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The Graham's scan algorithm calculates the convex hull of a set of points, which guarantees a convex polygon. The smallest area polygon containing the set of points is not the convex hull of those points.

To demonstrate that the smallest area polygon containing a set of points may not always be a convex hull of that set of points, let's consider a simple example.

Suppose we have a set of four points: A, B, C, and D, arranged in a square formation, as shown below:

A----B

|    |

|    |

D----C

If we calculate the convex hull of these points using the Graham's scan algorithm, we would obtain the convex hull as ABCDA, which is a square.

However, if we look for the smallest area polygon that contains these points, we can find a non-convex polygon. By connecting the points A, B, C, and D in that order, we form a quadrilateral:

A----B

\  /

 \/

 /\

/  \

D----C

This quadrilateral, ABCD, is not convex, as it has an internal angle greater than 180 degrees.

Hence, in this example, the smallest area polygon containing the set of points is not the convex hull of those points. This example demonstrates that the smallest area polygon can be non-convex, and the convex hull may not always provide the minimum area solution.

The Graham's scan algorithm specifically calculates the convex hull of a set of points, which guarantees a convex polygon. However, to find the smallest area polygon, other techniques or algorithms need to be applied.

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Answer:

y = -x - 2

Step-by-step explanation:

y-3=-1(x+5)

Expand.

y - 3 = -1x - 5

Add 3 on both parts.

y - 3 + 3 = -1x - 5 + 3

y = -1x - 2

Answer:

y intercept = -3

the slope of the line is 1

Step-by-step explanation:

y intercept is the value of y when x = 0

x = 0 when y = -3

Yes, The triangles are congruent by SSS i,e option(D)

When two corresponding sides and the angle included between them of one triangle match those of two corresponding sides and the angle included between them of another triangle, the two triangles are said to be congruent. Two triangles are said to be congruent if their three sides and three angles, in any orientation, are equal.

By applying the CPCTC (Corresponding Parts of Congruent Triangles are Congruent) theorem, the two sides of the triangle in issue are made equal, hence making the third sides equal.

Therefore, we can say the triangles are congruent by SSS i,e option(D)

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The numerical value of a dependent variable is dependent on the value of the independent variable. In other words, the numerical value of the dependent variable changes based on the value of the independent variable. For example, in the equation y = 2x + 3, the numerical value of y (the dependent variable) is dependent on the value of x (the independent variable). If x is 1, then the numerical value of y is 5 (2*1 + 3). If x is 2, then the numerical value of y is 7 (2*2 + 3). So, the numerical value of the dependent variable is dependent on the value of the independent variable.

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The correct simplification of the expression is c12 (option c).

The expression (c^4)^3 can be simplified using the exponent rules for powers of a power, which states that when a power is raised to another power, we can multiply the exponents.

Thus, we have:

(c^4)^3 = c^(43) [Using the rule (a^m)^n = a^(mn)]

Simplifying the exponent 4*3, we get:

c^(4*3) = c^12

Therefore, the correct simplification of the expression is c^12.

Option (c) is the correct answer as it correctly represents the simplified form of the given expression. Option (a) c^-1, option (b) c^7, and option (d) c^64 are not correct because they do not follow the exponent rules used to simplify the expression.

In summary, the expression (c^4)^3 simplifies to c^12, which is option (c) in the given options.

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Answer:

Step-by-step explanation:

Answer: x/3 ==> C

Step-by-step explanation:

(2x/3)^1/2 * (x/6)^1/2=

(2x/3 * x/6)^1/2=

(2x^2/18)^1/2=

(2x^2)^1/2 / 18^1/2=

(2x^2)^1/2 / (2*9)^1/2=

(2x^2)^1/2 / 3*2^1/2=

2^1/2 * (2x^2)^1/2 / 3*2=

(2(2x^2))^1/2 / 6=

(4x^2)^1/2 / 6=

4^1/2 * (x^2)^1/2 / 6=

2x/6=x/3 ==> C

We are asked to find the proportion of mild cases that were effectively dealt with using treatment A. First we will find the total number of cases that were dealt with using treatment A, that is:

Fr

Answer:

B is your answer

Step-by-step explanation:

have a great day!

