What's the slope of the line

The stress function satisfies the conditions of compatibility for a two-dimensional problem.

Given stress function is 50x² - 60xy - 70y²

To determine whether the stress function satisfies the conditions of compatibility for a two-dimensional problem, it is required to find the strains and then check for compatibility equations.

Strain components are given as,

εx = ∂υ/∂x + (du/dx)

εy = ∂υ/∂y + (du/dy)

γxy = ∂υ/∂y + (du/dx)

Here,

υ = 50x² - 60xy - 70y²

du/dx = 100x - 60

ydu/dy = -60x - 140y

∂υ/∂x = 100x - 60y

∂υ/∂y = -60x - 140y

∂²υ/∂y² = -140

∂²υ/∂x² = 100

Now,εx = 100x - 60

yεy = -140y - 60

xγxy = -60y - 60x

Taking derivative of εy w.r.t x,

∂(εy)/∂x = -60

Similarly, taking derivative of εx w.r.t y,

∂(εx)/∂y = -60

∴ The stress function satisfies the conditions of compatibility for a two-dimensional problem.

Stress components are given as,

σx = (C11εx + C12εy)

σy = (C21εx + C22εy)

τxy = (C44γxy)

Here,C11 = C22 = 100, C12 = C21 = -60 and C44 = 0

Therefore,

σx = 100(100x - 60y) - 60(-140y - 60x)

= 19600x - 8800

yσy = -60(100x - 60y) + 100(-140y - 60x)

= -19600y + 8800x

τxy = 0

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The probability of a randomly chosen bolt having a width between 941 and 959 mm is 0.6294, and the appropriate value for C such that a randomly chosen bolt has a width less than C with probability 0.8729 is 963.80 mm.

To calculate the probability of a bolt having a width between 941 and 959 mm, we need to standardize the values using the formula z = (x - μ) / σ, where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation. Thus, for the lower value of 941 mm, we get z = (941 - 951) / 10 = -1, and for the upper value of 959 mm, we get z = (959 - 951) / 10 = 0.8. Using a standard normal distribution table or a calculator, we can find the probabilities corresponding to these z-scores, which are 0.1587 and 0.7881, respectively. Therefore, the probability of a randomly chosen bolt having a width between 941 and 959 mm is the difference between these two probabilities, which is 0.6294, rounded to four decimal places.

To find the value of C such that a randomly chosen bolt has a width less than C with probability 0.8729, we need to use the inverse normal distribution function, also known as the z-score or percentile function. This function gives us the z-score corresponding to a given probability. Using a calculator or a table, we can find the z-score corresponding to a probability of 0.8729, which is 1.18, rounded to two decimal places.

To get the corresponding width, we use the formula x = μ + zσ, where μ and σ are the mean and standard deviation of the normal distribution, and z is the z-score we just found. Thus, C = 951 + 1.18 × 10 = 963.8 mm, rounded to two decimal places. Therefore, the appropriate value for C is 963.80 mm.

Therefore, the probability of a randomly chosen bolt having a width between 941 and 959 mm is 0.6294, and the appropriate value for C such that a randomly chosen bolt has a width less than C with probability 0.8729 is 963.80 mm.

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In summary: Mean (μ): 120, Standard deviation (σ): 6.93, Minimum usual value (μ - 2σ): 106.14 and Maximum usual value (μ + 2σ): 133.86

To find the mean mu μ of the binomial distribution, we use the formula mu = n*p. Therefore, mu = 200*0.6 = 120.

To find the standard deviation sigma σ, we use the formula sigma = sqrt(n*p*(1-p)). Therefore, sigma = sqrt(200*0.6*0.4) = 6.93.

Using the range rule of thumb, we can estimate the minimum usual value by subtracting 2 times the standard deviation from the mean, and the maximum usual value by adding 2 times the standard deviation to the mean. Therefore, the minimum usual value is mu - 2*sigma = 120 - 2*6.93 = 106.14, and the maximum usual value is mu + 2*sigma = 120 + 2*6.93 = 133.86.

