You need to make a scale model of your room for your art class. the scale is
3/4
inch represents 1 foot. what are the dimensions of your model?

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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The second container can hold approximately 1715 m³ of liquid.

Two containers have exactly the same shape, we can use their height ratio to determine the liquid capacity ratio.

Let's denote the height of the first container as H1 = 20 m and its liquid capacity as C1 = 320 m³.

We want to find the liquid capacity of the second container, C2, given its height H2 = 35 m.

The ratio of the heights is H2 / H1 = 35 m / 20 m = 7/4.

The ratio of the liquid capacities is equal to the ratio of the volumes, since the containers have the same shape. Therefore, we have:

C2 / C1 = (H2 / H1)³

Substituting the given values:

C2 / 320 m³ = (7/4)³

Simplifying the exponent:

C2 / 320 m³ = 343 / 64

To find C2, we can cross-multiply:

C2 = (343 / 64) × 320 m³

Calculating the result:

C2 ≈ 1715 m³

Therefore, the second container can hold approximately 1715 m³ of liquid.

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The question is incomplete the complete question is :

two containers are used to hold liquid. these containers have exactly the same shape. the first container has a height of 20 m, and it can hold 320 m³ of liquid. if the second container has a height of 35 m, how much liquid can it hold?

Answer:

Step-by-step explanation:

Nov 9, 2017

f'(x)=x2−5/2

Explanation:

y=√2x+5

First, we switch the

xs and ys to get

x=√2y+5

\(x^{2}\)

Now, we must rearrange to make y the subject:

x2=(√2y+5)2=2y+5

x2−5=2y

y=x2−52

Sensitivity analysis is performed in order to see how certain changes affect the optimal solution.

It is a tool used to analyze how variations in inputs to a mathematical model will impact the output or outcome. This helps decision-makers to better understand the robustness of their solutions, and identify the most critical inputs or parameters that affect the solution. In other words, sensitivity analysis helps to evaluate the impact of uncertainty or changes in the model on the optimal solution. It can also help to identify the range of values that the input variables can take without significantly affecting the optimal solution.
This analysis method involves adjusting key variables or parameters within a model to understand their impact on the final outcome. By conducting sensitivity analysis, decision-makers can identify the most critical factors in a problem and better understand the robustness of the optimal solution. By exploring the effects of varying inputs, it helps in assessing the risks and making informed decisions, ensuring the model's reliability and stability even when faced with uncertain or changing conditions.

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Answer:

The formula to find the area of a rectangle is l * w

Answer:

A=wl

Step-by-step explanation:

The equation for the area of a rectangle is length multiplied by width. I do not think your question is complete. I hope I've helped, please comment below if you have anything to add or any questions.

Multiply each payout by the corresponding probability and take the total:

E[X] = 0×0.5 + 5×0.2 + 8×0.15 + 10×0.1 + 15×0.05 = 3.95

The expected value = 3.92

"It describes the average of a discrete set of variables based on their associated probabilities."

\(E(x)=\Sigma[ xP(x)]\)

Multiply each value of the random variable by its probability and add the products.

For given question,

We have been given a payout probability distribution.

We need to find the expected value of the winnings.

First we multiply each value of the random variable by its probability .

0 × 0.5 = 0

5 × 0.2 = 1

8 × 0.15 = 1.2

10 × 0.1 = 1

15 × 0.05 = 0.75

Now, we find the sum of above products.

0 + 1 + 1.2 + 1 + 0.75 = 3.95

By using the formula of expected value,

\(\Rightarrow E(x)=\Sigma[ xP(x)]\\\\\Rightarrow E(x)=3.92\)

Therefore, the expected value = 3.92

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mean price for a theatre ticket in New York is $ 50.299

Mean can be expressed as the total sum of observations for the total number of observations.

In other words its the sum by the count

It gives the average measure of each entity.

The mean Price is sometimes called Average Price.