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Answer:

The equation of the ellipse is;

\(\dfrac{(x + 4)^2}{4^2} + \dfrac{(y - 0)^2}{1^2} = 1\)

Step-by-step explanation:

The parameters of the ellipse are;

The location of the center of the ellipse = (-4 0)

The coordinates of the vertex of the ellipse = (-8, 0)

The coordinates of the the co-vertex = (-4, 1)

The general form of the equation of an ellipse is presented as follows;

\(\dfrac{(x - h)^2}{a^2} + \dfrac{(y - k)^2}{b^2} = 1\)

The center of the above equation of an ellipse = (h, k)

The vertex of the above equation are; (h - a, k) and (h + a, k)

The co vertex of the above equation are; (h, k - b) and (h, k + b)

By comparison, we have;

h = -4, k = 0

For the vertex, we have;

When

h - a = -8

∴ -4 - a = -8

-a = -8 + 4 = -4

a = 4

When

h + a = -8

-4 + a = -8

∴ a = -4

a = 4 or -4

We note that a² = 4² = (-4)²

For the covertex, we have;

When

k - b = 1

0 - b = 1

b = -1

When k + b = 1

0 + b = 1

b = 1

∴ b = 1 or -1

b² = 1² = (-1)²

We can therefore write the equation of the ellipse as follows;

\(\dfrac{(x - (-4))^2}{4^2} + \dfrac{(y - 0)^2}{1^2} = \dfrac{(x + 4)^2}{4^2} + \dfrac{(y - 0)^2}{1^2} = 1\)

Therefore;

\(\dfrac{(x + 4)^2}{4^2} + \dfrac{(y - 0)^2}{1^2} = 1\)

Therefore, on average, Crunch Code has approximately 4 uncompleted projects in the system at any given time.

To calculate the average number of uncompleted projects in the system at any given time, we need to use Little's Law, which states that the average number of entities (in this case, projects) in a stable system is equal to the average arrival rate multiplied by the average time spent in the system.

Given:

Average arrival rate (λ) = 1 project every 4.8 hours

Average time spent in the system (W) = 19.2 hours

Using Little's Law, the average number of uncompleted projects (L) is given by:

L = λ * W

Substituting the values:

L = (1/4.8) * 19.2

= 0.208 * 19.2

≈ 3.9936

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To determine the vertices of image U′V′W′ after a 180° counterclockwise rotation, we can apply the following transformation rules:

Using these rules, we can find the vertices of image U′V′W′ as follows:

Therefore, the vertices of image U′V′W′ after a 180° counterclockwise rotation are U′(0, -2), V′(1, -3), and W′(3, -3).

So, the answer is option (b) U′(0, −2), V′(1, −3), W′(3, −3).

Answer:

falseeeeeeeee for sure

Step-by-step explanation:

can i get brianlissssstttt

The number of polynomials that can be formed with -2 and 5 as zeroes are more than 1.

What is a polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.x² -3x - 7 is an illustration of a polynomial with a single indeterminate x.

Given that the zeros of a polynomial are -2 and 5.

The polynomial that has a and b as zeors is p(x) = k[x² + (a+b)x + ab].

where k is a real number.

The polynomial that has -2 and 5 zeros is

p(x) = k[x² + (-2 + 5)x + (-2)×5]

p(x) = k[x² + 3x - 10]

Where k is a real number.

The number of real numbers is infinity.

The number of polynomials is infinity.

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The probability that the Players are assigned to go in the order given can be found to be 0.833 %.

First, we need to find out the number of ways that the baseball players can be assigned to go and this is:

= 5 × 4 × 3 × 2 × 1 = 120 ways

However, there is only one way in which Player A is assigned to go 1st, Players B is assigned to go 2nd, Player C is assigned to go 3rd, Player D is assigned to go 4th, and player E is assigned to go 5th.