So, in summary, the mean mu μ of the binomial distribution is 120, the standard deviation sigma σ is 6.93, the minimum usual value mu minus 2 sigma μ−2σ is 106.14, and the maximum usual value mu plus 2 sigma μ+2σ is 133.86.
For a binomial distribution, the mean (μ) and standard deviation (σ) can be calculated using the formulas:

μ = n * p
σ = √(n * p * (1 - p))

Given n = 200 and p = 0.6, we can find μ and σ:

μ = 200 * 0.6 = 120
σ = √(200 * 0.6 * (1 - 0.6)) = √(200 * 0.6 * 0.4) = √48 ≈ 6.93

Next, we can use the range rule of thumb to find the minimum and maximum usual values:

Minimum usual value (μ - 2σ):
120 - (2 * 6.93) = 120 - 13.86 ≈ 106.14

Maximum usual value (μ + 2σ):
120 + (2 * 6.93) = 120 + 13.86 ≈ 133.86

In summary:
Mean (μ): 120
Standard deviation (σ): 6.93
Minimum usual value (μ - 2σ): 106.14
Maximum usual value (μ + 2σ): 133.86

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Answer:0=4x^2+12x+9

Step-by-step explanation:

The standard form of the quadratic equation is y = 4x² + 12x + 9. Then the correct option is D. And the value of a, b, and c will be 4, 12, and 9.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2. Then we have

The equation is given below.

y = (2x + 3)²

Simplify the equation, then we have

y = 4x² + 12x + 9

Then the correct option is D.

Compare the equation with standard equation, then we have

a = 4

b = 12

c = 9

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Answer:

No you wouldn't because you are not dividing or multiplying by a negative number.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

When you solve the inequality, x is less than or equaled to -26.

Answer:

Your answer is 30

Step-by-step explanation:

Hope this helps

The probability that the basketball player hits all 4 shots is approximately 0.0416 or 4.16%.

To determine the probability that a basketball player hits all 4 shots during a game, when the player hits three-point shots 41% of the time, we have to apply binomial probability distribution.

Let X be the number of successful shots when taking 4 shots, the probability of success in each trial, p = 0.41 and the number of trials, n = 4.

Therefore, we can use the binomial probability distribution as given below: `P(X = k) = (n choose k) × p^k × q^(n-k)

`Where q = 1 - p = 1 - 0.41 = 0.59 is the probability of failure.In this case, k = 4, and we can calculate P(X = 4) as follows:`P(X = 4) = (4 choose 4) × 0.41^4 × 0.59^(4-4)`= (1) × (0.41)^4 × (0.59)^0= 0.0416

Therefore, the probability that the basketball player hits all 4 shots is approximately 0.0416 or 4.16%.

Note: A probability is a number between 0 and 1, and it can be represented as a fraction, decimal or percentage. In this case, we have represented the answer in percentage format.

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Answer:

so 10 +5+5=20

Step-by-step explanation:

so look a dime is 10 cent a nickel is 5 cent

The number of views in the four weeks round to the whole number is 48.

Here it is given that the initial number of views for a reader board was 25 and it gets increased at the rate of 18% per week.

We have to find the number of views in the fourth week.

On the first week the increase = 25 + 25× 18%

                                                   = 25 + 25 × 18/100

                                                   = 25 + 4.5

                                                   = 29.5

The second week increase = 29.5 + 29.5 × 18%

                                              = 29.5 + 5.31

                                                = 34.81

The third week increase = 34.81 + 34.81 × 18%

                                         = 34.81 + 6.2658

                                         = 41.0758

The fourth week increase = 41.0758 + 41.0758 × 18%

                                           = 41.0758 + 7.393644

                                            = 48.469444

Therefore the number of views in the four weeks is 48.

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Answer:

My thought is 7, but I may be very well wrong.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

A. It's 1/2

Step-by-step explanation:

I'm glad you came to me for help. Here's a concise explanation of how to use the Laplace transform method to solve a differential equation with a step function input.

Given a linear ordinary differential equation (ODE) with a step function input, we can follow these steps:1. Take the Laplace transform of the ODE, applying the linearity property and differentiating rules for Laplace transforms.2. Replace the step function with its Laplace transform (i.e., the Heaviside step function H(t-a) has a Laplace transform of e^(-as)/s).3. Solve the resulting transformed equation for the Laplace transform of the desired function (usually denoted as Y(s) or X(s)).4. Apply the inverse Laplace transform to obtain the solution in the time domain.Remember that the Laplace transform is a linear operator that converts a function of time (t) into a function of complex frequency (s). It can simplify the process of solving differential equations by transforming them into algebraic equations. The inverse Laplace transform then brings the solution back to the time domain.In summary, to solve a differential equation with a step function input using the Laplace transform method, you'll need to apply the Laplace transform to the ODE, substitute the step function's Laplace transform, solve the transformed equation, and then use the inverse Laplace transform to obtain the final solution.

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Answer:

19

Step-by-step explanation:

x = 4

y = 4^2 + 3 = 16 +3 = 19

According to the given information, 10 grey wolf pups will survive to adulthood.

