Consider the rectangular panel shown in the Figure below. Find the problem that the Airy's stress function 0 = xy3 solves. That is, find the tractions at the boundary of the panel.

Step-by-step explanation:

\( \frac{x}{8} = \frac{9}{24} \)

Cross multiply

We have

24x = 72

Divide both sides by 24

That's

\( \frac{24x}{24} = \frac{72}{24} \)

We have the answer as

3x² + 2x - 10

when x = - 1

Substitute the value of x into the expression

That's

3(-1)² + 2(-1) - 10

= 3 - 2 - 10

We have the answer as

When x = 0

That's

3(0) + 2(0) - 10

When x = 1

That's

3(1)² + 2(1) - 10

= 3 + 2 - 10

= 5 - 10

\( \sqrt{( - 9)} \)

First of all apply the radical rule

That's

\( \sqrt{ - a} = \sqrt{ - 1} \times \sqrt{a} \)

So we have

\( \sqrt{ - 9} = \sqrt{ - 1} \times \sqrt{9} \)

Using the imaginary rule

That's

\( \sqrt{ - 1} = i\)

We have

\( \sqrt{9} \times i\)

We have the final answer as

\( \frac{1}{x} \)

when x = 0

We have

\( \frac{1}{0} = 0\)

when x = 1

\( \frac{1}{1} = 1\)

when x = 2

We have

\( \frac{1}{2} \)

Hope this helps you

Abigail is currently 32 years old and Cynthia is currently 24 years old.

A system of equations refers to a set of two or more equations with the same variables. The solution to the system of equations is the set of values for the variables that satisfies all the equations simultaneously.

Let's assign variables to represent the ages of Abigail and Cynthia.

Let's say:

Abigail's current age = A

Cynthia's current age = C

According to the given information:

"Abigail is 8 years older than Cynthia."

This can be written as: A = C + 8.

"20 years ago, Abigail was 3 times as old as Cynthia."

This can be written as: A - 20 = 3(C - 20).

Now, we have a system of two equations.

We can solve them simultaneously to find the current ages of Abigail and Cynthia.

Substituting the value of A from equation 1 into equation 2:

(C + 8) - 20 = 3(C - 20)

Simplifying the equation:

C - 12 = 3C - 60

Bringing like terms together:

3C - C = 60 - 12

2C = 48

Dividing by 2:

C = 24

Now, substitute the value of C back into equation 1 to find A:

A = C + 8

A = 24 + 8

A = 32

Therefore, Abigail is currently 32 years old and Cynthia is currently 24 years old.

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42 adult tickets and 421 children tickets were purchased for the field trip, based on the given information that the total cost of the tickets was $995 and the children tickets cost $11 while the adult tickets cost $13, and the number of children tickets purchased was one more than ten times the number of adults tickets purchased.

Let's use variables to represent the unknown quantities in the problem:

Let x be the number of adult tickets purchased

Then the number of children tickets purchased is 10x + 1 (since it is one more than ten times the number of adults tickets purchased)

Using these variables, we can set up an equation based on the total cost of the tickets:

13x + 11(10x + 1) = 995

Simplifying and solving for x, we get:

23x + 11 = 995

23x = 984

x = 42.7826087 (rounded to 9 decimal places)

Since we can't purchase a fraction of a ticket, we'll round x down to the nearest whole number, which means 42 adult tickets were purchased. Then the number of children tickets purchased is:

10x + 1 = 10(42) + 1 = 421

So, 42 adult tickets and 421 children tickets were purchased.

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Answer:

(a)20π

(b)74π

Step-by-step explanation:

(a) 2π(5) + (2π(10) × 1/2) = 2π(5) + 2π(5)

= 2π(10)

= 20π

(b) π(5)^2 + (π(10)^2 × 1/2) = 25π + 50π

=75π

Answer: P=20 cm    S=75 cm²

Step-by-step explanation:

We have 2 semicircles with diameter d=10 cm and 1 semicircle with diameter D=20 cm

\(\displaystyle\\The\ length \ of \ the\ circle\ is\ \pi D\\The\ length\ of \ the\ semicircle \ is\ \frac{\pi D}{2}\)

\(\displaystyle\\a)\\P=2*\frac{\pi d }{2} +\frac{\pi D}{2} \\\\P=\pi d+\frac{\pi D}{2} \\\\P=\pi *(d+\frac{D}{2} )\\P=\pi *(10+\frac{20}{3} )\\\\P=\pi *(10+10)\\\\P=20\pi \ cm\\\\\)

