which means it divides the angle into two congruent angles.

By using the Side-Angle-Side (SAS) congruence criterion, we can conclude that △PQS ≅ △RQS. The shared side QS¯¯¯¯¯ is sandwiched between two congruent angles (∠QSP and ∠QSR) and is congruent to itself.

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Answer:

Thanks for letting me know I might try that later today

Step-by-step explanation:

:)

Trapezoid

---

hope it helps

sorry if i'm wrong

i used mental maths

Dude That's a square not a trapezoid