What is a fraction?

A fraction is a mathematical expression that represents a part of a whole or a division of one quantity by another.

Yellowstone National Park is home to a variety of wildlife, including the grey wolf. A survey conducted in the park recorded the birth of 25 grey wolf pups. However, it is estimated that only 2/5 of these pups will survive to adulthood.

To estimate the number of grey wolf pups that will survive to adulthood, we can use a simple mathematical formula. We multiply the total number of grey wolf pups by the estimated survival rate:

Survivors = (2/5) x 25

Therefore, we can estimate that 10 grey wolf pups will survive to adulthood.

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Answer:

8 meters per second.

Step-by-step explanation:

To find how many meters the cheetah travels per second, we need to divide 56 by 7.

This gives us 8, with no remainders, and our answer.

Answer:

27m/s

Step-by-step explanation:

distance(s) = 56m

Time(t) = 7sec

Speed(u) = ?m/s

using the formula

S = ut + ½at²

56 = 7u + ½ × 10 × 7²

56 = 7u + 5 × 49

56 = 7u + 245

7u = 245 – 56

7u = 189

u = 189/7

u = 27m/s

i hope i helped

Answer:

y =< 6x + 3

you copypasta looks weird, but I would go for option c if i read this correctly

Answer:

y=-2x-4

Step-by-step explanation:

6x + 3y=-12 subtract 6x to other side

3y=-12-6x divide 3 to every number

1y=-4-2x

The third polygon must have five sides as well, since the interior angles of the three polygons must add up to 360°.

The interior angle of a regular pentagon is 108°. Therefore, the three pentagons must have a total of 3 x 108° = 324°. The remaining 36° must come from the third polygon, which must also have five sides.

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The total area of the estate will be: 800 / 400 = 2 km². The population density of the village is 600 people/km². The area of the village is 6 km². Therefore, the total population of the village will be: 600 x 6 = 3600 people. The population density of the estate is 400 people/km². The population of the estate is 800 people.

The population density of the village and estate together will be: (3600 + 800) / (6 + 2) = 440 people/km². Hence, the population density of the village and estate together is 440 people/km².Therefore, the population density of the village and estate together is 440 people/km².

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Answer:

43

Step-by-step explanation:

b) The mean is 19.

c) The standard deviation is 0.974.

d) The binomial probability is 20.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given:

n = 20,  p = 0.95,  q = 1 - 0.95 = 0.05

a)  There are only two results per shot and they are independent of each other. Each pitch is independent of the outcome of the other pitches.

b) To calculate the mean of X.

{ E(x) = np }

So, E(x) = 95% of 20

             = 19

c) The Standard Deviation is √npq

= √95/10

= 0.974

d) The binomial probability

p(x = 19) = 20! / 19!(20-19)!

               =20 / 1

                20

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Answer:

Not 100% sure but I think it could be Sergio and Sylvester because they were less than the average life expectancy but like i said not 100% sure. Hope this helped

Step-by-step explanation:

To determine which constraints have slack, we need to examine the constraints in the given linear programming problem. Slack occurs when a constraint is not binding, meaning it is not fully utilized and has some available resources.

The constraints in the problem are as follows:

1. 3X₁ + 4X₂ + X₃ + 4X₄ + 4X₅ ≤ 3,200 (Labor constraint)

2. 20X₁ + 15X₂ + 8X₃ + 15X₄ + 10X₅ ≤ 12,000 (Raw Material #1 constraint)

3. 10X₁ + 20X₂ + 5X₃ + 22X₄ + 8X₅ ≤ 12,000 (Raw Material #2 constraint)

4. 2X₁ + 3X₂ + 6X₃ + 7X₄ + 2X₅ ≤ 3,000 (Painting constraint)

To determine slack, we need to check if the left-hand side of each constraint is less than or equal to the right-hand side. If it is less, then there is slack in that constraint.

1. Labor constraint: 3X₁ + 4X₂ + X₃ + 4X₄ + 4X₅ ≤ 3,200

  - If the left-hand side is less than 3,200, there is slack.

2. Raw Material #1 constraint: 20X₁ + 15X₂ + 8X₃ + 15X₄ + 10X₅ ≤ 12,000

  - If the left-hand side is less than 12,000, there is slack.

3. Raw Material #2 constraint: 10X₁ + 20X₂ + 5X₃ + 22X₄ + 8X₅ ≤ 12,000

  - If the left-hand side is less than 12,000, there is slack.