The probability is therefore:

= 1 / 120

= 0.833 %.

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Answer:

Can we get 24p-23 exactly

The number that is non-irrational is 5.73, because it can be written as a quotient of two integers.

A rational number is a number that can be written as a quotient of two integer numbers, while an irrational number can't be written like that.

Also, the square root of a non perfect square is also irrational.

Here the options are:

5.73, ,√73, √40

Notice that neither of the square roots of non perfect square numbers, so these are irrational numbers.

In other hand, if we see the first one:

5.73

We can rewrite this as:

5.73 = 573/100

So this is a quotient of two integers, then this is a rational number, so this is the correct option.

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In the formula =if(a1=b1, c1, c2), the result will be c2 if; A does not equal B

The IF function is probably one of the most famous functions in Microsoft Excel. The "IF Function" normally allows us to make logical comparisons between a value and what we expect. This means that an IF statement can possibly have two results. The first result would be if your comparison is True, while the second result will be if your comparison is False.

Now, this means hat the IF function has 3 arguments namely;

From the above definitions when they are applied to the question, since a1 = b1, then we can say that the result can be c2 if A is not equal to B.

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Answer:

x = 3 oz of seeds

y = 7 oz of seeds

Step-by-step explanation:

1. x + y = 10 oz (total amount of snack mix in ounces; oz)

2. $1.50x + $2.50y = $22 (how much the seeds and dried fruit costs)

3. Solve the system of equations using algebra.

$1.50 x + $1.50y = $15

$1.50 x + $2.50y = $22

There are $1.50x's in both of the equations, so cancel them out.

Subtract $2.50y by $1.50y and $22 by $15. y = 7

4. Plug in the y value in one of the equations.

x + 7 = 10; x = 3

Answer:

D

Step-by-step explanation:

1. Find which of these 4 (four) has a y-intercept of positive 4, in this case, B and D. Recall, that the y-intercept means when X is 0 (zero) what is the value of Y?

2. Find the slope of B and D
The formula to find slope is change in y/change in x (Y/X)

B:

X: 0 - 4 = -4
Y: 4 - 0 = 4

4/-4 = -1

D:

X: 0 - -4 = 4

Y: 4 - 0 = 4

4/4 = 1

The required Poisson distribution used to model the elapsed time between the occurrence of successive events for a poisson random variable

We have to find distribution model used to model elapse the time between the occurrence of successive events for Poisson random variable.

we know that, Poisson distribution

P(x=x) = e^-λ(λ)^x/x!

Time between succeess,

P(y>x) = e^-λy

and, P(y<x) = 1- e^-λy

They are exponential distribution.

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Answer:

Step-by-step explanation:

5x² - 15x - 4 = 0

Add 4 to both sides.

5x² - 15x = 4

The coefficient of 5x² is 5, divide both sides by 5.

x² - 3x = 4/5

The coefficient of -3x is -3. Let b=-3.

Then we need to add (b/2)^2=9/4 to both sides to complete the square.

Add 9/4 to both sides.

x² - 3x + 9/4 = 61/20

Factor left side.

(x-3/2)² = 61/20

Take square root of both sides.

x-3/2 = ± √(61/20)

Add 3/2 to both sides.

x = 3/2 ± √(61/20)

Two things that would be desirable in a ratio of 5:1 but not in a ratio of 1:5 are sugar and salt. In terms of taste and health considerations, having a higher proportion of salt than sugar is typically preferred.

The ratio of 5:1 implies that for every unit of the first thing, there are five units of the second thing. In this case, let's consider sugar and salt. Sugar is commonly used as a sweetener in various food and beverage products. It adds a pleasant taste to dishes and treats. However, an excess of sugar in the diet can lead to various health issues, including weight gain, tooth decay, and an increased risk of chronic diseases like diabetes. On the other hand, salt is used for enhancing the flavor of food. It adds a savory taste and helps to bring out the natural flavors of ingredients. While some amount of salt is necessary for our bodies to function properly, consuming excessive salt can lead to high blood pressure and other cardiovascular problems.

