(a) Consider the differential equation -u"(x) = x in (0,1), (0) = u(1) = 0. (1) = (x-x), show that u(x) is a solution to (1).
(ii) Derive the weak formulation of problem (1) and show it is well posed, specify any forms and spaces introduced.
[You may use without proof the ld inequalities proved in lectures but must indicate clearly which inequality you are using when doing so.]

The dimensions of the wooden block are 14cm tall, 4cm long and 3 cm wide.

In three dimensional space prism is a polyhedron where two ends are similar.

Given that volume of rectangular prism is 168 cubic centimeters.

And the wooden block is 2x cm tall, (x-4) cm wide and (x-3) cm long.

And also given that a wooden block in a set of building blocks is a rectangular prism.

That means,

Volume of wooden block = Volume of rectangular prism = 168 cm³

Volume of wooden block ;

length × width × height = 168 cm³

Substituting given values in above expression,

2x (x-3) (x-4) = 168 cm³

2x (x²-7x + 12) = 168 cm³

2x³ - 14x²+ 24x = 168 cm³

Simplifying the above equation;

2x³ - 14x²+ 24x- 168 = 0

x³ - 7x²+ 12x- 84 = 0

The factor of above cubic equation is x = 7.

Now the 2x = 14 , x-3 = 4, x-4 = 3.

Therefore the dimensions of the wooden block are 14cm tall, 4cm long and 3 cm wide.

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To evaluate the integral S[(414) i + (7) j+ (5 + 3t) k] dt from 0 to 1, we can simply integrate each component of the vector separately with respect to t:

∫(0 to 1) (414) i dt = (414t)i evaluated from 0 to 1 = 414i

∫(0 to 1) (7) j dt = (7t)j evaluated from 0 to 1 = 7j

∫(0 to 1) (5 + 3t) k dt = (5t + 3/2 t^2)k evaluated from 0 to 1 = (5/2)k

Therefore, the value of the integral is:

S[(414) i + (7) j+ (5 + 3t) k] dt from 0 to 1 = 414i + 7j + (5/2)k

As for the second integral, S[(484) i + (7)]+(5t + 3) k] dt from 0 to 1, there seems to be a typo in the expression. The vector inside the integral has an unmatched parentheses, and it is unclear what the limits of integration are for each variable. If you could provide me with the corrected expression or more information about the integration limits, I would be happy to help you evaluate it.

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Answer:

200 miles I think

Step-by-step explanation:

80÷2=40

meaning 40 miles per hour, so 40×5=200

The amount that Josephine will be paid is $644.30.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.

In this situation, Josephine earns a salary of $560.00 per week, plus a commission of 10% on all sales and she sold $843 worth of goods.

The amount she'll be paid will be:

= $560 + (10% × $843)

= $560 + $84.3

= $644.30

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As per the standard deviation, the area of the shaded region is 0.7619 (option c).

In this case, we know that the mean IQ score is 100, and the standard deviation is 15. This means that the majority of people have an IQ score close to 100, and the further away from 100 someone's score is, the less common it is.

Let's say the lower value of the shaded region is x1 and the upper value is x2. We can find the z-scores for these values:

z1 = (x1 - 100) / 15

z2 = (x2 - 100) / 15

Without knowing the specific values of x1 and x2, we can't calculate the exact probability. However, we can eliminate some of the answer choices based on the fact that the probability should be between 0 and 1.

If one of the answer choices is greater than 1, we know that it's incorrect. Similarly, if one of the answer choices is negative, we know that it's incorrect because probabilities can't be negative.

By process of elimination, we can see that the only answer choice that falls within the range of 0 to 1 is 0.7619.

Therefore, the correct answer is option (c).

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Answer:

The answer to your problem is ↓

Part A: 110.8 feet

Part B: $77

Step-by-step explanation:

Calculation: Part A.

6.2 x 4 = 24.8 

24.8 x 2 = 49.6

4 x 3 = 12

12 x 2 = 24

6.2 x 3 = 18.6

18.6 x 2 = 37.2

49.6 + 24 + 37.2 = 110.8

Calculation: Part B.

