-1/2 (4x - 18)= -(2x -34) I need help plz :)

The dimensions will be x = 7.5 cm and y = 7.5 cm where x is the side of the base and y is the height of the solid.

We are given that:

The solid has a square base.

So, the area of the base will be:

A = x²  ( where x = side of the square)

Also, it is a rectangular solid, so let the height be y.

Volume will be:

V = x² × y

V = x²y

The surface area is given as:

S = 337.5 cm²

x² + x² + xy + xy + xy+ xy = 337.5 cm²

2x² + 4 x y = 337.5 cm²

y = (337.5- 2 x²) / (4 x)

Plug into the equation of volume:

V = x² (337.5- 2 x²) / (4 x)

V = (337.5 x- 2 x³) / 4

Differentiate with respect to x:

V' = (337.5 - 6 x²) / 4

Put it equal to 0:

337.5 - 6 x² = 0

x² = 337.5 / 6

x = ±7.5

Dimension will be:

x = 7.5 cm ( as it cannot be negative)

y = 7.5 cm.

Therefore, the dimensions will be x = 7.5 cm and y = 7.5 cm where x is the side of the base and y is the height of the solid.

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Your question was incomplete. Please refer the content below:

A rectangular solid (with a square base) has a surface area of 337.5 square centimeters. Find the dimensions that will result in a solid with maximum volume.

We can create a committee with 2 women and 2 men in (D) 60 ways.

To find the number of ways to select 2 women out of 4, we can use the combination formula C(4, 2) = 4! / (2! * (4 - 2)!) = 6. Similarly, to select 2 men out of 5, we can use the combination formula C(5, 2) = 5! / (2! * (5 - 2)!) = 10. To find the total number of ways to create a committee with 2 women and 2 men, we need to multiply the number of ways to select women and men: 6 * 10 = 60.

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Answer:

c = 3

Step-by-step explanation:

12 divided by 4 is 3

Answer:

C= 3

Step-by-step explanation:

A boxplot is a visual display that provides information about the distribution of a dataset. When we want to determine the percentage of data that falls within a certain range, we need to look at the boxplot and find the interquartile range (IQR). The IQR is the difference between the first and third quartiles, which contains the middle 50% of the data. So, approximately 50% of the data lie between 4 and 8 hours.

A boxplot shows the median, quartiles, and possible outliers. To determine the percentage of data that falls between two values, we need to calculate the proportion of the IQR that corresponds to this range. For example, if the IQR is from 2 to 10, and we want to know the percentage of data between 4 and 8, we need to calculate the proportion of the IQR that corresponds to this range. This can be done by subtracting the lower value of the range from the upper value and dividing by the IQR:

Proportion = (8 - 4) / (10 - 2) = 4 / 8 = 0.5

Therefore, approximately 50% of the data lie between 4 and 8 hours. The answer is (C) about 50%.

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The minimal point does not have x = 0.

