expand the following

x(3x-2)​

For the utility function U(x, y) = \((x^4)/(y^4)\), we can derive the indifference curve equations by setting the utility function equal to the given values U = 1, U = 2, and U = 3.

1. When U = 1:

  \((x^4)/(y^4) = 1\)

 \(x^4 = y^4\)

  Taking the fourth root of both sides, we get:

  x = y

2. When U = 2:

  \((x^4)/(y^4) = 2\)

  \(x^4 = 2y^4\)

  \(x = (2^(1/4)) * y\)

3. When U = 3:

  \((x^4)/(y^4) = 3\)

  \(x^4 = 3y^4\)

  \(x = (3^(1/4)) * y\)

The indifference curves for this utility function are shaped like a rectangular hyperbola, where the ratio of x to y remains constant along each curve.

(b) For the utility function U(x, y) = y - 2x, the indifference curves can be derived by setting the utility function equal to the given values U = 1, U = 2, and U = 3.

1. When U = 1:

  y - 2x = 1

  y = 2x + 1

2. When U = 2:

  y - 2x = 2

  y = 2x + 2

3. When U = 3:

  y - 2x = 3

  y = 2x + 3

The indifference curves for this utility function are straight lines with a slope of 2. They have a positive slope, indicating a positive marginal rate of substitution between x and y.

(c) Both utility functions satisfy completeness, transitivity, and monotonicity.

1. Completeness: The preferences are complete if, for any two bundles of goods, the consumer can compare and rank them. Both utility functions provide a ranking of bundles based on their utility values, indicating completeness.

2. Transitivity: Transitivity implies that if bundle A is preferred to bundle B, and bundle B is preferred to bundle C, then bundle A must be preferred to bundle C. Both utility functions satisfy this assumption.

3. Monotonicity: Monotonicity assumes that more is better. If a bundle has higher quantities of both goods compared to another bundle, it should be preferred. Both utility functions satisfy this assumption as well.

The violations of these assumptions would affect the shape and properties of the indifference curves. For example, if completeness is violated, there may be some bundles that cannot be compared or ranked, resulting in incomplete indifference curves.

If transitivity is violated, there may be cycles of preferences, leading to inconsistent indifference curves. If monotonicity is violated, the indifference curves may not have a consistent upward slope. However, in the case of the given utility functions, all assumptions are satisfied, allowing for well-defined indifference curves.

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Answer:

17C5+11C5

Step-by-step explanation:

Well there are 17 and chooses 5 that's 17C5

there are 11 men abd chooses 5 that's 11C5

so add them up

17C5+11C5

The combination helps us to know the number of ways an object can be selected without a particular manner. The number of ways in which 5 men and 5 women can be selected is 2,858,856.

Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.

The combination helps us to know the number of ways an object can be selected without a particular manner. A combination is denoted by 'C'.

\(^nC_r = \dfrac{n!}{(n-r)!r!}\ , \ \ ^nP_r = \dfrac{n!}{(n-r)!}\)

where,

n is the number of choices available,

r is the choices to be made.

Given that from a group of 17 women and 11 men, a researcher wants to randomly select 5 women and 5 men for a study.

Now, the number of ways for selection can be written as,

Number of ways in which men can be selected = ¹¹C₅ = 462

Number of ways in which women can be selected = ¹⁷C₅ = 6188

Further, the number of ways for selection can be written as,

Number of ways = Number of ways in which men can be selected × Number of ways in which women can be selected

Number of ways = 462 × 6188

Number of ways = 2,858,856

Hence, the number of ways in which 5 men and 5 women can be selected is 2,858,856.

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Answer:

1 is the closest to 28/31

Step-by-step explanation:

0 is technically 28 spaces away and 1/2 is around 13 spaces away but 1 is only 3. :)

Answer:

y = 20x

Step-by-step explanation:

Using the process of elimination, it definitely cannot be A. B was in consideration until realising that the height is proportional to time therefore B was incorrect. C was also wrong as 180/9 = 20 not 90 leaving D as the correct option.