Total number of Tickets = 11.7 million

Total Cost = $588.5 million

Mean Price = Total Cost / Total Number of Tickets

= 588.5 million / 11.7 million

= $ 50.299

mean price for a theatre ticket in New York is $ 50.299

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Answer:

-5

Step-by-step explanation:

25-3x=40

3x=25-40

3x=-15

x=-15/3

x=-5

Answer:

=−5

Step-by-step explanation:

1. Rearrange terms

25−3=40

−3+25=40

2. Subtract 25 from both sides of the equation

−3+25=40

−3+25−25=40−25

3. Simplify

If you subtract the numbers

−3=15

4. Divide both sides of the equation by the same term

−3=15

−3÷-3=15÷-3

5. Simplify

If you divide the numbers

=−5

And thats the answer

I hope this helped     :)

Answer:

11/20 is less than

Step-by-step explanation:

Since 11/20 is a fraction and 1 is a whole number.

The correct statement is "Each point on the​ least-squares regression line represents the predicted y-value at the corresponding value of x". Thus, Option C is correct.

A least-squares regression line is a mathematical model that is used to predict the value of a dependent variable (y) based on the value of an independent variable (x). The regression line is created by fitting a line to the data set that minimizes the differences between the actual y-values and the predicted y-values (the line).

Each point on the regression line represents the predicted y-value for a given value of x. In other words, if we know the value of x, we can use the regression line to predict the value of y that is most likely to occur based on the data set. The least-squares regression line is a useful tool for understanding the relationship between two variables and making predictions about future values.

A is incorrect because it states that each point on the least-squares regression line represents the actual y-value of the data set at that corresponding value of x, which is not necessarily the case. The regression line is a model that predicts y-values based on the relationship between x and y, but it is not necessarily equal to the actual y-values in the data set.

B is incorrect because it states that each point on the least-squares regression line represents the ideal y-values at that corresponding value of x, which is not a characteristic of a regression line. A regression line represents a predicted y-value based on the data set and the relationship between x and y, but it does not necessarily represent ideal values.

D is incorrect because it states that each point on the least-squares regression line represents one of the points in the data set, which is not necessarily the case. A regression line represents a predicted y-value based on the data set and the relationship between x and y, and it may not necessarily match the actual data points in the data set.

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Answer:

62?

Step-by-step explanation:

I just subtracted 76 and 14, I don't know if i'm right

Answer:

3x-2

Step-by-step explanation:

JL = JM - LM

= 5x-8 - (2x-6)

= 5x-8 -2x+6

= 5x-2x -8+6

= 3x-2

Answer:

A

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Remember, a radical is the same thing as an exponent, but as a fraction. Therefore, instead of taking the 12th of the root, you can put \(8^4\) to the 12th power like this: \((8^4)^{\frac{1}{12} }\)

The two exponents can multiply together, so now it'll be \(8^{\frac{4}{12} }\) which is \(8^{\frac{1}{3} }\) when reduced

\(8^{\frac{1}{3} }\) is the same thing as \(\sqrt[3]{8}\)

Now, think about which number, when multiplied by itself 3 times is equal to 8... that number is 2--your answer

Answer:

2

Step-by-step explanation:

make it simple.. use a scientific calculator.

= ¹²√8⁴

= ¹²√4096

= 2

The given equation is a vertical parabola in standard form. To find the focus and directrix, we first need to determine the vertex.

The vertex is (0, -2). The focus is located at a distance of p units vertically above the vertex, where p is the distance from the vertex to the focus. In this case, p = 2. So the focus is at (0, 0). The directrix is located p units vertically below the vertex.

Therefore, the directrix is the horizontal line y = -4. The answer is (b) 2004-06-02-06-00 files/  directrix: 2004-06-02-06-00 files/ .

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Answer:

C. Yes, there is an outlier at 110. This means that one person's age was 110, which is 25 years older than the next closest age.

Step-by-step explanation:

An outlier is a data point that sticks out like a sore thumb. It's so different from the rest of the data that it makes you wonder if it's a mistake or a miracle. One way to spot an outlier is to use the 1.5IQR rule, where IQR stands for interquartile range. The interquartile range is the gap between the third quartile (Q3) and the first quartile (Q1) of the data. The 1.5IQR rule says that any data point that is more than 1.5*IQR above Q3 or below Q1 is an outlier.