\(b)\\\displaystyle\\The\ area \ of \ the\ circle\ is\ \frac{\pi D^2}{4} \\The\ area\ of \ the\ semicircle \ is\ \frac{\pi D^2}{8}\\\\S=2*\frac{\pi d^2}{8} +\frac{\pi D^2}{8} \\\\S=\frac{2*\pi *10^2}8} +\frac{\pi *20^2}{8} \\\\S=\frac{2*\pi*100 }{8} +\frac{\pi *400}{8} \\\\S=\frac{200\pi }{8}+\frac{400\pi }{8} \\\\S=\frac{600\pi }{8} \\\\S=75\pi \ cm^2\)

The Function result are : F(x) = 0  F(3) =-3 are the integer or the reduced function.

A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is called the domain of the function and the set Y is called the co-domain of the function. Persian mathematicians Al-Biruni and Sharaf al- Din al-Tusi. Functions were originally an idealization of how one variable depends on another. For example, planetary positions are functions of time. Historically, this concept was elaborated in his late 17th century calculus, and by the 19th century the functions considered were differentiable (i.e. they had a high degree of regularity). The concept of functions was formalized in set theory at the end of the 19th century, greatly expanding the scope of the concept.

According to the Question:

For f(g) = 0, work inside out and find g(0) first. This is the y value at x=0 in the g-plot. -3. Then substitute this answer into the f(x) formula so that f(g(0)) -> f(-3) = f(x) replace x = - 3 in the graph please look. You can see that the y value is +3. So f(g(0))=3

One more thing. Then I think you can understand the remaining two methods. Start with a y value of f(-6)=0 and work from the inside again, inserting it into g(0) = -3 . So g(f(-6))=-3

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It is important to consider external costs when determining the appropriate price for garbage collection.

Instead, they should provide a step-by-step explanation in their answer. The terms "people pay nothing", "extra pound of garbage", "demanded", and "marginal cost" are relevant to the question.

A price for garbage collection that is appropriate is one that takes into account the external costs of garbage disposal that the community is faced with.

The quantity of free garbage collection now demanded is 40.

(b) If a fee of $4 per pound were charged, then the quantity demanded would be 20.Social demand curve when an external benefit of $2 per pound exists can be drawn as follows:

To plot a social demand curve, we need to sum up the marginal private benefit of each unit of the good (which in this case is free garbage collection) with the marginal external benefit of each unit.

The marginal private benefit curve is already given.

The marginal external benefit is $2 per pound. Thus, the social demand curve is given as follows:

(d) The optimal level of garbage collection if the marginal cost of collecting garbage were constant at $6 per pound can be calculated as follows:

At equilibrium, marginal social benefit (MSB) = marginal social cost (MSC).

MSB = marginal private benefit (MPB) + marginal external benefit

(MEB) = P - 0.5 + 2 = P + 1.5MSC = marginal private cost (MPC) = $6Equating the two, we get:

P + 1.5 = $6P = $4.5At P = $4.5, Q = 30.

This is the optimal level of garbage collection using the social demand curve.

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The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.

The sample variance is a measure of how much the individual data points in a sample vary from the mean.

It is calculated by finding the average of the squared differences between each data point and the mean.

To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:

Calculate the mean (average) of the data set:

Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90

Subtract the mean from each data point and square the result:

(93 - 90)^2 = 9

(89 - 90)^2 = 1

(91 - 90)^2 = 1

(87 - 90)^2 = 9

(91 - 90)^2 = 1

(89 - 90)^2 = 1

Calculate the sum of the squared differences:

9 + 1 + 1 + 9 + 1 + 1 = 22

Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):

Variance = 22 / 5 = 4.4

It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.

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The numbers that will be chosen when Corey selects all of the numbers that are less than -5 but greater than -20 include -9, -11 and -15.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Based on the information, the inequality will be expressed as:

-20 < x < -5

In this case, the numbers have to be from -6 to -19. The numbers illustrated in the options are -9, -11 and -15.

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The height of the cylinder is approximately 2.93 cm.

We can use the formula for the volume of a cylinder which is given as:

V = π\(r^2h\)

where V is the volume, r is the radius of the circular base, h is the height of the cylinder and π is the mathematical constant pi.