Answer:

0.5(5 × 10) - 1

Step-by-step explanation:

((5 × 10) × 0.5) - 1

((50) × 0.5) - 1

25 - 1

24

The amount of mortar needed for the cmu wall is 27.21 cubic feet of mortar.

To determine the amount of mortar needed for the cmu wall which is 907 square feet, the number of cubic feet of mortar per 100 square feet of wall must be converted to cubic feet of mortar per 1 square foot of wall. This is done by dividing the given number of cubic feet of mortar per 100 square feet of wall (3.0) by 100.

Therefore, the number of cubic feet of mortar per 1 square foot of wall is 0.03. Now, to find the number of cfm of mortar needed for the 907 sq ft cmu wall, multiply the number of cfm of mortar per 1 sqft of wall (0.03) by the sqft of wall (907). Therefore, the amount of mortar needed for the cmu wall which is 907 square feet is 0.03 x 907 = 27.21 cubic feet of mortar.

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9514 1404 393

Answer:

  b.  slope: 2; y-intercept: -20

Step-by-step explanation:

The y-intercept is the first point in the table, where x=0. That eliminates choices A and D.

The slope is the difference in y divided by the difference in x. Using the first and second points in the table, this is ...

  (-10 -(-20))/(5 -0) = 10/5 = 2

The slope is 2; the y-intercept is -20.

Answer:

$450

Step-by-step explanation:

The volume of the given composite shape formed with a combination of cone & rectangular prism in cubic feet is 880 cubic feet and approximately cubic inches is 1,520,640 in3.

Various solid figures or shapes have various volumes. We have investigated a variety of three-dimensionally specified solids and shapes, such as cubes, cuboids, cylinders, cones, etc. A shape created from two or more basic shapes is referred to as a composite, compound, or complicated shape. Any three-dimensional shape, figure, or solid's volume is simply the quantity of space it occupies or contains. By finding the product of the dimensions we can calculate the volume of a solid or 3D figure. The measurement units are cubic units. These solids can be of various shapes like cube, cuboid also called rectangular prism, cone, cylinder, sphere , hemishphere, frustum, etc.

Volume of cone = \(\frac{\pi\ r^2h}{3}\)

Volume of cuboid=L.W.H

Given that the solid shape is made up of cone & cuboid(also called rectangular prism)

Volume of solid= volume of cone+volume of rectangular prism

Given dimensions:

Cone:radius(r) = 8 ft

         height(h) = 12 ft

Cuboid: Length(L) = 8 ft

            Width(W) = 7 ft

            Height(H) = 2 ft

Given that π = 3

Volume of solid =  \(\frac{\pi\ r^2h}{3}\) + L.W.H

                          =  \(\frac{3(8^2)(12)}{3} +8(7)(2)\)

                         = 64(12) + 56(2)

                         = 768 + 112

                         = 880

Volume of solid=880 cubic feet.

We know that 1 foot = 12 inches, & 1 cu. ft = 12x12x12 cu. inches

on converting volume into inches we get:

Volume of solid = 880 x 12 x 12 x 12 cubic inches

                          = 1,520,640 cu. inches.

Volume of solid is 1,520,640 in3

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The rate of the river current is 5 mph.
Let x represent the rate of the river current. When Kellen travels upstream, she goes against the current, so her effective speed will be (15 - x) mph. When she travels downstream, she goes with the current, so her effective speed will be (15 + x) mph.

We're given that the time it takes to travel 2 miles upstream is the same as the time it takes to travel 4 miles downstream. We can express time as distance divided by speed.

So, we have the equation:

(2 mi) / (15 - x) = (4 mi) / (15 + x)

Now, we need to solve for x:

Cross-multiply:

2(15 + x) = 4(15 - x)

Distribute:

30 + 2x = 60 - 4x

Add 4x to both sides:

6x = 30

Divide by 6:

x = 5

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The distance from the origin to the line is 0.

To derive the formula for the distance from a point P to a line using the cross product property, let's consider a line represented by a vector equation as L: r = a + t * b, where r is a position vector on the line, a is a known point on the line, b is the direction vector of the line, and t is a parameter.

Now, let's consider a vector connecting a point P to a point Q on the line, given by the vector PQ: PQ = r - P.