4. Painting constraint: 2X₁ + 3X₂ + 6X₃ + 7X₄ + 2X₅ ≤ 3,000

  - If the left-hand side is less than 3,000, there is slack.

Based on this analysis, the constraints with slack are the labor constraint (constraint 1), the raw material #1 constraint (constraint 2), the raw material #2 constraint (constraint 3), and the painting constraint (constraint 4).

Regarding the objective function coefficient for X₅, we can determine the range of values that it can take without changing the solution quantities. Since X₅ does not appear in any of the constraints, its coefficient in the objective function does not affect the feasibility of the problem. Therefore, the objective function coefficient for X₅ can range from negative infinity to positive infinity without changing the solution quantities.

Lastly, the impact of increasing the units of painting (X₅) on Z (the objective function) cannot be determined solely based on the given information. The impact of a change in X₅ on Z depends on the specific coefficients in the objective function and how they interact with the coefficients in the constraints.

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Answer:

  15

Step-by-step explanation:

Each bracelet takes 28+10 = 38 elastic bands. If you have 600 bands, you can make ...

  600/38 = 15 30/38 . . . bracelets

You can make 15 complete bracelets.

__

You will have 30 elastic bands left over.

The last sentence of the proof states, "By the Pythagorean theorem, since a squared plus b squared equals c squared, the sum of f and e is equal to c."

The proof establishes the proportions and similarities between the triangles in the diagram. It shows that the ratios of corresponding sides in the similar triangles hold true, leading to the proportions a/c = c/a and b/c = c/e. These proportions can be rearranged to obtain a2 = cf and b2 = ce.

The next step in the proof adds b2 to both sides of the equation a2 = cf, resulting in a2 + b2 = cf + b2. Since b2 = ce, we substitute ce into the equation, giving us a2 + b2 = cf + ce.

The final step applies the converse of the distributive property, which states that if a + b = c, then a(b + d) = ab + ad. In this case, we have a2 + b2 = cf + ce, which can be rewritten as a2 + b2 = c(f + e).

Therefore, the last sentence of the proof concludes that because a2 + b2 = c2 (as derived from the previous steps), it follows that f + e = c. This statement completes the proof and establishes the relationship between the lengths of the sides and the altitude in the right triangle. Option C is correct.

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Answer:

-7b

Step-by-step explanation:

Ok soo you have add the terms.

1b+(-8b)=-7b

Have a good!!

Answer:

-9b

Step-by-step explanation:

i'm assuming this is just combining like terms so if you ignore the (b) you will have

6-5+(-8)

-1+(-8)

-9

then you put back the variable and you get -9b

Answer:

2.5 pounds

Step-by-step explanation:

Complete Question

Luke has a cylinder with a radius of 5 inches and a height of 6 inches. What is the volume of his cylinder in cubic inches?

Answer:

471.24 cubic inches

Step-by-step explanation:

The formula for the volume of a cylinder =

πr²h

r = Radius = 5 in

h = Height = 6 in

Hence,

Volume = π × (5 in)² × 6 in

= 471.24 cubic inches

Therefore, the volume of his cylinder in cubic inches = 471.24 cubic inches

Answer:

40

Step-by-step explanation:

we can ask as

How many groups of 360 hundredth are there in 9 hundredth.

Mark me as brainliest.

Answer:

w = -8

Step-by-step explanation:

Distribute: -6 = 2w + 10

Remove the 10: -6 -10 = 2w +10 -10 ---> -16 = 2w

Isolate the variable: -16/2 = 2w/2

Answer: -8 = w

The true statements are:

The coordinates of the shape are given as:

Start by plotting the coordinates of ABCD on the coordinate plane.

Next, connect the dots on the plane

From the connected dots, we can see that the shape formed is a square

Start by calculating the distance between adjacent points using the distance formula

\(d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}\)

So, we have:

\(AB = \sqrt{(10 -6)^2 + (-6 +9)^2} = 5\)

\(BC = \sqrt{(6 -3)^2 + (-9 +5)^2} = 5\)

\(CD = \sqrt{(3 -7)^2 + (-2 +5)^2} = 5\)

\(DA = \sqrt{(7 -10)^2 + (-2 +6)^2} = 5\)

The perimeter (P) of the shape is calculated as:

\(P = 4 \times AB\)

\(P = 4 \times 5 = 20\)

The area (A) of the shape is calculated as:

\(A =AB \times BC\)

\(A =5 \times 5 = 25\)

Hence, the perimeter and the area of the shape is 20 units, and 25 unit squares

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