Same as the beginning of Part A:

6.2 x 4 = 24.8 

24.8 x 2 = 49.6

4 x 3 = 12

12 x 2 = 24

6.2 x 3 = 18.6

49.6 + 24 + 18.6 = 92.2

92.2 x .83 = 76.526

We then need to round ‘ 76.526 ‘

Rounded = 77

Thus the answer to your problem is ↓

Part A: 110.8 feet

Part B: $77

Answer:

$76.526

Step-by-step explanation:

Front and back: length = 6.2 feet, width = 4 feet

Left and right: length = 3 feet, width = 4 feet

Top and bottom: length = 6.2 feet, width = 3 feet

The area of each face is:

Front and back: A = lw = (6.2)(4) = 24.8 square feet

Left and right: A = lw = (3)(4) = 12 square feet

Top and bottom: A = lw = (6.2)(3) = 18.6 square feet

The total surface area is the sum of the areas of all six faces:

SA = 2(24.8) + 2(12) + 2(18.6) SA = 49.6 + 24 + 37.2 SA = 110.8 square feet

Part B: To find the cost of covering the bench in ceramic tiles, we need to find the surface area of the bench excluding the bottom face that is on the ground. This is the same as the total surface area minus the area of the bottom face:

SA’ = SA - A(bottom) SA’ = 110.8 - 18.6 SA’ = 92.2 square feet

The cost of covering one square foot of the bench is $0.83, so the total cost is:

C = SA’ x $0.83 C = 92.2 x $0.83 C = $76.526

Rounding to the nearest cent, the cost is $76.53.

Received message. Part A: To find the total surface area of the bench, we need to find the area of each face of the rectangular prism and add them up. The formula for the area of a rectangle is A = lw, where l is the length and w is the width. The dimensions of the bench are 6.2 feet by 3 feet by 4 feet, so we can label the faces as follows: - Front and back: length = 6.2 feet, width = 4 feet - Left and right: length = 3 feet, width = 4 feet - Top and bottom: length = 6.2 feet, width = 3 feet The area of each face is: - Front and back: A = lw = (6.2)(4) = 24.8 square feet - Left and right: A = lw = (3)(4) = 12 square feet - Top and bottom: A = lw = (6.2)(3) = 18.6 square feet The total surface area is the sum of the areas of all six faces: SA = 2(24.8) + 2(12) + 2(18.6) SA = 49.6 + 24 + 37.2 SA = 110.8 square feet Part B: To find the cost of covering the bench in ceramic tiles, we need to find the surface area of the bench excluding the bottom face that is on the ground. This is the same as the total surface area minus the area of the bottom face: SA' = SA - A(bottom) SA' = 110.8 - 18.6 SA' = 92.2 square feet The cost of covering one square foot of the bench is $0.83, so the total cost is: C = SA' x $0.83 C = 92.2 x $0.83 C = $76.526 Rounding to the nearest cent, the cost is $76.53.

The required measure of the angle ∠spq of a rhombus is 110°.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
For rhombus,
m∠spr=(2x + 15)°
m∠qpr=(3x−5)°

And,
m∠spr = m∠qpr
2x + 15 = 3x - 5
x = 20

Now,
∠spq = m∠spr + m∠qpr
        = 2x + 15 + 3x - 5

        = 5x + 10
        = 5(20) + 10
        = 110°

Thus, the required measure of the angle ∠spq of a rhombus is 110°.

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Answer:

A

Step-by-step explanation:

Thats how the mean works lol

Answer:

For an experiment, the temperature of a liquid must stay above 60.4°F. The starting temperature of the liquid is 90.7°F. It is placed in a cooler, which lowers its temperature 3°F each minute.

How many minutes can the liquid can stay in the cooler?

Select from the drop-down menus to correctly complete the statement.

The liquid can stay in the cooler fewer than 10.1 minutes.

Step-by-step explanation:

A 25-meter-long towing vessel is pulling barges forward. The ship is required to display a minimum of two white masthead lights at night.

A commercial vessel that is pulling, pushing, hauling aboard, or any mixture of pulling, pressing, or hauling alongside, is referred to as a towing vessel.

Thus, a 25-meter-long towing vessel is pulling barges forward. The ship is required to display a minimum of two white masthead lights at night.