The distance between the point P and the line L can be represented as the length of the perpendicular line segment from P to the line. This line segment is orthogonal (perpendicular) to the direction vector b of the line.

Using the cross product property |u x v| = |u| |v| sinθ, where u and v are vectors, θ is the angle between them, and |u x v| represents the magnitude of their cross product, we can determine the distance d as follows:

d = |PQ x b| / |b|

Now, let's compute the cross product PQ x b:

PQ = r - P = (a + t * b) - P

PQ x b = [(a + t * b) - P] x b

= (a + t * b) x b - P x b

= a x b + t * (b x b) - P x b

= a x b - P x b (since b x b = 0)

Taking the magnitude of both sides:

|PQ x b| = |a x b - P x b|

Finally, substituting this result into the formula for d:

d = |a x b - P x b| / |b|

This gives us the formula for the distance from a point P to a line.

To find the distance from the origin to the line, we can choose a point on the line (a) and the direction vector of the line (b) to substitute into the formula. Let's assume the origin O (0, 0, 0) as the point P, and let a = (x₁, y₁, z₁) be a point on the line. We also need to determine the direction vector b.

Using the given information, we can find the direction vector b by subtracting the coordinates of the origin from the coordinates of point a:

b = a - O = (x₁, y₁, z₁) - (0, 0, 0) = (x₁, y₁, z₁)

Now, we can substitute the values into the formula:

d = |a x b - P x b| / |b|

= |(x₁, y₁, z₁) x (x₁, y₁, z₁) - (0, 0, 0) x (x₁, y₁, z₁)| / |(x₁, y₁, z₁)|

= |0 - (0, 0, 0)| / |(x₁, y₁, z₁)|

= |0| / |(x₁, y₁, z₁)|

= 0 / |(x₁, y₁, z₁)|

= 0

Therefore, the distance from the origin to the line is 0. This implies that the origin lies on the line itself.

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Answer:

1: 41

2: 85

3: 95

4: 85

5: 36

6: 49

7: 106

The average is the arithmetic mean of all the observations of a set of numbers. The number of times Brandon rolls above the average is 7.

The average is the arithmetic mean of all the observations of a set of numbers. it is found by dividing the sum of all the observations of the set by the number of observations in the set.

\(\rm{Average=\dfrac{Sum\ of\ observations}{Number\ of\ observations}\)

In order to know the number of times Brandon rolls the dice above the average, we first need to calculate the average of the twenty rolls.

The average of the 20 times dice rolls,

\(\rm Average = \dfrac{6+1+3+4+4+4+6+5+5+3+6+4+4+5+2+3+5+4+4+2}{20}\)

\(\rm Average = \dfrac{80}{20} = 4\)

Thus, the average of the 20 rolls of the dice is 4.

Now, the number of times the result of the dice roll is above 4(x>4) is 7.

Hence, the number of times Brandon rolls above the average is 7.

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Answer:

Step-by-step explanation:

Answer:

B. DX = YZ

Step-by-step explanation:

Answer:

x = 36

Step-by-step explanation:

the numbers are both multiplied by 3

Answer:

a translation left 6 units and up 4 units

Answer:

Step-by-step explanation:

The figures are congruent, so all you need do is pick 1 point from each figure and tell what it does. I'm going to go from Figure J to figure K

I will pick the point (-4,8) on J. It is the furthest point upwards.

Where is that same point on K? It is at (2,4)

So what happened?

You've moved from -4 to 2 on the x value.

You've moved from 8 to 4 on the y value

You moved right (-4 to 2) = 6 units and

down (8 - 4) = 4 units

What would happen if you went from K to J

This time you have moved 6 units left and 4 units up.

Answer:

Since the length of the drawing is 200 ft. and equivalent to 13.33 in. with a scale of 15 ft to 1 in. and the length of the paper is 11 in., Adoncia's drawing will not fit on the sheet of paper

Step-by-step explanation:

The given parameters are;

The scale of the drawing is 15 ft = 1 in.

The actual dimensions of the monument;

Height = 80 ft.

Length = 200 ft.

Therefore, we have;

The required dimension of the paper height = 80/15 = 16/3 = 5.33 in.

The required dimension of the paper length = 200/15 = 40/3 = 13.33 in.

The given paper dimension by 11 in. which is of a dimension of that of a standard  letter paper size of 8.5 in. by 11 in.

Drawing length, 13.33 in. > Paper length > 11 in.

Adoncia's drawing will not fit on the sheet of paper.

The equation has a single z-intercept at x = -3.In conclusion, the correct answer is: No x-intercepts

To determine the z-intercepts of the function y = -2x^2 - 12x - 18, we need to find the values of x where the function intersects the z-axis, which corresponds to the y-coordinate being zero.

Setting y = 0, we have:

0 = -2x^2 - 12x - 18

Now, let's solve this quadratic equation for x.

-2x^2 - 12x - 18 = 0

Dividing both sides by -2 to simplify the equation, we get:

x^2 + 6x + 9 = 0

This equation can be factored as:

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

The factor (x + 3) appears twice, indicating a repeated root.

Therefore, the equation has a single z-intercept at x = -3.

In conclusion, the correct answer is:

• No x-intercepts

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The barrier measures about 27.8 feet in length, according to the provided statement.

The Pythagorean Theorem is crucial to mathematics. Although you'll likely hear about it for your initial time in algebra, you'll actually use it in all subsequent math classes, including precalculus, calculus, geometry, and trigonometry.

The Pythagorean formula can be used to determine how long the vertical barrier is. According to the Pythagorean theorem, the square for the dimension of the hypotenuse, the longest side in a right triangle, is equivalent to the total of the squares of the remaining two sides.

In this case, the length and width of the garden form the two legs of a right triangle, and the diagonal fence is the hypotenuse. So we have:

Length of hypotenuse² = Length² + Width²

Substituting the given values, we get:

Length of hypotenuse² = 22² + 17²

Length of hypotenuse² = 484 + 289

Length of hypotenuse² = 773

Length of hypotenuse = √(773)

Using a calculator or simplifying by hand, we get:

Length of hypotenuse ≈ 27.8 feet

Therefore, the length of the fence is approximately 27.8 feet.

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Answer:

yes

Step-by-step explanation:

You have the correct intercepts

Step-by-step explanation:

When someone receives a "pay raise", that means that their income/salary increases.

Jerold earns $865 in one week. He receives a 25% pay raise. That means his income has increased by 25% of what he currently earns in one week. We can calculate the percentage of something by converting that percent into a decimal and multiplying it with the value that percent is being applied to.

We can do this two ways.

The first way, we can convert 25% into 0.25, and multiply that with 865:

0.25 × 865 = 216.25

Then, we add $216.25 to Jerold's old salary, $865:

$865 + $216.25 = $1081.25

The second way does everything in one step. When you multiply a number by 1, you always get that same number for the answer.

1 × 33 = 33, 1 × 382 = 382...

So, instead of multiplying by 0.25 and then adding that to Jerold's old salary, we can multiply by 1.25 instead (1, his original salary, + 0.25, the difference between his old and new salary),.

1.25 × $865 = $1081.25.

You can use either method to calculate the answer, but the second method is more efficient.

The required equation model to determine the new weekly pay rate is x = 865[1 + 25%] or x = 865[1.25].

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Jerold's weekly pay rate is $865. He receives a 25% pay raise.
Let the new weekly pay rate be x,
According to the question,
x = 865 + 25% of 865
x = 865[1  + 25%]
x = 865[1.25]
x = $1081.25

Thus, the required equation model to determine the new weekly pay rate is x = 865[1 + 25%] or x = 865[1.25].

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A chemical element's atom is a particular type of particle of substance. A positively charged electron or many negatively charged electrons encircle the central nucleus of an atom.

Electrons: If an electron leaves an atom, it is said to be ionized. Ionization can occur through various processes, such as collision with another particle or exposure to electromagnetic radiation.

Protons: Protons are found in the nucleus of an atom, and are held in place by the strong nuclear force. If a proton were to leave the nucleus, it would no longer be a stable atom and it would become an ion.