Therefore, it is generally recommended to have a lower proportion of sugar and a higher proportion of salt in our diet, making a ratio of 5:1 desirable. However, a ratio of 1:5, where salt is five times more than sugar, would result in an excessively salty taste and pose health risks. Thus, the preference for a 5:1 ratio of sugar to salt and not the other way around is based on taste preferences and health considerations.

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4. f(x,y) is homogeneous of degree 2.

5. a) f(x,y) is homothetic with h(x,y) = xy and g(x) = x-1

4. Show that f(x,y)=\(x^2\)y is homogeneous, and find its degree of homogeneity:

A function is said to be homogeneous of degree k, if it satisfies the condition:

f(tx,ty) = \(t^k\)f(x,y)

We have f(x,y) = \(x^2\)y. Let’s check if it satisfies the above condition:

f(tx,ty) = \((tx)^2(ty) = t^3x^2y = t^2(x^2y\)) = \(t^2\)f(x,y)

Hence f(x,y) is homogeneous of degree 2.

5. Which of the following functions f(x,y) are homothetic? Explain.

(a) f(x,y)=\((xy)^2\)+1

(b) f(x,y)=\(x^2+y^3\)

Let us first understand the meaning of homothetic transformation.

A homothetic transformation is a non-rigid transformation of the Euclidean plane that preserves the direction of the straight lines but not their length. It stretches or shrinks the plane by a constant factor called the dilation.

Let’s now find out whether the given functions are homothetic or not.

(a) f(x,y)=\((xy)^2\)+1

In order to check if f(x,y) is homothetic or not, we need to check if the function satisfies the following condition:

f(x,y) = g(h(x,y))

where g is a strictly monotonic function and h is a homogeneous function with degree 1

We have

f(x,y) = \((xy)^2\)+1

Let’s assume g(x) = x - 1, then g(x+1) = x

Similarly, let’s assume h(x,y) = (xy), then h(tx,ty) = \(t^2\)h(x,y)

Now, we have

g(h(x,y)) = h(x,y) - 1 = (xy) - 1

Thus f(x,y) is homothetic with h(x,y) = xy and g(x) = x-1

(b) f(x,y)=\(x^2+y^3\)

We can’t write this function in the form f(x,y) = g(h(x,y)) where h(x,y) is a homogeneous function with degree 1. Hence this function is not homothetic.

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The given questions are related to the concept of vector spaces in linear algebra. A vector space is a collection of vectors that satisfy certain axioms, such as closure under addition and scalar multiplication.

In the first question, we are given two vectors and asked to determine whether they are linearly independent or dependent. Linear independence means that no vector in the set can be expressed as a linear combination of the other vectors in the set. Linear dependence means that at least one vector in the set can be expressed as a linear combination of the other vectors in the set.In the second question, we are given sets of vectors and asked to determine whether they form a basis for R3, the three-dimensional vector space.

A basis is a set of vectors that span the entire vector space and are linearly independent. In other words, any vector in the vector space can be expressed as a linear combination of the basis vectors, and no basis vector can be expressed as a linear combination of the other basis vectors.The concept of vector spaces is fundamental in linear algebra and has many applications in fields such as physics, engineering, and computer science.

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Let y be the length of the third side. By the Pythagorean theorem,

y² + x² = 3² = 9

so that

y = √(9 - x²)

(taking the positive root because one expects length to be positive)

Then by the definitions of sine, cosine, and tangent, we have

sin(θ) = x / 3   →   θ = sin⁻¹(x / 3)

cos(θ) = √(9 - x²) / 3   →   θ = cos⁻¹(√(9 - x²) / 3)

tan(θ) = x / √(9 - x²)   →   θ = tan⁻¹(x / √(9 - x²))

Answer: 12

Step-by-step explanation:

Answer:

12

Step-by-step explanation: