1.Suppose that G is a weighted graph and S is a subgraph of G. What is the total weight of S? 2. Determine whether the following is true or false: If G is a weighted Hamiltonian graph, then the Nearest Neighbour algorithm is guar- anteed to find a shortest Hamilton circuit in G. 3. Describe the input and the output of Kruskal's Algorithm?

Answer:

x = 13

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² = 5² + 12² = 25 + 144 = 169 ( take the square root of both sides )

x = [tex]\sqrt{169}[/tex] = 13

It should be noted that the probability of obtaining a sample mean of 39.1 hours or less is quite low (0.035), it can be considered unusually short.

The mean of the sampling distribution of the sample mean, μ, is equal to the population mean, which is μ = 40 hours.

The standard deviation of the sampling distribution is σ(μ) = 5 / √100

= 5 / 10

= 0.5 hours.

Plugging in the values, we get (40.6 - 40) / 0.5

= 0.6 / 0.5

= 1.2.

Looking up the z-score of 1.2 in the standard normal distribution table (or using a calculator), we find that the probability is approximately 0.884.

Now, let's calculate P(≤39.1). Similarly, we calculate the z-score as (x - μ) / σ(μ), where x = 39.1 hours. Plugging in the values, we get (39.1 - 40) / 0.5

= -0.9 / 0.5

= -1.8.

Using the z-score table or a calculator, we find that the probability is approximately 0.035.

This probability represents the area under the curve to the left of -1.8, which is a left-tailed probability.

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The correct answer is A. Yes. the argument conforms to the Law of Detachment.

Yes, the argument does illustrate the Law of Detachment. The Law of Detachment is a valid form of reasoning in propositional logic that states that if a conditional statement (p → q) is true and the antecedent (p) is true, then the consequent (q) can be inferred as true.

In the given argument:

The conditional statement "If the fuse has blown, then the light will not go on" can be represented as p → q, where p represents "the fuse has blown" and q represents "the light will not go on."

The given information states that the fuse has blown, which means that p is true.

According to the Law of Detachment, if p → q is true and p is true, we can conclude that q is also true. Therefore, we can infer that "the light will not go on" (q) is true.

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Plot direction fields and trajectories. Analyze eigenvalues to determine stability and type of critical point.

For system (a):

The direction field and trajectories should be plotted based on the given matrix:

[3 5] [x]

[3 -2] * [y]

To determine the type and stability of the origin as a critical point, we can analyze the eigenvalues of the matrix. The eigenvalues are found by solving the characteristic equation:

det(A - λI) = 0,

where A is the given matrix and λ is the eigenvalue.

For system (b):

The direction field and trajectories should be plotted based on the given matrix:

[1 -5] [x]

[4 1] * [y]

To determine the type and stability of the origin as a critical point, we can again analyze the eigenvalues of the matrix.

For system (c):

The direction field and trajectories should be plotted based on the given matrix:

[-6 3] [x]

[ -4 -2] * [y]

To determine the type and stability of the origin as a critical point, we once again analyze the eigenvalues of the matrix.

Analyzing the eigenvalues will allow us to determine if the critical point is a stable node, unstable node, saddle point, or any other type of critical point.

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the solution to the equation on the interval [0, 2π) is x = 3π/4.

To solve the equation, we want to find the values of x that satisfy the equation within the given interval.

First, we isolate the cosine term by subtracting 1 from both sides:

√2 cos(x) = -1

Next, we divide both sides by √2:

cos(x) = -1/√2

To find the solutions, we need to determine the angles whose cosine value is equal to -1/√2. We can use the unit circle or reference angles to determine these angles.

In the interval [0, 2π), the angle that satisfies cos(x) = -1/√2 is x = 3π/4.

Therefore, the solution to the equation on the interval [0, 2π) is x = 3π/4.

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Answer:-4

Step-by-step explanation:

The probability that a plant produces between 15 and 19 strawberries is given as follows:

47.5%.

The two parameters that are needed to calculate a probability are listed as follows:

Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.

The desired areas for this problem are given as follows:

Hence the probability is given as follows:

34 + 13.5 = 47.5%.

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Answer:

Thats so hard oh my gosh!

Step-by-step explanation:

Answer:4 degrees

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Just graph the equation and where they intercept is the solution.

Just use desmos graphing calculator if you don't know how to graph.

The standard error of the distribution of differences in sample means is approximately 2.8.