(a) Kuhn-Tucker conditions for the minimal value of fThe Kuhn-Tucker conditions are a set of necessary conditions for a point x* to be a minimum of a constrained optimization problem subject to inequality constraints. These conditions provide a way to find the optimal values of x1, x2, ..., xn that maximize or minimize a function f subject to a set of constraints. Let's first write down the Lagrangian: L(x, y, λ1, λ2, λ3) = f(x, y) - λ1(x+y-1) - λ2(xy-3) - λ3x - λ4y Where λ1, λ2, λ3, and λ4 are the Kuhn-Tucker multipliers associated with the constraints. Taking partial derivatives of L with respect to x, y, λ1, λ2, λ3, and λ4 and setting them equal to 0, we get the following set of equations: 4x - 2y - λ1 - λ2y - λ3 = 0 2y - 2x - λ1 - λ2x - λ4 = 0 x + y - 1 ≤ 0 xy - 3 ≤ 0 λ1 ≥ 0 λ2 ≥ 0 λ3 ≥ 0 λ4 ≥ 0 λ1(x + y - 1) = 0 λ2(xy - 3) = 0 From the complementary slackness condition, λ1(x + y - 1) = 0 and λ2(xy - 3) = 0. This implies that either λ1 = 0 or x + y - 1 = 0, and either λ2 = 0 or xy - 3 = 0. If λ1 > 0 and λ2 > 0, then x + y - 1 = 0 and xy - 3 = 0. If λ1 > 0 and λ2 = 0, then x + y - 1 = 0. If λ1 = 0 and λ2 > 0, then xy - 3 = 0. We now consider each case separately. Case 1: λ1 > 0 and λ2 > 0From λ1(x + y - 1) = 0 and λ2(xy - 3) = 0, we have the following possibilities: x + y - 1 = 0, xy - 3 ≤ 0 (i.e., xy = 3), λ1 > 0, λ2 > 0 x + y - 1 ≤ 0, xy - 3 = 0 (i.e., x = 3/y), λ1 > 0, λ2 > 0 x + y - 1 = 0, xy - 3 = 0 (i.e., x = y = √3), λ1 > 0, λ2 > 0 We can exclude the second case because it violates the constraint x, y ≥ 0. The first and third cases satisfy all the Kuhn-Tucker conditions, and we can check that they correspond to local minima of f subject to the constraints. For the first case, we have x = y = √3/2 and f(x, y) = -1/2. For the third case, we have x = y = √3 and f(x, y) = -2. Case 2: λ1 > 0 and λ2 = 0From λ1(x + y - 1) = 0, we have x + y - 1 = 0 (because λ1 > 0). From the first Kuhn-Tucker condition, we have 4x - 2y - λ1 = λ1y. Since λ1 > 0, we can solve for y to get y = (4x - λ1)/(2 + λ1). Substituting this into the constraint x + y - 1 = 0, we get x + (4x - λ1)/(2 + λ1) - 1 = 0. Solving for x, we get x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4. We can check that this satisfies all the Kuhn-Tucker conditions for λ1 > 0, and we can also check that it corresponds to a local minimum of f subject to the constraints. For this value of x, we have y = (4x - λ1)/(2 + λ1), and we can compute f(x, y) = -3/4 + (5λ1^2 + 4λ1 + 1)/(2(2 + λ1)^2). Case 3: λ1 = 0 and λ2 > 0From λ2(xy - 3) = 0, we have xy - 3 = 0 (because λ2 > 0). Substituting this into the constraint x + y - 1 ≥ 0, we get x + (3/x) - 1 ≥ 0. This implies that x^2 + (3 - x) - x ≥ 0, or equivalently, x^2 - x + 3 ≥ 0. The discriminant of this quadratic is negative, so it has no real roots. Therefore, there are no feasible solutions in this case. Case 4: λ1 = 0 and λ2 = 0From λ1(x + y - 1) = 0 and λ2(xy - 3) = 0, we have x + y - 1 ≤ 0 and xy - 3 ≤ 0. This implies that x, y > 0, and we can use the first and second Kuhn-Tucker conditions to get 4x - 2y = 0 2y - 2x = 0 x + y - 1 = 0 xy - 3 = 0 Solving these equations, we get x = y = √3 and f(x, y) = -2. (b) Show that the minimal point does not have x=0.To show that the minimal point does not have x=0, we need to find the optimal value of x that minimizes f subject to the constraints and show that x > 0. From the Kuhn-Tucker conditions, we know that the optimal value of x satisfies one of the following conditions: x = y = √3/2 (λ1 > 0, λ2 > 0) x = √3 (λ1 > 0, λ2 > 0) x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4 (λ1 > 0, λ2 = 0) If x = y = √3/2, then x > 0. If x = √3, then x > 0. If x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4, then x > 0 because λ1 ≥ 0.

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The phase change takes place when the temperature increases from -40°C to 0°C at 10 atm is solid-liquid change phase(melting).

Phase change refers to the process of a substance changing from one physical state to another, such as solid to liquid, liquid to gas, or solid to gas. These changes occur as a result of changes in temperature or pressure, and are characterized by changes in the physical properties of the substance, such as its volume, density, and viscosity.