Neutrons: Neutrons are also found in the nucleus of an atom and are held in place by the strong nuclear force. If a neutron were to leave the nucleus, it would no longer be a stable atom, and it would become a different element.

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Let the three consecutive even number be,

x, x+2, x+4

Sum of the numbers is 1002.

Hence, the numbers are,

332, 332+2, 332+4

Hence, the answer is 332, 334, 336.

Since the proposed side length of the square is between 6 and 7, we can assume that it is 6.5 hence, the lengths will be d = 6.5 and c = 9.19.

Here is what we were given:

Side length of square = 6 > x <7

A convenient assumption for this is 6.5

We also know that d and c and the base of two right triangles. where their hypotheses' are equal to the side lenght of the square = 6.5

we also know that the in between the line formed by D and C is a 90 degree angle.

Hence the sum of the other angle will be 45 degrees each.

This is  based on sum of angles in a triangle.

Hence,

c = b /sin(β)

= 6.5/sin (45)

= 6.5/0.70710678118

 c = 9.19

d = √c² - b²

 = √(9.19238815542512² - 6.52²)

= √42.25

d = 6.5

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The sum of interior Angles of Hexagon is always 720°

Any hexagon's internal angles add up to 720° in all cases. By dividing 720° by 6, we may get the size of each interior angle of a regular hexagon. As a result, we have:

720°÷6 = 120°

In a regular hexagon, each inside angle is 120°.

An example of a regular hexagon with equal-length sides and angles is shown in the diagram below. By multiplying the six 120° angles together, we can demonstrate that the result is 720°.

Therefore, the interior angles of a hexagon are always added up to 720°.

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Answer:

13w+4 or 4+13w

Step-by-step explanation:

w is the same as one then it will be 4+w(1)+12w =12w+w(1)=13w

4 over here does not have friend therefore it renains to be 4 =13w+ 4

a)  Ideal assignment, each power shovel should be assigned one truck at all times. b) Minimum Five trucks are required to avoid idle time for the power shovel. c) The cost of operating each truck can be minimized to $0.62 per minute. d) Five trucks should be assigned to the power shovel to minimize the cost per truck load hauled.

The ideal assignment of trucks to the power shovel is to have one truck assigned to the power shovel at all times, so that as soon as one truck is loaded, it can immediately be replaced by another truck, and there is no waiting time for the power shovel. so, three trucks should be assigned to each power shovel.

To prevent idle time for the power shovel, we need to have a truck arrive as soon as the previous truck has been loaded and left. Therefore, the minimum number of trucks required is equal to the cycle time divided by the time to load a truck:

Cycle time = time to load + travel time + dumping time + return time = 4 + 8 + 4 + 3 = 19 minutes

Minimum number of trucks = cycle time / time to load a truck = 19 / 4 = 4.75

Since we cannot have a fractional number of trucks, we need to round up to the nearest integer. Therefore, the minimum number of trucks required is 5.

The cost of operating the power shovel is $25 per hour, which is equivalent to $0.42 per minute (since there are 60 minutes in an hour). The cost of operating each truck is $37 per hour, which is equivalent to $0.62 per minute.

To minimize the cost per truck load hauled, we need to find the optimal number of trucks to assign to the power shovel. Let's assume that x trucks are assigned to the power shovel. Then, the total cost per truck load hauled is given by:

Total cost = (cost per power shovel minute) * (cycle time) + (cost per truck minute) * (time to load + travel time + return time) / x

Substituting the values we calculated earlier:

Total cost = (0.42) * (19) + (0.62) * (4 + 8 + 3) / x

Total cost = 8.88 + 1.56 / x

To minimize the total cost, we need to find the value of x that minimizes this expression. Taking the derivative of the expression with respect to x and setting it equal to zero, we get:

d(Total cost) / dx = -1.56 / x^2 = 0

x^2 = 1.56 / 0

x = ∞

Since we cannot assign an infinite number of trucks to the power shovel, this means that the total cost is minimized when we assign as many trucks as possible to the power shovel, which is equal to the minimum number of trucks we calculated earlier. Therefore, the optimal number of trucks to assign to the power shovel is 5.

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