We are given that the area of each base is 124 cm^2, which means that πr^2 = 124. Therefore, the radius of the circular base can be found as:

r^2 = 124/π

r ≈ 6.28 cm (rounded to 2 decimal places)

The volume of the cylinder is given as 116π \(cm^3\). Substituting the values of r and V in the formula, we get:

116π = π\((6.28)^2h\)

Simplifying the equation:

116 = \((6.28)^2h\)

h =\(116/(6.28)^2\)

h ≈ 2.93 cm (rounded to 2 decimal places)

Therefore, the height of the cylinder is approximately 2.93 cm.

In conclusion, we can find the height of a cylinder by using its volume and the area of its base by plugging the values in the formula for the volume of a cylinder. In this problem, the height of the cylinder is approximately 2.93 cm.

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Answer:

The answer is A

Step-by-step explanation:

Answer:

693

Step-by-step explanation:

find the square root of each

1 times 1 =1

8 times 8 =64

13 times 13 =169

18 times 18 is 324

no whole number for 693

Number of lollipops in the bag are 36.31 lollipops.

It is a number between 0 and 1 that describes the likelihood of a specific outcome, with 0 indicating that an event will not occur and 1 indicating that an event will certainly occur.

A probability of 0.5, for example, indicates that an event has a 50% chance of occurring. A probability of 0.2 indicates that an event has a 20% chance of occurring, and so on.

Probability can be expressed in several ways:

as a percentage, between 0% and 100%

as a ratio, such as 1:4

There are two types of probability:

Probability theory provides a framework for modeling various phenomena in the natural and social sciences, as well as in engineering and computer science. It is used in many fields such as finance, economics, statistics, and weather forecasting.

We know that the lollipops are 18.95 - 31% - 33% = 18.95 - .31 - .33 = 18.95 - .64 = 18.31 lollipops in the bag that are not apple flavored.

So 18.31 lollipops + 18 apple flavored lollipops = 18 + 18.31 = 36.31 lollipops in the bag.

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The lender's good faith estimate is D. the lender made a poor estimate; it was higher than 0.5% of the actual closing costs.

It should be noted that a lender simply means an individual or an organization that lends people money.

In this case, the lender's good faith estimate is that the lender made a poor estimate; it was higher than 0.5% of the actual closing costs.

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Answer:

It's

A: The lender made a very good estimate; it was within 0.25% of the actual closing costs.

Step-by-step explanation:

The answer will be .25 and .25 for both set of question. using probablity.

What is Probability ?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities.

Total number of students =1-juniors+chemistry+neither+both

(a) For both a junior and chemistry major =1/4 =. 25

(b) probability that she is also a chemistry major will be 1/4 =. 25

Hence The answer for the above two set of qustion will be .25 and .25.

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Up 8 Units, Hope this helps :)

SOLUTION

We want to calculate the amount of drug remaining in the blood stream at any given time

To do this we are told to use the formula

So, to get each we substitute the values 550 and each value of time t into the equation.

For t = 0 hours we have

Hence for t = 0, the answer is 550.000 to the nearest thousandth

Now for t = 1 hour, we have

Hence for t = 1 hour the answer is 400.983 to the nearest thousandth

Now, let us run this using the excel sheet

Now, we input the time(s) and the formula into the excel sheet, we have

After imputing the formula, next we set it to 3 decimal places, then we click and run

After doing this, here is the final answer to your question

Answer: Combine -2.4 + 3.4t

Step-by-step explanation:

First, rearrange the expression to group like terms:

−

3.6

+

1.2

−

1.9

t

+

5.1

t

(

−

3.6

+

1.2

)

+

(

−

1.9

t

+

5.1

t

)

Now, combine the like terms:

−

2.4

+

(

−

1.9

+

5.1

)

t

The simplified form of the expression (−3.6 − 1.9t + 1.2 + 5.1t) will be 3.2t – 2.4.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

The algebraic expression is given below.

⇒ −3.6 − 1.9t + 1.2 + 5.1t

The constant terms are added or subtracted with constant terms.

And the variable terms are added or subtracted with variable terms.

Then the expression will be

⇒ −2.4+ 3.2t

Thus, the simplified form of the expression (−3.6 − 1.9t + 1.2 + 5.1t) will be 3.2t – 2.4.

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Answer: they both have four sides (quadrilateral)

Step-by-step explanation:

Answer:

Quarderlaterals with reflecting (or parrel) sides of the same length.

