Help me please i need help

The function in variable w giving the cost C (in dollars) of constructing the box is C(w) = 30w² + 270/w. The result is obtained by using the formula of volume and area of the box.

We have a rectangular storage container without a lid.

The formula of volume of the box is

V = l × w × h

Where

So, the height is

10 = 2w × w × h

10 = 2w² × h

h = 10/2w²

h = 5/w²

To find the total cost, calculate the area of base and sides of the box!

See the picture in the attachment!

The base area is

A₁ = 2w × w = 2w² m²

The sides area is

A₂ = 2(2wh + wh)

A₂ = 2(3wh)

A₂ = 6wh

A₂ = 6w(5/w²)

A₂ = 30/w m²

The total cost is

C = $15(2w²) + $9(30/w)

C = $30w² + $270/w

The function of the total cost is

C(w) = 30w² + 270/w

Hence, the function of constructing the box is C(w) = 30w² + 270/w.

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The measure of angle ZCOD is 27°.

Since A, O, and B are collinear, angles AOC and COB form a linear pair, which means their sum is 180°. Therefore:

x + 50° = 180°

Solving for x, we get:

x = 130°

Next, we can use the fact that angles AOC and BOA are vertical angles, which means they are congruent. Therefore:

x = 103°

Substituting x with 130°, we get:

130° = 103° + COD

Solving for COD, we get:

COD = 27°

Finally, since angles AOD and COB are alternate interior angles, they are congruent. Therefore:

77° = 50° + ZCOD

Solving for ZCOD, we get:

ZCOD = 27°

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--The complete question is, Given that points A, O, and B are collinear, find the measure of angle ZCOD, where:

Angle AOC is denoted by x and measures 90°

Angle BOA measures 103°

Angle AOD measures 77°

Angle COB measures 50°.

Please note that point O is located between points A and B.--

Correlational research is concerned with examining relationships among variables. It focuses on understanding the associations or connections between different variables and how they relate to each other.

This type of research aims to explore the extent and direction of the relationship between variables without manipulating them.

In correlational research, researchers measure two or more variables and analyze their statistical relationship using techniques such as correlation analysis. The goal is to determine whether there is a positive or negative association between the variables, or if they are unrelated.

Correlational research does not involve establishing causation or determining differences between conditions, but rather focuses on understanding the patterns and strength of relationships between variables in order to identify potential associations or predict outcomes.

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Answer:

They would send 14 astronauts (two space shuttles) and the other  four astronauts will remain on Earth.

Step-by-step explanation:

18 divided into 7 would be 2 4/7... You would need three more astronauts to fill a third shuttle.

The simplified expression of the given expression is \(\frac{6\sqrt{10}}{7}$.\)

What is expression ?

An expression is a mathematical phrase that can contain numbers, variables, operators, and symbols. It can be a combination of terms, factors, and/or coefficients, and may involve addition, subtraction, multiplication, division, exponents, roots, and/or other mathematical operations. Expressions can be simplified, evaluated, or manipulated using algebraic rules and properties.

We can simplify the expression as follows:

\(\frac{\sqrt{40\cdot9}}{\sqrt{49}}=\frac{\sqrt{4\cdot10\cdot3\cdot3}}{\sqrt{7\cdot7}}\\ \\ \\=\frac{\sqrt{4}\cdot\sqrt{10}\cdot\sqrt{3}\cdot\sqrt{3}}{\sqrt{7}\cdot\sqrt{7}}\\ \\ \\=\frac{2\cdot3\sqrt{10}}{7}\\ \\ \\={\frac{6\sqrt{10}}{7}}.\)

Therefore, the simplified expression of the given expression is \(\frac{6\sqrt{10}}{7}$.\)

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The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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Based on the calculations, the sample standard deviation is equal to 4.

A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:

\(Z=\frac{\bar x\;-\;u}{\delta}\)

Where:

In Statistics, the standard deviation of a data sample is the square root of the variance and as such, this given by:

Note: Variance, δ² = 16

Taking the square root of the variance, we have:

Standard deviation, δ = √16

Standard deviation, δ = 4.

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Complete Question:

A sample of n=225 scores has \(\bar x\) = 103 and δ² = 16. What is the sample standard deviation?

As per the law of sine, the value of ∠ABC is 13°

Law of sine:

In math, the law of sine refers the relationship between the sides and angles of non-right (oblique) triangles.

Given,

Triangle ABC is drawn with AB = 3.6 units. BC = 4.2 units, and BCA = 28°. Here we need to find the measure of ∠ABC.

According to the law of sine, the given measures of the given triangle  are written as,

=> sin 28°/4.2 = sin x°/3.6

Apply the value of sin 28° = 0.27, then we get,

=> 0.27/4.2 = sin x/3.6

=> 0.972/4.2 = sin x

=> sin x = 0.2314

=> x = sin⁻¹(0.2314)

=> x = 13°

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Answer:

= 6x

Step-by-step Evaluation:

Evaluate for x=6

((−2)(−3))(6)

((−2)(−3))(6)

=36

(hope this helps you) :)

Answer:

64

Step-by-step explanation:

Hello, we can write this two digit number 'ab', a and b being positive integer between 0 and 9.

For instance , 54, a = 5 and b =4

The number can be written 10*a+b (54=5*10+4, for instance)

The sum of a two digit number is 10.

a + b = 10

The value of the number is 16 times the units digit.

10a + b = 16b <=> 10a = 16b - b = 15b

\(<=> a = \dfrac{15}{10}b=\dfrac{3}{2}b=\dfrac{3}{2}(10-a)=15-\dfrac{3}{2}a\\\\<=> \dfrac{2+3}{2}a = 15\\\\<=> 5a=30 <=> a = 6\)

and then, b = 10 - 6 = 4.

So the solution is 64.

Thank you

Answer:

tbh- you seem like you would be funny,nice, and pretty

Step-by-step explanation: Love ya ;)

Answer:

C

Step-by-step explanation:

12 /13   is definitely less than 36/30   because 36/30 =  1  1/5

Step-by-step explanation:

-1/4, -1/5, -1/6, -1/7, -1/8, 1/8, 1/7, 1/6, 1/5, 1/4

Answer:

The answer A

Step-by-step explanation:

The value of 2.50 represents the base amount Jeremiah must pay in order to secure the ride

Data;

To calculate the cost of the ride, we have an equation given as

\(p = 180x + 2.50\\\)

To solve this problem, all we need to do is to substitute the number of miles into the equation.

The value of 2.50 in the equation represents the minumum value you will have to pay for the ride.

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Answer:

A

Step-by-step explanation:

A = 9, 7, 5, -2, -6, -8

Therefore , the solution of the given problem of expressions function comes out to be  4x³ - 23x² + 44x - 9 + 117/(x-3)

Instead of generating estimates at random, variable it is better to use movable numbers, which can be growing, decreasing, or blocking. They could only help one another by sharing tools, information, or solutions to issues equation. An assertion of truth might include defenses, elements, and notations for mathematical operations like additional rejection, synthesis, and mixture.

Here,

=> 3 | 4  -11  28  -15  6

The first coefficient, (4), is then lowered to the lowest row:

=>   3 | 4  -11  28  -15  6

    4

    -----

The outcome is then entered in the following column after being multiplied by the constant term of the divisor (-3), as follows:

=>   3 | 4  -11  28  -15  6

    4  -12

    -----

The two values in the second column are then added:

=>   3 | 4  -11  28  -15  6

    4  -12  16

    -------- Adding the outcome to the value in the rightmost column after the result:

=>   3 | 4  -11  28  -15  6

    4  -12  16  -27

    -------------

       4  -23  44

The remainder is represented by the bottom row's final number (44) while the other numerals in the bottom row (The quotient's factors are (4, -23, and 44). (in descending order of degree).

Consequently, we can write:

=> 4x³ - 23x² + 44x - 9 + 117/(x-3)

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The value of a car that depreciates over time can be modeled by the function \(J(t)=27000(0.9)^{2t+2}\) has an equivalent form of \(J(t) = 21870(0.81)^t\).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

The value of the car is given as:

\(J(t)=27000(0.9)^{2t+2}\)

The equation can be written as:

\(J(t)=27000(0.9)^{2t} (0.9)^2\\\\J(t) = 27000(0.81)^t(0.81)\\\\J(t) = 21870(0.81)^t\)

Hence, the value of a car that depreciates over time can be modeled by the function \(J(t)=27000(0.9)^{2t+2}\) has an equivalent form of \(J(t) = 21870(0.81)^t\).

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Answer:

7.8

Step-by-step explanation:

because if you square 5 and 6 you get 25 and 36. Add them together and you get 61. Square 61 to get 7.8102... which you can round to 7.8

The equation to find the hypotenuse of a right triangle is a^2+b^2=c^2

Answer:

9-2 /10-2

7/8

4+3/5+3

7/8

fraction is 7/8

The given series is Σ(-1)^n (7n – 5)/(8n + 5) for n = 1 to infinity.
To apply the Alternating Series Test, we need to check if the series satisfies the following two conditions:
1) The terms of the series alternate in sign.
2) The absolute value of the terms decreases as n increases.

1) The given series alternates in sign because of the (-1)^n factor.
2) To check if the absolute value of the terms decreases as n increases, we can find the ratio of consecutive terms:

b_n = (7n – 5)/(8n + 5)
b_n+1 = (7(n+1) – 5)/(8(n+1) + 5)

So, b_n+1/b_n = [(7n+12)/(8n+13)] * [(8n+5)/(7n-5)]
= (56n^2 + 43n + 60)/(56n^2 - 41n - 65)

We can observe that the numerator is always greater than the denominator for n >= 1. Therefore, b_n+1/b_n < 1 for all n >= 1, which means that the absolute value of the terms decreases as n increases.

Since the series satisfies both conditions of the Alternating Series Test, we can conclude that the series converges.

To evaluate lim bn as n approaches infinity, we can use the fact that bn is a rational function of n. By dividing both numerator and denominator by n, we can write:

b_n = (7 - 5/n)/(8 + 5/n)

As n approaches infinity, both the numerator and denominator approach constants (7 and 8, respectively). Therefore, lim bn = 7/8.

So, the series Σ(-1)^n (7n – 5)/(8n + 5) converges to a limit of 7/8.

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Mathematical approaches to aggregate planning involve using quantitative methods to determine the optimal production and resource allocation strategies over a specified planning horizon. These approaches utilize mathematical models to optimize various factors such as production costs, inventory levels, and customer demand.

One mathematical approach to aggregate planning is linear programming, which formulates the planning problem as a linear optimization model. Linear programming considers constraints such as capacity limits, labor availability, and demand variability to find the best allocation of resources and production levels. The objective is to minimize costs or maximize profit while meeting demand requirements.

Another approach is the use of mathematical forecasting techniques to predict future demand. Time series analysis, regression analysis, and other statistical methods can be employed to forecast demand patterns. These forecasts serve as inputs to mathematical models, such as inventory control models or production planning models, which determine the optimal production levels and inventory policies based on the anticipated demand.

Simulation modeling is another mathematical approach where computer-based simulations are used to evaluate different scenarios and make decisions about production levels, inventory levels, and workforce scheduling. These models consider various factors like demand variability, production capacity, and resource availability to simulate the system's behavior and analyze the impact of different planning strategies.

Overall, mathematical approaches to aggregate planning provide a systematic and quantitative way to optimize production and resource allocation decisions, considering factors such as demand, capacity, costs, and constraints. These approaches help organizations make informed decisions to meet customer demand efficiently while minimizing costs and maximizing operational performance.

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Answer:

36

Step-by-step explanation:

divide then subtract

The dimensions of the rectangular enclosure for his garden is length of 7.5 m and width of 7.5 m.

Let x represent the length of the garden and y represent the width of the garden.

Perimeter = 2(x + y)

30 = 2(x + y)

x + y = 15

y = 15 - x

Area (A) = length * width

A = xy

A = x(15 - x)

A = 15x - x²

Maximum area is at dA/dx = 0:

dA/dx = 15 - 2x

0 = 15 - 2x

2x = 15

x = 7.5 m

y = 15 - x = 15 - 7.5 = 7.5 m

The dimensions of the rectangular enclosure for his garden is length of 7.5 m and width of 7.5 m.

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a) To graph the marginal utility of x, we need to find the derivative of the utility function with respect to x. Given that y=1, the utility function becomes U=x^(1/5). Taking the derivative of U with respect to x, we get dU/dx = (1/5)x^(-4/5). This represents the marginal utility of x.