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Answer: 4.8

Step-by-step explanation: 268.8 divided by 56 is 4.8

Answer:  4(5z−2)

Step-by-step explanation: Brainliest pls

the third equation satisfies the value of m =18.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given the value of m and the need to find the equation that satisfies the value,

For equation 1

1) 2m + 36 = 58

Simplifying the equation:

=> 2m = 58 -36

=> 2m = 22

=> m = 11

For equation 2

2) 56m = 20m -36

Simplifying the equation:

=> 56 -20m = -36

=> 36m = -36

=> m = -1

For equation 3

3) 4m + 38 = 110

Simplifying the equation:

=> 4m = 72

=> m = 18

therefore, the third equation satisfies the value of m =18.

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Complete question:

which equation is true when the value of m is 18?

1) 2m + 36 = 58

2) 56m = 20m -36

3) 4m + 38 = 110

1. find equation of line with given data :

b) from the given table, we get y - intercept (c) = -4

now let's find slope (m) :

so, the required equation will be :

c) from the given graph we can see that y - intercept (c) = 3

now, let's find the slope (m) :

the equation will be :

d) From this graph we get y - intercept (c) = -4

slope :

so, required equation will be :

Answer:

Step-by-step explanation:

It is an arithmetic sequence with common difference d = -7

a₂₉ = a₄ + (29-4)d = -61 + 25(-7) = -236

32 can be written as product of factors 4 × 8 and 2 × 16

The factor of a number is a number that divides the given number completely without any remainder. The factors of a number can be positive or negative.

Given number

32

factoring 32

32 = 2 × 2 × 2 × 2 × 2

32 = 4 × 8

32 = 2 × 16

Hence, product of factors 4 × 8 and 2 × 16 is 32.

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Answer:

Where is the Box Plot

Step-by-step explanation:

Answer:

where did you repost

Step-by-step explanation:

where

The study aims to investigate anxiety levels in New York City after the pandemic, using a cross-sectional survey design, measuring anxiety through standardized questionnaires, considering demographic characteristics, and testing for significant differences among groups using appropriate statistical analyses.

To study anxiety in New York City after the pandemic, a suitable research design would be a cross-sectional survey or a longitudinal study. A cross-sectional survey involves collecting data at a specific point in time, while a longitudinal study would track changes in anxiety levels over an extended period.

To measure anxiety, commonly used tools include standardized questionnaires such as the Generalized Anxiety Disorder 7 (GAD-7) scale or the State-Trait Anxiety Inventory (STAI). These scales assess the severity and frequency of anxiety symptoms experienced by individuals.

When selecting demographic characteristics for inclusion in the study, it would be important to consider factors that could potentially influence anxiety levels. Relevant demographic variables may include age, gender, socioeconomic status, employment status, educational background, and any other factors known to impact mental health outcomes.

Null hypothesis: There is no significant difference in anxiety levels among different demographic groups in New York City after the pandemic.

Alternative hypothesis: There are significant differences in anxiety levels among different demographic groups in New York City after the pandemic.

To test these hypotheses, appropriate statistical analyses would depend on the research design and specific research questions. Some  possible statistical analyses could include:

Descriptive statistics: Calculate means, standard deviations, and frequency distributions to summarize anxiety levels and demographic characteristics.

Chi-square test: Assess the association between categorical demographic variables and anxiety levels.

Analysis of variance (ANOVA) or t-tests: Compare anxiety levels across different groups defined by continuous demographic variables (e.g., age, socioeconomic status).

Regression analysis: Examine the relationship between anxiety levels (dependent variable) and multiple demographic variables (independent variables) while controlling for potential confounding factors.

Structural equation modeling (SEM): Explore complex relationships between various demographic factors, anxiety levels, and potential mediators or moderators.

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Answer:

  (c)  two right triangles, each with both legs 40 inches long

Step-by-step explanation:

You want to know which pair of triangles are congruent, given their descriptions.

There are basically 4 theorems that allow you to claim congruence of triangles:

  AAS, ASA, SAS, SSS

A fifth one applies to right triangles only: HL.