In this case, the first quartile (Q1) is 75, the third quartile (Q3) is 85, and the interquartile range (IQR) is 10. So, any data point that is more than 1.5*10 = 15 above 85 or below 75 is an outlier. The only data point that does this is 110, which is 25 above 85. That means 110 is an outlier.

What does this outlier mean in this situation? It means that one person who came to the senior center that afternoon was way older than the rest of the folks. The average age of the visitors was not changed by this outlier, since it was just one out of 12 data points. But, the outlier does mess up the range and the standard deviation of the data, making them bigger than they would be without the outlier.

Answer:The answer is C

Step-by-step explanation:I did the test.

Answer:

slope= 2/3 & y intercept= -2

Step-by-step explanation:

to find the slope:

3y-2x= -6

or, slope= -( coefficient of x)/(coefficient of y)

= -(-2)/3

=2/3

to find the y intercept:

3y=2x-6

or, for X=0

3y= -6

or, y= -2

F. M⁻¹ s⁻¹

D. M⁻¹

If the reaction is first order in A, the rate law is rate = k[A], where k is the rate constant. Since the rate of the reaction is 1.6 x 10⁻³ M/s and the concentration of A is 0.11 M, we can find the value of the rate constant by plugging in the given values:

1.6 x 10⁻³ M/s = k(0.11 M)

Solving for k:

k = (1.6 x 10⁻³ M/s) / (0.11 M) = 14.55 x 10⁻⁴ s⁻¹

So the rate constant for a first order reaction in A is 14.55 x 10⁻⁴ s⁻¹.

If the reaction is second order in A, the rate law is rate = k[A]², where k is the rate constant. Since the rate of the reaction is 1.6 x 10⁻³ M/s and the concentration of A is 0.11 M, we can find the value of the rate constant by plugging in the given values:

1.6 x 10⁻³ M/s = k(0.11 M)²

Solving for k:

k = (1.6 x 10⁻³ M/s) / (0.11 M)² = 0.1395 x 10⁻³ M⁻¹ s⁻¹

So the rate constant for a second order reaction in A is 0.1395 x 10⁻³M⁻¹ s⁻¹.

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Given that the discharge current decreases to 27% of its initial value in 1.40 ms, we can use the equation of discharge current:

The capacitance of the capacitor is 0 F.

Part A:

Given that the discharge current decreases to 27% of its initial value in 1.40 ms, we can use the equation of discharge current:

I = I₀e^(-t/RC)

Here,

I₀ = initial current

R = resistance

C = capacitance

t = time

We are given that the current is 27% of the initial value, so the equation becomes:

0.27 = \(1e^(-1.40*10^-3/RC)\)

Simplifying the equation, we find:

RC =\(3.28* 10^-3 s\)   ----(1)

Part B:

The time taken to discharge a capacitor through a resistance R is given by:

t = RC ln (Vc/V₀)

where Vc = voltage across the capacitor at time t and V₀ = initial voltage across the capacitor.

Substituting the values, we have:

\(1.40*10^-3\) = C*90 ln (0/100)

Since a fully discharged capacitor has a voltage of 0, we set Vc = 0. Thus, the equation becomes:

\(1.40*10^-3\)= C*90 ln (0)

The natural logarithm of 0 is negative infinity. Therefore, the equation becomes:

\(1.40*10^-3\)= C*90*(-infinity)

Simplifying further, we find:

C = 0

Thus, the value of capacitance is 0 F.

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Answer:

24 A-(8+8)

Step-by-step explanation:

Answer: 4(6a-4) This is one equivalent expression of 24a-16.

The least expensive C.A.R.S. that can be built to those specifications has dimensions of approximately 4.3088 m x 2.1544 m x 1.7321 m and will cost about $265.47 to build.

Let's start by looking at the dimensions of the base. We know that the length of the base is twice its width. Let's represent the width of the base as "x." This means that the length of the base is "2x." The area of the base is simply the product of the length and the width, which is 2x * x = 2x².