When we graph the marginal utility of x, we put the marginal utility on the vertical axis and x on the horizontal axis. Since x^(-4/5) is positive for all positive values of x, the graph of the marginal utility of x will have a positive slope that decreases as x increases. The shape of the graph will resemble a downward-sloping curve that approaches zero as x approaches infinity.

b) The MRS (Marginal Rate of Substitution) for this consumer is the rate at which the consumer is willing to trade one good for another while keeping the total utility constant. In this case, the MRS is the negative ratio of the marginal utility of x to the marginal utility of y. Mathematically, MRS = -(dU/dx)/(dU/dy).

Since y is a constant and dU/dy = 0, the MRS simplifies to MRS = -(dU/dx)/0 = undefined. This means that the consumer is not willing to trade any amount of y for x, as the marginal utility of y is zero. The consumer only derives utility from x and does not value y in terms of marginal utility.

The graph of the marginal utility of x will have a positive slope that decreases as x increases. The MRS for this consumer is undefined, indicating that the consumer does not value y in terms of marginal utility.

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The expression at the upper and lower limits and the difference is

∫[0,1]√(4-3\(x^2\)) dx \(=(2 - (3/2)(1)^2) - (2 - (3/2)(0)^2) = (2 - 3/2) - (2 - 0) = (4/2 - 3/2) = 1/2.\)

To evaluate the integral ∫√(4-3\(x^2\)) dx, where the interval of integration is 0≤x≤1, we can use various techniques such as substitution or integration by parts. Let's proceed with the method of substitution to simplify the integral and find its value.

First, let's identify a suitable substitution for the integral. Since the expression inside the square root contains a quadratic term, it is beneficial to let u be equal to the square root of the quadratic expression. Therefore, we set u = √(4-3\(x^2\)).

Next, we need to find the differential of u with respect to x. Taking the derivative of both sides with respect to x, we have du/dx = (-6x)/(2√(4-3\(x^2\))) = -3x/√(4-3\(x^2\)).

Now, we can rewrite the integral in terms of the new variable u. Substituting u = √(4-3\(x^2\)) and du = (-3x/√(4-3\(x^2\))) dx into the integral, we have:

∫√(4-3\(x^2\)) dx = ∫u du

Our new integral is now much simpler, as it reduces to the integral of u with respect to u. Integrating u, we get:

∫u du = (1/2)\(u^2\) + C,

where C is the constant of integration.

Now, we can substitute back for u in terms of x. Recall that we set u = √(4-3x^2). Therefore, the final result becomes:

∫√(4-3x^2) dx = (1/2)(√\((4-3x^2))^2 + C = (1/2)(4-3x^2) + C = 2 - (3/2)x^2 + C.\)

To find the definite integral over the interval [0, 1], we need to evaluate the expression at the upper and lower limits and find the difference:

∫[0,1]√(4-3\(x^2\)) dx\(= (2 - (3/2)(1)^2) - (2 - (3/2)(0)^2) = (2 - 3/2) - (2 - 0) = (4/2 - 3/2) = 1/2.\)

Therefore, the value of the definite integral ∫√(4-3\(x^2\)) dx over the interval [0, 1] is 1/2.

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The total income produced by a continuous income stream in the first 15 year is $2000.

What is continuous income?

We can see the money flowing into the account continuously rather than in a lot of discrete payments if the deposits are made often enough and the intervals between deposits are short compared to the account's overall lifespan. This scenario will be referred to as a constant revenue stream.

The rate of flow is given by the following​ function is

f(t) = 2000

Where t is the time in year.

Putting t = 15 in the given function.

f(15) = 2000

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Complete Question
The complete Question is attached

Better yet, let y = 6 and solve for x.

6 = x^2 –2x + 5

Now solve for x.

The measure of tangent angle QIA is 180 degrees.

m/QIA = 180 degrees.

If IA is the diameter of the circle, it means that angle QIA is a right angle (90 degrees). Since QN is tangent to the circle at point I, it is perpendicular to the radius IA at that point.

Therefore, in triangle QIA, we have a right angle at Q and a right angle at I. This implies that angle IQA is also 90 degrees.

In a right triangle, the sum of the angles is 180 degrees. Since angles QIA and IQA are both right angles, the remaining angle in the triangle, angle QAI, must be:

180 degrees - 90 degrees - 90 degrees = 0 degrees

Angle QAI is a degenerate angle, which means it has a measure of 0 degrees. Therefore, the measure of tangent angle QIA is 180 degrees.

To summarize, m/QIA = 180 degrees.

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