These tell you that you need to have three matching parts: 3 sides, 2 sides and the angle between (except right triangle), or 1 side and 2 angles.

An isosceles triangle with only one or two sides defined is not sufficient.

A right triangle with only the hypotenuse defined is not sufficient.

A right triangle with two legs and the (right) angle between them has a sufficient number of matching parts to be able to claim congruence to another triangle similarly defined.

There were 13 small boxes shipped and 6 large boxes shipped.

Let's denote the number of small boxes as 's' and the number of large boxes as 'l'.

According to the given information, the volume of each small box is 6 cubic feet, so the total volume of all small boxes can be calculated as 6s cubic feet.

Similarly, the volume of each large box is 13 cubic feet, so the total volume of all large boxes can be calculated as 13l cubic feet.

We are also given that the combined volume of all the boxes is 156 cubic feet, so we can write the equation:

6s + 13l = 156 ...(1)

Additionally, we know that a total of 19 boxes were shipped, so we can write another equation:

s + l = 19 ...(2)

Now, we have a system of equations (equation 1 and equation 2) that we can solve simultaneously to find the values of 's' and 'l'.

To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method here.

From equation 2, we can rewrite it as s = 19 - l.

Substituting this value of s into equation 1, we get:

6(19 - l) + 13l = 156

Simplifying the equation:

114 - 6l + 13l = 156

Combining like terms:

7l = 42

Dividing both sides by 7:

l = 6

Now, we can substitute this value of l back into equation 2 to find the value of s:

s + 6 = 19

s = 13

The number of small boxes shipped is 13, and the number of large boxes shipped is 6.

There were 13 small boxes shipped and 6 large boxes shipped.

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Under the given transformation, the image of the set S = {(u, v) | 0 ≤ u ≤ 3, 0 ≤ v ≤ 2} is the set {(x, y) | 0 ≤ x ≤ 12, -2 ≤ y ≤ 3}.

To find the image of the set S under the given transformation, we substitute the bounds of S into the equations for x and y and determine the resulting range of values.

The set S is defined as {(u, v) | 0 ≤ u ≤ 3, 0 ≤ v ≤ 2}. We will find the image of each boundary point and then determine the range of values for the transformed set.

For u = 0 and v = 0:

x = 2(0) + 3(0) = 0

y = 0 - 0 = 0

The point (0, 0) is transformed to (0, 0).

For u = 3 and v = 0:

x = 2(3) + 3(0) = 6

y = 3 - 0 = 3

The point (3, 0) is transformed to (6, 3).

For u = 0 and v = 2:

x = 2(0) + 3(2) = 6

y = 0 - 2 = -2

The point (0, 2) is transformed to (6, -2).

For u = 3 and v = 2:

x = 2(3) + 3(2) = 12

y = 3 - 2 = 1

The point (3, 2) is transformed to (12, 1).

Now, let's consider the range of transformed points for the x and y coordinates.

For the x-coordinate, we observe that the minimum value is 0 (from point 1) and the maximum value is 12 (from point 4). Therefore, the range of x is [0, 12].

For the y-coordinate, we observe that the minimum value is -2 (from point 3) and the maximum value is 3 (from point 2). Therefore, the range of y is [-2, 3].

Combining the ranges of x and y, we have the image of set S as:

{(x, y) | 0 ≤ x ≤ 12, -2 ≤ y ≤ 3}

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Answer:

15.0721 quarts

Step-by-step explanation:

20 cups= 5.0721 quarts

10 quarts+5.0721=15.0721 quarts

if you need to convert the quarts just search 15.0721 quarts to whatever you need to convert it too.

hope this helps

To ensure the best test results, Anita should be provided with the following information before her spirometry:

1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.

2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.

3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.

4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.

The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.

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The total amount of profit from the Avocado Rolls is $1000.00, if the restaurant sold 100 orders of these in one day.

The profit from selling 4 Avocado Rolls for $12.00, with a cost of $2.00 to make each roll, is:

Profit per order = Selling price per order - Cost per order

Profit per order = $12.00 - $2.00

Profit per order = $10.00

Therefore, the total profit from selling 100 orders of Avocado Rolls would be:

Total profit = Profit per order x Number of orders

Total profit = $10.00 x 100

Total profit = $1000.00

Therefore, the total amount of profit from the Avocado Rolls is $1000.00.