Phase changes are classified into two types: physical and chemical. Physical phase changes involve a change in the physical state of a substance without any change in its chemical composition, such as the melting of ice to liquid water or the boiling of water to steam. Chemical phase changes, on the other hand, involve a change in the chemical composition of a substance, such as the formation of a chemical compound through a reaction.

The diagram you provided shows the phase diagram of carbon dioxide at a pressure of 10 atm. It shows that the melting point of solid carbon dioxide is -100°C and the boiling point of liquid carbon dioxide is -87°C.

When the temperature increases from -40°C to 0°C, the carbon dioxide is in the solid state at -40°C. As the temperature increases, it will reach the melting point of -100°C, causing a phase change from solid to liquid.

Therefore, the phase change that takes place when the temperature increases from -40°C to 0°C at 10 atm is a solid-liquid phase change, also known as melting.

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Pi is approximately 3.14 and is commonly used in academic equations.

The first 100 digits of pi are 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679

Answer:

5.76106287

Step-by-step explanation:

Answer: 5.76106287488

Step-by-step explanation:

Answer:

it 982y

Step-by-step explanation: the kid just do your work

Answer:

19.5km^2

Step-by-step explanation:

4500 times 6.5%

divide 292.5 by 15

then you get 19.5

Answer:

[-6,-3]

Step-by-step explanation:

So we have the compound inequality:

\(2x+7\leq x+4\leq 3x+16\)

Let's solve for each of the inequalities:

1)

We have:

\(2x+7\leq x+4\)

Subtract x from both sides:

\(x+7\leq 4\)

Subtract 7 from both sides:

\(x\leq -3\)

So that's one of our answers.

2)

We have:

\(x+4\leq 3x+16\)

Subtract 3x from both sides:

\(-2x+4\leq 16\)

Subtract 4 from both sides:

\(-2x\leq 12\)

Divide both sides by -2. Since we're dividing by a negative, flip the sign:

\(x\geq -6\)

Therefore, our entire answer is:

\(-6\leq x\leq -3\)

This means all values in between -3 and -6 including -3 and -6.

In interval notation, this is:

\([-6,-3]\)

So, A is -6.

And B is -3.

And we're done :)

In the analyze stage of the data life cycle, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations

The data life cycle is defined as the time period that that data exist in you system. Usually the data management experts finds the six or more stages in the data life cycle

The data analyst is the person who use the interpreted data and analyze the data in order to solve the problems

The analyze stage is the one of the main stages of the data life cycle. In the stage data analyst will use the spreadsheet to aggregate the data in the system and use the formulas to perform the calculations in the system

Therefore, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations

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The linear equation doesn't have a solution.

The linear equation given is illustrated as: 4x-(2x-1) = x+5+x-6

This will be solved thus:

4x - 2x + 1 = x+5+x-6

4x - 2x + 1 = 2x - 1.

2x + 1 = 2x - 1

Collect like terms

2x - 2x = -1 - 1

0 = -2

This illustrates that the equation doesn't have a solution.

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Mia would have to work 26.1 hours (approx. 26) to earn $124.00

4.75x=124

divide 4.75 by 4.75 and divide 124 by 4.75

x=26.1

Answer: (x-6)2 + (y+3)2=4

Step-by-step explanation:

I’m smart like dat cuh

The answer is (x-6)^2+(y+3)^2=4

The cubic polynomial interpolation function for the given data using different methods is as follows:

Polynomial Coefficient Interpolation Method: p(x) = -1x³ + 4x² - 2x - 8

Newton Interpolation Method: p(x) = -8 + 6(x+1) - 4(x+1)(x-0) + 2(x+1)(x-0)(x-2)

Lagrange Interpolation Method: p(x) = -4((x-0)(x-2)(x-3))/((-1-0)(-1-2)(-1-3)) - 8((x+1)(x-2)(x-3))/((0-(-1))(0-2)(0-3)) + 2((x+1)(x-0)(x-3))/((2-(-1))(2-0)(2-3)) + 28((x+1)(x-0)(x-2))/((3-(-1))(3-0)(3-2))

Polynomial Coefficient Interpolation Method: In this method, we find the coefficients of the polynomial directly. By substituting the given data points into the polynomial equation, we can solve for the coefficients. Using this method, the cubic polynomial interpolation function is p(x) = -1x³ + 4x² - 2x - 8.