The standard error of the distribution of differences in sample means, ¯x1−¯x2, can be calculated using the formula:

SE(¯x1 - ¯x2) = sqrt[s1²/n1 + s2²/n2]

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

In this case,

Population 1 has a sample size of n1 = 120, a mean of ¯x1 = 81, and a standard deviation of s1 = 11.

Population 2 has a sample size of n2 = 70, a mean of ¯x2 = 73, and a standard deviation of s2 = 17.

Substituting these values into the formula,

SE(¯x1 - ¯x2) = sqrt[11²/120 + 17²/70]≈ 2.8

Therefore, the standard error of the distribution of differences in sample means is approximately 2.8.

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Answer:

(-3,2)

Step-by-step explanation:

3/4 of eight is six so go to two and then find the x, as x wasn't on the numbers it is not a multiple of two, so three was the closest number

may be wrong

Answer:

x = 18

Step-by-step explanation:

∠ GFH and ∠ EFH form a right angle GFE , then

2x + 3x = 90 ← equation for the angle

5x = 90 ( divide both sides by 5 )

x = 18

decimal = 0.26

percent = 26%

Step-by-step explanation:

✧ [tex] \underline{ \underline{ \large{ \tt{G \: I \: V \: E \: N \: \:E \: Q \: U \: A \: T \: I \: O \: N}}}} : [/tex]

❀ [tex] \underline{ \underline{ \large{ \tt{ \: T \: O \: \: F\: I\: N \: D}}} }: [/tex]

☄ [tex] \underline{ \underline{ \large{ \tt{S \: O \: L\: U \: T \: I\: O \: N}}}} : [/tex]

♨ [tex] \large{ \sf{5 = 2x - 3}}[/tex]

~Swap the sides of the equation :

⇾ [tex] \large{ \sf{2x - 3 = 5}}[/tex]

~We want to remove the 3 first. Since the original equation is -3 , we are going to use the opposite operation and add 3 to the both sides :

⇾ [tex] \large{ \sf{2x - 3 + 3 = 5 + 3}}[/tex]

⇾ [tex] \large{ \sf{2x \: \cancel{ - 3} \: \cancel{ + 3}}} = 8[/tex]

⇾ [tex] \large{ \sf{2x = 8}}[/tex]

~Now , We need to think about how to remove the coefficient 2. Since the opposite of multiplication is division , we are going to divide both sides of the equation by 2 :

⇾ [tex] \large{ \sf{ \frac{2x}{2} = \frac{8}{2}}} [/tex]

⇾ [tex] \boxed{ \large{ \sf{x = 4}}}[/tex]

☯ [tex] \underline{ \underline{ \large{ \tt{C \: H \:E \: C \: K}}}}: [/tex]

☪ [tex] \large{ \tt{L \: H \: S : \: 5 }}[/tex]

[tex] \large{ \tt{R \: H \: S \ \: : \: 2x - 3 = 2 \times 4 - 3 = 8 - 3 = \underline{ \tt{5}}}}[/tex] [ Plug the value of x ]

☥ Since this is a true statement , our answer ( x = 4 ) is correct. Yay! We got our answer :)

♕ [tex] \large{ \boxed{ \underline{ \large{ \tt{Our \: Final \: Answer : \boxed{ \underline{ \bold{ \text{x = 5}}}}}}}}}[/tex]

[tex] \underline{ \underline{ \text{H \: O\: P \: E \: \: I \: \: H \: E \: L \: P \: E \: D}}}[/tex] !! ♡

[tex] \underline{ \underline{ \text{H \: A \: V \: E \: A \: W \: O \: N \: D \: E \: R \: F \: U \: L \: D \: A\: Y \: / \: N\: I \: G\: H \: T}}}[/tex] !! ツ

☃ [tex] \underline{ \underline{ \tt{C \:A \: R \: R \: Y \: \: O \:N \: \: L \: E \: A \: R\: N \: I \: N \: G}}} [/tex] !!✎

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer: D

Step-by-step explanation:

She uses a sample size of n=200, and 50%  of all customers would actually buy coffee.

The change that would result in the highest power for her test is D. increase the significance level to α = 0.01 and use a sample size of n = 300.

The significance level simply means the probability of rejecting the null hypothesis when it is true.

It should be noted that the power of the test depends on 4 factors which are the sample size, standard deviation, effect size, and significance level.

In the given scenario, the larger sample size will increase the power of the test and a higher significance level will result in a higher power.