Step-by-step explanation:

Squares always have 4 equal sides

Parrallegrams always have two sides that are parrel to each other that are the same lenghth.

Therefore, the probability that the bus will arrive tomorrow between 8:00 AM and 8:02 AM is 20%.

To find the probability that the bus will arrive tomorrow between 8:00 AM and 8:02 AM, we need to consider the time range during which the bus could arrive.

The bus always arrives between 8:00 AM and 8:10 AM, which means there are 10 minutes in total for the bus to arrive.

The desired time range is between 8:00 AM and 8:02 AM, which is a 2-minute interval.

To find the probability, we divide the desired time range (2 minutes) by the total time range (10 minutes):

Probability = Desired time range / Total time range

= 2 minutes / 10 minutes

= 1/5

= 0.2

= 20%

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The  probability that the sample mean would differ from the true mean by greater than 158 dollars if a sample of 226 persons is randomly selected is 0.99

mean per capita income is 19,695 dollars per annum , μ = 19695

a variance of 802,816, σ² = 802816

Standard deviation σ = √802816= 896

Sample size = 226

To find the probability that the sample mean would differ from the true mean by greater than 158 dollars i.e. less than 19537 dollars and more than 19853 dollars.

The formula for z-score :-

\(z = \frac{x - mean}{\frac{\alpha }{\sqrt{n} } } \\\)

For x = 19537 dollars

\(z = \frac{19537 - 19695}{\frac{\ 896 }{\sqrt{226} } } \\\)

z = -2.65

For x = 19853 dollars

\(z = \frac{19853 - 19695}{\frac{\ 896 }{\sqrt{226} } } \\\)

z = 2.65

The P-value=

P(z < -2.65) + P(z > 2.65 = 2P(z > 2.65) = 2x. 0.495975

= 0.99

Therefore, the  probability that the sample mean would differ from the true mean by greater than 158 dollars if a sample of 226 persons is randomly selected is 0.99

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They will lift the same weight (which is 26 kilograms) after one set.

Mason starts at 19kg bar and adds 7kg after each set, so after x sets, he will be lifting:

M(x) = 19 + 7*x

And Jack starts at 18kg, and after each set adds 8kg, then in this case the linear equation is:

J(x) = 18 + 8*x

They will lift the same weight when:

M(x) = J(x)

19 + 7*x =  18 + 8*x

19 - 18 = 8x - 7x

1 = x

So they will be lifting the same weight after one set, and that is:

J(1) = 18 + 8*1 = 26

26 kilograms.

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Answer:

x = -6

Step-by-step explanation:

Distribute the 2 into the brackets:

2x + 10 = -2

leave the 2x alone on one side:

2x = -2 -10

2x = -12

divide both sides by 2:

x = -6

Answer:

Hi po the answer is ab

Step-by-step explanation:

hope it help

Answer:

hope its help

Step-by-step explanation:

Answer:

So to get the length of the side of this cube you have to find the cube root of 216 . And that is 6.( Use the trick that you can learn on you tube to find out the cube root .)

So a cube has equal lengths width and heights . This means that each of the cube's six faces is a square . The total surface area is therefore six times the area of one face.. to work out one face area .you multiply one width by height . . In this case it is 6 X 6 = 36

36 cm squared. Is one cube face . Multiply this by 6 for each of the 6 faces. 36X6 = 216 cm2 . In this case volume is equal to surface area of once face x 6 .

Step-by-step explanation:

I'm not sure if i did right or not but i hope it helps

(a, b) = (1, 2) and (c, d) = (6, -6)

(a, b) = (2, 0) and (c, d) = (5, -4)

(a, b) = (3, -2) and (c, d) = (4, -2).

1) Note that since the adjacent angles in a parallelogram sum up to 180°, thus,

∠BDE = 180 -115 = 65°

∠DEC = 180 - 60 = 120°

Also:

∠BED = 60° (Angles on a straight line.)

Since we know ∠BDE and ∠BED, thus:
∠DBE = 180 - ∠BDE - ∠BED (Sum of Angles in a triangle)

∠DBE = 180 - 65 - 60

Thus:
∠DBE = x = 55°

2 )We know that the midpoint of the line segment joining (a, b) to (c, d) is (3.5, -2).

The midpoint formula is:

Midpoint = ((a+c)/2, (b+d)/2)

We can use this formula to create two equations based on the coordinates given:

3.5 = (a+c)/2 ---- (1)

-2 = (b+d)/2 ---- (2)

We have two equations with two variables (a, b, c, d). We can solve for one of the variables and then use that solution to find the other variables.