Next, let's look at the dimensions of the sides. The height of the box is going to be represented by "h." The length of each side is going to be equal to the length of the base, which we already know is 2x. The width of each side is going to be equal to the width of the base, which is just x. So the area of each side is simply 2hx.

Now we can use the formula for the volume of a rectangular prism to find the value of "h" in terms of "x." The volume of the box is given as 10 m^3, so:

V = lwh = (2x)(x)(h) = 10

Simplifying this equation, we get:

2x²h = 10

Solving for "h," we get:

h = 5/x²

Now that we have an expression for "h" in terms of "x," we can use it to find the total surface area of the box, which is the sum of the area of the base and the area of the four sides. We can then use this expression to find the minimum cost for a given volume of the box.

The total surface area of the box is given by:

A = 2x² + 4(2hx)

Substituting the expression we found for "h" into this equation, we get:

A = 2x² + 4(2x)(5/x²)

Simplifying this equation, we get:

A = 2x² + 40/x

Now we can take the derivative of this expression with respect to "x" and set it equal to zero to find the value of "x" that will minimize the cost of the box. Differentiating and setting equal to zero, we get:

dA/dx = 4x - 40/x² = 0

Solving for "x," we get:

x^3 = 10

Taking the cube root of both sides, we get:

x ≈ 2.1544

Now we can use this value of "x" to find the dimensions of the least expensive C.A.R.S. that can be built to those specifications. The length of the base is twice the width, so:

Length = 2x ≈ 4.3088

Width = x ≈ 2.1544

Height = 5/x² ≈ 1.7321

So the dimensions of the least expensive C.A.R.S. that can be built to those specifications are approximately: Length = 4.3088 m Width = 2.1544 m Height = 1.7321 m

These dimensions will allow us to build a C.A.R.S. with a volume of 10 m^3, while using the least amount of material possible, which means that the cost will be minimized. We can verify this by calculating the total surface area of the box and the cost of the materials needed.

The total surface area of the box can be calculated by substituting the values we found for "x" and "h" into the expression we derived earlier:

A = 2(2.1544)² + 4(2)(5)/(2.1544)² ≈ 28.2742 m²

Now we can calculate the cost of the materials needed to build the box:

Cost = (Area of base)(Cost per square meter for base) + (Area of sides)(Cost per square meter for sides)

Cost = (2.1544²)(10) + (28.2742 - 2(2.1544²))(6) ≈ $265.47

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Answer:

498 m

Step-by-step explanation:

The AAA theorem states that triangles are similar if all three corresponding angles are equal.

1. Compare triangles FHS and ILS

(a) Reason for similarity

∠F = ∠I = 90°

∠S is common.

∴ ∠H = ∠L

(b) Calculate SL

\(\begin{array}{rcl}\dfrac{SF}{SH} & = & \dfrac{SI}{SL}\\\\\dfrac{225}{380} & = & \dfrac{225 + 475}{SL}\\\\225SL & = & 380 \times 700\\& = & 266000\\SL & = & \textbf{1182 m}\\\end{array}\)

2. Compare triangles ILS and GLE

(a) Reason for similarity

∠I = ∠G = 90°

∠L is common.

∴ ∠S = ∠E

(b) Calculate LE

\(\begin{array}{rcl}\dfrac{IS}{GE} & = & \dfrac{LS}{LE}\\\\\dfrac{700}{180} & = & \dfrac{1182}{LE}\\\\700LE & = & 180 \times 1182\\& = & 212800\\LE & = & \textbf{304.0 m}\\\end{array}\)

3. Calculate EH

               LE + EH + HS = LS

304.0 m + EH + 380 m = 1182 m

                  EH + 684 m = 1182 m

                                 EH = 498 m

The distance from E to H is 498 m.

Answer:

8

24

3

yes

Step-by-step explanation:

the original area of the figure is  4 · 2 which equals 8.

Since the dilation that is needing to be done is by a scale factor of 3 then all we need to do is multiply the original area by 3, which gives us the new area 24.

So because the only transformation was a dilation that didn't significantly change the figure then we can say that both figures are similar.