Profit is the financial gain that a business or an individual makes after deducting all the expenses incurred to generate that gain. In other words, profit is the difference between the revenue earned from the sale of goods or services and the total costs or expenses associated with producing or delivering them.

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Answer:

8:16

7:14

Step-by-step explanation:

all equal to 1:2

Answer:

8:16

7:14

Step-by-step explanation:

5/10 = 1/2

8/16 = 1/2

7/14 = 1/2

Answer:

The evidence is not sufficient to suggest that the theft rate of Nissan Maxima cars are higher than national rate

Step-by-step explanation:

The number of cars that where reported stolen in 1999 = 2.2% = 0.022

The number of Nissan Maxima cars in the sample = 400

The number of Nissan Maxima cars that were reported stolen = 12

The level of significance, α = 0.05 level

The critical-z at 0.05 = 5% level = 1.645

The percentage of Nissan Maxima cars reported stolen, \(\hat p\) = 12/400×100  = 3%

The test statistic is given as follows;

\(z=\dfrac{\hat{p}-p_0}{\sqrt{\dfrac{p_0 \cdot (1 - p_0)}{n}}}\)

Therefore

\(z=\dfrac{0.03-0.022}{\sqrt{\dfrac{#0.022 \cdot (1 - #0.022)}{400}}} \approx 1.0908\)

The test statistic = 1.0908

The p-value P(Z > 1.0908) = 1 - P(Z > 1.0908) = 1 - 0.86214 = 0.13768

Given that the critical-z is larger than the absolute value of the test statistic, the given data is statistically insignificant, we fail to reject the null hypothesis

There is not enough statistical evidence to suggest that the theft rate of Nissan Maxima cars are higher than national rate.

Answer:

Step-by-step explanation:

   Number of candies that her sister gave = x

Total candies that Pam has now = 27

  x +  15 = 27

       x + 15 = 27

   x + 15 - 15 = 27 - 15

               x  = 12

Answer:

Equations :

27 - 15 = x

15 + x = 27

Step-by-step explanation:

So, we know that 1. Pam starts with 15 candies. and 2. Pam ends up having 27 candies. This means, that she gained candy.

To figure out how many candies her sister gave, her, we have to find the difference between 27 and 15 becuase she goes from having 15 to having 27 after her sister had given some.

x will represent how many cadies Pams' sister had given her :

27 -  15 = x

12 = x

This means Pams' sister gave 12 candies to Pam. To make sure we are correct, we can simply start with how many candies Pam started with (15). And add how many we think her sister added (12)

15 + 12

15 + 12 = 27

Therefore proving, and meaning, that Pams' sister gave her 12 candies.

Possible Equations :

27 - 15 = x

End total (27) minus starting total (15).

15 + x = 27

Starting total (15) plus how many she gained (x) equal to end total (27).

The measure of arc CD is 4x + 15, and that the measure of angle DEA is 120 degrees, we can use the fact that the sum of the measures of the arcs in a circle is equal to 360 degrees to solve for x.

Now we can write the equation:

(6x + 5) + (4x + 15) + 240 = 360

10x + 260 = 360

Subtracting 260 from both sides:

10x = 100

Dividing both sides by 10:

x = 10

The value of x is 10, the measure of arc CD is 55 degrees, and the measure of angle DEA is 120 degrees.

Given that the measure of arc AB is 6x + 5 and the measure of arc CD is 4x + 15, and that the measure of angle DEA is 120 degrees, we can use the fact that the sum of the measures of the arcs in a circle is equal to 360 degrees to solve for x.

Let's call the center of the circle E. Since DEA is a central angle, the measure of arc DE is equal to twice the measure of angle DEA, so arc DE has a measure of 2 * 120 = 240 degrees.

Now we can write the equation:

(6x + 5) + (4x + 15) + 240 = 360

Simplifying the left side:

10x + 260 = 360

Subtracting 260 from both sides:

10x = 100

Dividing both sides by 10:

x = 10

So the value of x is 10.

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