Newton Interpolation Method: This method involves constructing a divided difference table to determine the coefficients of the polynomial. The divided differences are calculated based on the given data points. Using this method, the cubic polynomial interpolation function is p(x) = -8 + 6(x+1) - 4(x+1)(x-0) + 2(x+1)(x-0)(x-2).

Lagrange Interpolation Method: This method uses the Lagrange basis polynomials to construct the interpolation function. Each basis polynomial is multiplied by its corresponding function value and summed to obtain the final interpolation function. The Lagrange basis polynomials are calculated based on the given data points. Using this method, the cubic polynomial interpolation function is p(x) = -4((x-0)(x-2)(x-3))/((-1-0)(-1-2)(-1-3)) - 8((x+1)(x-2)(x-3))/((0-(-1))(0-2)(0-3)) + 2((x+1)(x-0)(x-3))/((2-(-1))(2-0)(2-3)) + 28((x+1)(x-0)(x-2))/((3-(-1))(3-0)(3-2)).

These interpolation methods provide different ways to approximate a function based on a limited set of data points. The resulting polynomial functions can be used to estimate function values at intermediate points within the given data range.

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The height of the curve for a given value of x is closely related to the probability of an observation falling in an interval around x.

The height of the curve, also known as the probability density function (PDF), represents the relative likelihood of different values occurring in a distribution. In probability theory, the area under the curve within a specific interval represents the probability of an observation falling within that interval.

Therefore, the height of the curve at a particular value of x reflects the probability of an observation being close to that value.

The concept of the PDF and its relationship to probability is fundamental in statistical analysis. By examining the height of the curve at different points, we can assess the likelihood of observing specific values or ranges of values.

This information is crucial for making inferences, estimating probabilities, and conducting hypothesis testing in various fields such as finance, biology, and social sciences.

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Step-by-step explanation:

In set a, every element in the domain has only 1 image in the range. This is called a one-to-one correspondence.

However in set b, there is a many-to-one correspondence as more than 1 element in the domain has the same image.

The application rate is 3 (per DM$).

The given below table shows the monthly production volume, direct materials, direct labor, and manufacturing overheads for the past three months at Gizzard Wizard (GW):

Month Prod. Volume DM ($)DL ($)MOH ($)May 1000$400.00$600.00$1200.00

June 400160.00240.00480.00

July 1600640.00960.001920.00

By using DM$ to apply overhead, we have to find the application rate. We know that the total amount of manufacturing overheads is calculated by adding the cost of indirect materials, indirect labor, and other manufacturing costs to the direct costs. The formula for calculating the application rate is as follows:

Application rate (per DM$) = Total MOH cost / Total DM$ cost

Let's calculate the total cost of DM$ and MOH:$ Total DM$ cost = $400.00 + $160.00 + $640.00 = $1200.00$

Total MOH cost = $1200.00 + $480.00 + $1920.00 = $3600.00

Now, let's calculate the application rate:Application rate (per DM$) = Total MOH cost / Total DM$ cost= $3600.00 / $1200.00= 3

Therefore, the application rate is 3 (per DM$).

Hence, the required answer is "The application rate for GW is 3 (per DM$)."

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If a 10-year-old can perform the same tasks as the average 15-year-old, then the child's "mental age" is 15, and their "IQ" is 150.

The concept of mental age, introduced by Alfred Binet, refers to an individual's level of cognitive functioning compared to others in their age group. It is a measure of intellectual development. In this case, the 10-year-old's mental age is considered to be 15 because they can perform tasks typically expected of a 15-year-old.

IQ (Intelligence Quotient) is a standardized measure of intelligence. It is calculated by dividing an individual's mental age by their chronological age and multiplying it by 100. In this scenario, if the 10-year-old's mental age is 15, their IQ would be 150 (15/10 * 100 = 150).

Therefore, the child's mental age is 15, and their IQ is 150.

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Robert's rowing rate in still water is 8 miles per hour, and the speed of the current is 2 miles per hour.