The 8 painters will take 12 hours and 9.6 minutes to paint the office. The result is obtained by comparing the two variables, worker and time duration.

If the they work at the same rate, find the time needed for the 8 painters to finish their job!

Let's say

We convert the unit of time in hours.

t₁ = 7 h 36 min

t₁ = (7 + 36/60) h

t₁ = (7 + 0.6) h

t₁ = 7.6 hours

If they work at the same rate, the number of workers and time durations of each day are directly proportional. So,

w₁/w₂ = t₁/t₂

5/8 = 7.6/t₂

t₂ = 8/5 × 7.6

t₂ = 12.16 hours

In hours and minutes,

t₂ = 12 h + (0.16 × 60) min

t₂ = 12 h 9.6 min

Hence, to paint the office, the 8 painters will take 12 hours and 9.6 minutes.

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Answer: $47,000 at 10% annually is ≈ $77,297.70 and $47,000 at 5% monthly is ≈ $569,611.01

Step-by-step explanation:

Use the compound interest formula. A=P(1+r/n)^nt

Answer:

Step-by-step explanation:

Answer: 6

there are 24 fish and 4 tanks so divide 24 by 4 and you'll have 6

Answer:

the number of fish in each tank is 6

Step-by-step explanation:

becuause 24 divided be 4 is 6

Answer:

Step-by-step explanation:

For an expression to be a polynomial term, it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions.

so, C part is correct

Answer:

To create a linear model that represents the amount of fuel on the plane as a function of flight time, we can use the given information that the jet can travel 14,430 kilometers before needing to refuel. We also know that the flight from Los Angeles to Melbourne is 16 hours long. Therefore, we can use the ratio of the distances traveled in 18 hours and 16 hours to estimate the amount of fuel that would be left on the plane after 18 hours of flight.

The ratio of the distances traveled is:

18 hours / 16 hours = 1.125

This means that the jet would have traveled 1.125 times the distance it travels in 16 hours by the time 18 hours has passed. So, the distance traveled in 18 hours would be:

14,430 km × 1.125 ≈ 16,241 km

Now, we can use a proportion to find the amount of fuel left on the plane after 18 hours:

63,500 gallons / 14,430 km = x gallons / 16,241 km

Solving for x, we get:

x ≈ 71,270 gallons

Therefore, the linear model that represents the amount of fuel on the plane as a function of flight time, in hours, is:

fuel (in gallons) = -265.6 × time (in hours) + 134,800

This equation was obtained by fitting a linear regression model to the given data, where the fuel is the dependent variable and the time is the independent variable. The negative slope of the line (-265.6) indicates that as the flight time increases, the amount of fuel on the plane decreases. The intercept of the line (134,800) represents the amount of fuel on the plane at the start of the flight.

Answer:

You're in a hurry so no explaining

x = 4 and y = -5 ( here)

Hope this helped

Hope this helped All the best!!

The correct standard form for the given LP model is option C: Max(Z) = 3x1 + 2x2, subject to the constraints 11x1 + 3x2 - 5 <= 33, 8x1 + 5x2 + 5 >= 40, and 7x1 + 10x2 + 5 >= 70, with x1, x2 >= 0. This option aligns with the original objective function and constraints of the LP model.

To convert the LP model into standard form, we need to rewrite the constraints with the variables on the left-hand side and constants on the right-hand side, with inequality signs (<= or >=) consistent throughout. Additionally, we introduce slack or surplus variables to transform any non-standard constraints.

In option C, the constraints are correctly transformed as 11x1 + 3x2 - 5 = 33, 8x1 + 5x2 + 5 >= 40, and 7x1 + 10x2 + 5 >= 70. These constraints are consistent with the original model. The objective function remains the same, Max(Z) = 3x1 + 2x2.

Option A has incorrect signs in the transformed constraints, and option B introduces surplus variables (+5) instead of slack variables (-5), resulting in an incorrect standard form. Option D includes a non-standard term with a dollar sign, which is inconsistent with linear programming conventions.

Therefore, option C is the correct standard form, adhering to the original LP model's objective function and constraints.

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