Let's solve equation (1) for c:

7 = a + c

c = 7 - a

Substitute c = 7 - a into equation (2):

-2 = (b+d)/2

-4 = b + d

d = -4 - b

So, we have found two expressions for c and d in terms of a and b:

c = 7 - a

d = -4 - b

Therefore, the possible coordinates for (a, b) and (c, d) are:

(a, b) = (1, 2) and (c, d) = (6, -6)

(a, b) = (2, 0) and (c, d) = (5, -4)

(a, b) = (3, -2) and (c, d) = (4, -2)

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a. The standard error of the mean can be calculated using the formula:

Standard Error of the Mean = standard deviation / square root of sample size.

In this example, the standard deviation is given as 80 minutes and the sample size is 40. Plugging these values into the formula:

Standard Error of the Mean = 80 / √40 ≈ 12.727

Therefore, the standard error of the mean in this example is approximately 12.727 minutes.

b. To find the likelihood that the sample mean is greater than 320 minutes, we need to calculate the z-score for this value and then find the corresponding probability from the z-table.

The formula for z-score is:

z = (x - μ) / (σ / √n)

In this case, x is the sample mean of 320 minutes, μ is the population mean (330 minutes), σ is the standard deviation (80 minutes), and n is the sample size (40).

Plugging in these values:

z = (320 - 330) / (80 / √40) ≈ -0.447

Now, referring to Appendix B1 for the z-values, we can find the corresponding probability. The z-value of -0.447 corresponds to a probability of approximately 0.3264.

Therefore, the likelihood that the sample mean is greater than 320 minutes is approximately 0.3264.

c. To find the likelihood that the sample mean is between 320 and 350 minutes, we need to calculate the z-scores for these values and then find the corresponding probabilities from the z-table.

Using the same formula as in part b, we can calculate the z-scores:

For 320 minutes:
z = (320 - 330) / (80 / √40) ≈ -0.447

For 350 minutes:
z = (350 - 330) / (80 / √40) ≈ 1.118

Referring to Appendix B1, the z-value of -0.447 corresponds to a probability of approximately 0.3264, and the z-value of 1.118 corresponds to a probability of approximately 0.8686.

To find the likelihood between these two values, we subtract the probability corresponding to the lower z-value from the probability corresponding to the higher z-value:

0.8686 - 0.3264 ≈ 0.5422

Therefore, the likelihood that the sample mean is between 320 and 350 minutes is approximately 0.5422.

d. To find the likelihood that the sample mean is greater than 350 minutes, we can use the z-score formula:

z = (x - μ) / (σ / √n)

Plugging in the values:
z = (350 - 330) / (80 / √40) ≈ 1.118

Referring to Appendix B1, the z-value of 1.118 corresponds to a probability of approximately 0.8686.

Therefore, the likelihood that the sample mean is greater than 350 minutes is approximately 0.8686.

e. In this example, we assume that the distribution of times for taxpayers to prepare, copy, and electronically file an income tax return follows a normal distribution. This assumption is based on the given statement that the distribution of times follows the normal distribution.

By assuming a normal distribution, we can use z-scores and the z-table to calculate probabilities and make inferences about the sample mean. However, it is important to note that this assumption may not hold true in all cases, and other statistical methods may need to be used if the data does not follow a normal distribution.

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Answer:

see explanation

Step-by-step explanation:

Solving

4x + 8 = 20 ( subtract 8 from both sides )

4x = 12 ( divide both sides by 4 )

x = 3

Each pack contains 3 paintbrushes

Answer:

x=3

Step-by-step explanation:

since the equation to use has already been given,you just have to group the like terms and solve for x

4x+8=20

4x=20-8

4x=12

then divide both sides by 4 in order to remain with x on one side

4x/4=12/4

x=3

each pack contains 3 paint brushes.

I hope this helps

Answer:

\(let \: the \: angle \: be \: \alpha \\ \tan( \alpha ) = \frac{p}{b} \\ \tan(16.8) = \frac{2.7}{x} \\ x = \frac{2.7}{0.30 } \\ x = 9 \\ now \: by \: using \: pythagoras \: theorem \: \\ h = \sqrt{p {}^{2} } + b {}^{2} \\ h = \sqrt{ {2.7}^{2} } + {9 }^{2} \\ h = 9.396\)