Therefore, the test is done with the largest sample size and highest significance level of 0.10

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Answer:

Step-by-step explanation:

X-intercept: y=0:

6x +2×0 = 12

6x = 12

 x = 2          

Y-intercept: x=0:

6×0 + 2y = 12

2y = 12

 y = 6      

Answer:

a) 10 yards and 10[tex]\sqrt{3}[/tex] yards

Step-by-step explanation:

The intersection of the support beams in the middle form four right angles, since all four sides are equal.  Because you know two angles of the triangle on the right hand side (90° and 30°), you can calculate the third angle (given that a triangle has 180°):

180°-90°-30° = 60°

This is a 30-60-90 triangle (if you don't know what that is, you can look it up).  In a 30-60-90 triangle, the hypotenuse is 2x.  In this case, the hypotenuse is 10 yards, so you can set up an equation given that information:

2x = 10

x = 5

Now that you know x of the 30-60-90 triangle, you can solve for the other two sides of the triangle.

The side directly across from the 30° angle is just x, which is equal to 5.  The side directly across from the 60° angle is x[tex]\sqrt{3}[/tex], which in this case would be 5[tex]\sqrt{3}[/tex].

Because you want the full length of both beams, you'd multiple both sides by two to get the length of both entire beams:

5*2 = 10

(5[tex]\sqrt{3}[/tex])*2 = 10[tex]\sqrt{3}[/tex]

*I hope this makes sense!*

Answer:

I think it is 2/12

The linear equation is defined by y = mx +b is called ''Slope-intercept form''.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The linear equation is defined by,

⇒ y = mx + b

Now, We know that;

The equation defined as;

⇒ y = mx + b

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

Hence, The linear equation is defined by y = mx +b is called ''Slope-intercept form''.

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Answer:

Step-by-step explanation:

As I figured out, any number that is not 0, meaning any number with a value is a Significant Digit. For example, in 3003 there's only 2 significant digits. The easiest way to figure these things out is adding the digits.

I hope this helps :D

The volume of a cone with diameter 18 cm and height 15 cm is b. V = 1272.3 cm^(3).

To calculate the volume of a cone, we use the formula:

V = (1/3) * π * r^2 * h

where V is the volume, π is the mathematical constant approximately equal to 3.14159, r is the radius of the cone's base, and h is the height of the cone.

Given that the diameter of the cone is 18 cm, we can calculate the radius by dividing the diameter by 2:

r = 18 cm / 2 = 9 cm

Substituting the values into the volume formula:

V = (1/3) * π * 9^2 * 15

Calculating:

V ≈ 1272.3 cm^3

Therefore, the volume of the cone is approximately 1272.3 cm^3.

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Answer:

5 feet

Step-by-step explanation:

Answer:

sine=opposite/hypotenuse

sin52.2=x/150

sin0.790=x/150

x=118.5

Therefore, the value of c is 2/9.

The joint density of X and Y is given by f (x,y) = c(1/2) x² y², 1.

We are to calculate the value of c.

Step-by-step solution: It is given that joint density of X and Y is f (x,y) = c(1/2) x² y², 1.

The joint probability density function f(x, y) satisfies the following properties:f(x, y) ≥ 0 for all x and y.f(x, y) is continuous in x and y.∫∞−∞∫∞−∞f(x, y)dxdy = 1

From the given joint density function, we can compute marginal density of X and marginal density of Y by integrating over the other variable, as follows: P(X = x) = ∫ f(x, y) dy and P(Y = y) = ∫ f(x, y) dx

Let's calculate the marginal density of X.P(X = x) = ∫ f(x, y) dy∫ f(x, y) dy = c(1/2) x² ∫y² dy Limits of integration are from -1 to 1.P(X = x) = c(1/2) x² [(1/3) y³]1 and -1.∫ f(x, y) dy = c(1/2) x² [(1/3) (1³ - (-1)³)]P(X = x) = c(1/2) x² [(1/3) (1 - (-1))]P(X = x) = c(1/2) x² (2/3)P(X = x) = (1/3) c x²P(X = x) = 1,

integrating over all possible values of x, we obtain:1 = ∫ P(X = x) dx= ∫ (1/3) c x² dx Limits of integration are from -1 to 1.1 = (1/3) c [(1/3) x³]1 and -1.∫ P(X = x) dx = (1/3) c [(1/3) (1³ - (-1)³)]1 = (1/3) c [(1/3) (1 - (-1))]1 = (1/3) c (2)1/2 = (2/9) c2/9 = c

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Answer:

Step-by-step explanation:

The joint density of X and Y is given by the function f (x,y) = c1/2x²y², 1. The value of c is 18.