Let's start by assuming that the rate of the current is c, and Robert's rowing rate in still water is r. As a result, the following equation can be used to determine the rate of travel downstream:24 = (r + c) × 3

This equation can be simplified by dividing both sides by 3 and then subtracting c from both sides, giving:8 - c = r

Then, to figure out Robert's speed upstream, we'll use the following equation:2r - 4c = 24

Multiplying the first equation by 2 and then subtracting it from the second equation yields:

2r - 4c

= 24 - 2r - 2c-4c

= -3r + 12-3r = -4c + 12

Dividing both sides by -3, we obtain

:r = (4c - 12)/3Substituting this into the first equation:

24 = (4c - 12)/3 + cMultiplying both sides by 3 and then simplifying:

72 = 4c - 12 + 3c7c

= 84c = 12Therefore, the rate of the current is 2 miles per hour, and Robert's rowing rate in still water is 8 miles per hour.

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Answer:

Just for fun, the probability of rolling a die 60 times and getting no ones is

(600)(5/6)60=0.0018% .

Step-by-step explanation:

This 10 ones is the value with the highest probability of occurring. It has a probability of  (6010)(1/6)10∗(5/6)50≈13.7% .

Answer:

300 pretty sure

Step-by-step explanation:

Answer:

alternate interior angles

Step-by-step explanation:

They are on opposite sides of the line and they are equal to each other

Answer:

Below

Step-by-step explanation:

 b2 = 3 * b1    <===given

Area of a trapezoid =    (b1 + b2)/2    *   height      b1 and b2 are the bases

     32         =   (b1 + 3 b1)  / 2    *  4

               32 = 4b1 /2 * 4

                  32 = 8 b1

                   4 = b1    then b2 = three times this = 12 ft

Answer: sqrt(2)/2  which is choice D

======================================================

Explanation

(3pi/4) radians converts to 135 degrees after multiplying by the conversion factor (180/pi).

The angle 135 degrees is in quadrant 2. We subtract the angle 135 from 180 to find the reference angle

180-135 = 45

Then you can use a 45-45-90 triangle to determine that the ratio of opposite over hypotenuse is sqrt(2)/2

sine is positive in quadrant 2

------------

Alternatively, you can use a unit circle. Refer to the diagram below. In red, I've circled the angle 3pi/4 radians. The terminal point for this angle has a y coordinate of sqrt(2)/2

Recall that y = sin(theta).

The inference that in this age group, women are at greater risk of developing asthma is incorrect, as the study only provides information on the prevalence of asthma in men and women and does not establish causality or risk.

The inference that women are at greater risk of developing asthma cannot be made solely based on the information given in the statement. While the prevalence of asthma is higher among women (9 per 100) than among men (6 per 100), additional statistical analyses such as calculating relative risks or conducting hypothesis tests are required to determine if this difference is statistically significant and to establish a causal relationship between gender and asthma.

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Answer:

Radius =21,  height = 45  
Lateral Surface Area = \(5937.61\) cm²
Total Surface Area = \(8708.49\)  cm²

Radius = 28, height =28
Lateral Surface Area =  \(4926.01\) cm²

Total Surface Area  =  \(9852.03\) cm²

Step-by-step explanation:

If r is the radius of a cylinder with height h

Lateral surface area

\(L = 2\pi rh\)

Top and bottom surface area for each which is a circle is \(\pi r^2\)

So total bottom and top surface area = \(2 \pi r^2\)

Total surface area =

\(2\pi rh + 2\pi r^2 = 2\pi r(h + r)\)

For r = 21, h = 45
\(L = 2 \pi \cdot 21 \cdot 45 = 1890 \pi = 5937.61 \;cm^2\)

\(T = 2\pi \cdot 21 (21 + 45) = 2772 \pi = 8708.4948\;cm^2\)

For r = 28, h = 28

\(L = 1568\pi = 4926.01 cm^2\)

\(T = 3136\pi = 9852.03 \;cm^2\)

Answer:

D

Step-by-step explanation:

1/2 is the same as square root

the square of 8 is 2 root 2

then x squared is 2

and y is 2

16 is to the power of 1/4 is 2