We are required to find the value of c.

First, we need to know the definition of joint density.

A joint probability density function (PDF) is a statistical measure that describes the probability of two or more random variables occurring simultaneously in terms of their PDFs.

It's a measure of the probability of an event happening as a function of two variables, usually expressed as f(x,y).

So, in this problem, we have given the joint density of x and y is f(x,y) = c/2x²y², 1.

We can solve it by integrating it over the entire range.

The probability density function of X and Y can be found by integrating over the whole sample space.

[tex]$$\begin{aligned}&\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}f_{X,Y}(x,y)dxdy=1\\&\implies\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}f_{X,Y}(x,y)dxdy\\&=\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}c\frac{1}{2}x^2y^2dxdy=1\\&=\frac{c}{2}\int_{-\infty}^{\infty}x^2dx\int_{-\infty}^{\infty}y^2dy\\&=\frac{c}{2}\cdot \frac{1}{3}\cdot \frac{1}{3}=1\end{aligned}$$[/tex]

Hence, [tex]$$\implies c=\boxed{18}$$[/tex].

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Answer:

$1.25 is NOT 12.5% dollars. It is 125% of a dollar.

Step-by-step explanation:

We have 1 and 1/4 dollars. 1 and 1/4 as a percentage is 125%

The typical fluctuation is based on the square root of the variance, which is equal to 5.

The typical fluctuation is based on the square root of the variance, which is equal to 3.7.

The typical fluctuation is based on the square root of the variance, which is equal to 3.7.

The Poisson distribution does not account for the finite probability of zero events occurring, and it can not handle problems where the expected number of events is very large, as it assumes an infinite number of successes, which is not the case in real life.

1) Binomial distribution

Binomial distribution is the probability distribution of obtaining exactly r successes in n independent trials with two possible outcomes of a given event.

The best value for the expected number of heads when a coin is flipped 100 times is 50.0, with the uncertainty being 5.0.

The typical fluctuation is based on the square root of the variance, which is equal to 100 x 0.5 x (1-0.5) = 25, which gives the fluctuation to be 5 (the square root of 25).

The Poisson distribution is an excellent approximation for binomial distributions, especially when n is large and p is small.

2) Binomial distribution

The best value for the expected number of times getting a '6' when a die is rolled 100 times is 16.7, with an uncertainty of 4.1.

The typical fluctuation is based on the square root of the variance, which is equal to 100 x (1/6) x (5/6) = 13.9, which gives the fluctuation to be 3.7 (the square root of 13.9)..

3) Binomial distribution

The expected number of times not getting a '6' when a die is rolled 100 times is 83.3, with an uncertainty of 4.1.

The typical fluctuation is based on the square root of the variance, which is equal to 100 x (5/6) x (1/6) = 13.9, which gives the fluctuation to be 3.7 (the square root of 13.9).

Poisson distribution

The Poisson distribution is a good approximation for the binomial distribution because n is large and p is small. Furthermore, the Poisson distribution can be used to predict the probability of a specific number of events occurring in a specific amount of time, which makes it ideal for modeling the number of radioactive decays or the number of phone calls to a call center.

However, the Poisson distribution does not account for the finite probability of zero events occurring, and it can not handle problems where the expected number of events is very large, as it assumes an infinite number of successes, which is not the case in real life.

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Answer:

-8.875

Step-by-step explanation:

8 7/8 > -71/8 > -8.875

The body's position at time t is given by the equation s(t) = [tex]4.9t^2 + 15t + 20[/tex].

To find the body's position at time t,

we need to integrate the velocity function with respect to time and apply the initial condition.

Given:

v = 9.8t + 15

s(0) = 20

First, integrate the velocity function with respect to time to obtain the position function:

∫v dt = ∫(9.8t + 15) dt

s(t) = [tex]4.9t^2 + 15t + C[/tex]

Next, we apply the initial condition s(0) = 20 to determine the value of the constant C:

s(0) =[tex]4.9(0)^2 + 15(0) + C[/tex]

20 = C

Now, we have the complete position function:

s(t) =[tex]4.9t^2 + 15t + 20[/tex]

In conclusion, To find the position of the body at time t,

we integrated the velocity function with respect to time,

applied the initial condition to determine the constant,

and obtained the position function s(t) = [tex]4.9t^2 + 15t + 20[/tex].

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