System of equations!!!

To find if a relation is a function, identify if there is more that one value of y for the same value of x (if there are more than one value for one value of x is not a function)

Ordered pairs (x,y)

1.

x y

1 -2

-2 0

-1 2

1 3

2.

x y

1 1

2 2

3 5

4 10

5 15

After answering the presented question, we can conclude that Hence the probability of the basketball player making the following basket is 22/25, or around 0.88.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.

The likelihood of a basketball player making a shot can be estimated as follows:

P(attempting a shot) = 1 - P (missing a shot)

As a result, the likelihood of the player making a shot can be computed as follows:

P(shooting) = 1 - (3/25)

P(attempting a shot) = 22/25

Hence the likelihood of the basketball player making the following basket is 22/25, or around 0.88.

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The correct answer is d. emergent.

An emergent leader is an individual who grows into the leadership role naturally, often due to circumstances or necessity. They are not appointed or assigned to the position of leadership but rather emerge from the group or organization based on their skills, qualities, or actions.

Emergent leaders may possess certain qualities or demonstrate their competence and ability to guide and influence others. They gain recognition and respect from their peers, leading to their emergence as leaders within the group or organization.

This type of leadership often occurs in situations where formal leadership structures may be absent or ineffective, and individuals step up to take charge based on their capabilities and the needs of the group.

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The simplified expression without absolute value signs is x - 2.

To simplify the expression |x - 2| when x > 2, we can use the fact that if x is greater than 2, then x - 2 will be positive. In this case, |x - 2| simplifies to just x - 2.

This simplification is based on the understanding that the absolute value function, denoted by | |, returns the positive value of a number. When x > 2, x - 2 will be positive, and the absolute value function is not needed to determine its value. In this case, the expression simplifies to x - 2.

However, it's important to note that when x ≤ 2, the expression |x - 2| would simplify differently. When x is less than or equal to 2, x - 2 would be negative or zero, and |x - 2| would simplify to -(x - 2) or 2 - x, respectively.

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The population of the country will be twice what it was in 1980 approximately 67.8 years after 1980, which would be around 2047.

To find out when the population will be twice what it was in 1980, we need to set up an equation and solve for t.

Let's first determine the population in 1980:

N(0) = 217e0.0102(0) = 217

So, the population in 1980 was 217 million.

Now, we want to find out when the population will be twice that amount:

2(217) = 434

We can set up an equation:

434 = 217e0.0102t

Divide both sides by 217:

2 = e0.0102t

Take the natural logarithm of both sides:

ln(2) = 0.0102t

Solve for t:

t = ln(2)/0.0102

t ≈ 67.8

Therefore, the population of the country will be twice what it was in 1980 approximately 67.8 years after 1980, which would be around 2047.

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Answer:

Step-by-step explanation:

bottom left is 13a + 2b

bottom right is 15y - 6

Answer:

1) 13a + 2b

2) 15y² - 6

Step-by-step explanation:

3a + 2(b + 5a)

3a + 2b + 10a

13a + 2b

3y² + 3(4y² - 2)

3y² + 12y² - 6

15y² - 6

The solution when solved for b is 14 degrees because angles b and b + 56 are vertically opposite.

When a transversal cuts two parallel lines, some of the angles become congruent.

From the given diagram, the given angles are equal according to the vertical angles theorem.

Both angles are vertically opposite become they meet at a point of intersection.

Hence 5b = b + 56

5b - b = 56

4b = 56

b = 56/4

b = 14

Hence the solution when solved for b is 14 degrees because angles b and b + 56 are vertically opposite.

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Answer:

slope = 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (4, 7)

m = \(\frac{7-3}{4-2}\) = \(\frac{4}{2}\) = 2

Answer:

-32

Step-by-step explanation:

(1-3)^5

(-2)^5

32

Answer:

-32

Step-by-step explanation:

The slopes for each segment are given as follows:

The lengths of each segment are given as follows:

Hence DE = 0.5 = AC, and thus DE is the midsegment of triangle ABC.

The slope of a set of two points is given by the change in y between the two points divided by the change in x between the two points.

Both segments in this problem, DE and AC, are horizontal lines, meaning that the change in y is of zero while the change in x is different of zero, thus the slope is calculated as follows:

Slope = Zero/Constant different of Zero = Zero.

The lengths of each of the horizontal segments is obtained subtracting the x-coordinates, as follows:

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Answer:

2x + y = 18

y = 4x - 12

x = 5,  y = 8

Step-by-step explanation:

x = 1st number

y = 2nd number

We can use the substitution method as we know what 'y' equals; that value will get plugged in for 'y' in the first equation as follows:

2x + 4x - 12 = 18

6x - 12 = 18

6x = 30

x = 5

y = 4(5) - 12 which is 20-12 or 8

y = 8

Claribel needs to pay $875 for 17 months to gym, $25 for one time membership fee and $50 for 17 months.

A set or group of equations that you solve all at once is referred to as a "system" of equations. A linear equation can be represented as Ax + By +C = 0, Where A, B are coefficient and C is the constant. Linear equations (those that graph as straight lines) are easier to understand than non-linear ones.

To find the amount for Claribel, we have to find the monthly fee and one time membership fee for the gym.

Let x be one time membership fee for the gym and y be the monthly fees, so the system of equations will be,

x + 6y = 325

x + 9y = 475

Now, subtracting the above equations, we get

3y = 150

y = 50

Now, putting the value of y in first equation, we get

x + 6(50) = 325

x+300 = 325

x = 25

Now, finding the amount for Claribel,

One time membership fee + 17(Monthly Fee) = Total Amount

Putting the values,

Total Amount = 25 + 17(50)

= 25 + 850

=$ 875

Therefore, Claribel needs to pay $875 for 17 months to gym.

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Answer:

(-5,5) and (0,-0.1) , solutions to the equation

(5,5) and (10,5) ...not solution to the inequality

Step-by-step explanation:

5,5) and (0,-0.1) ,,,they are solutions to the inequality since they lie in the required region (unshaded region)

(5,5) and (10,5) ,,,they lie in the shaded region which is the required region hence not among the required points.

1. x<=20

2. k<0

3. d<-3

4. m<=11

5. a>=3

6. 6<-5

This should help

Answer:

50 per hour

Step-by-step explanation:

(a) Orthogonal projection matrix P:In a two-dimensional vector space, let L be a line. Let w be the nonzero vector that spans the line. P is the orthogonal projection matrix that projects a vector onto the line if it is multiplied by it. The vector is projected orthogonally onto the line if it is closest to the line.

(b) Find Proj(x), where line L is spanned by w: Using the formula for orthogonal projection:Proj(x) = ((x·w)/(w·w))wwhere "·" indicates the dot product.

(c) Find (the vector that is perpendicular to line L):Vector which is perpendicular to line L can be found by computing the vector projection of the vector (1,0) onto the vector w. Since (1,0) is a vector on the x-axis, it is perpendicular to the direction of w. Let v be the vector obtained from the vector projection, and let z be the vector (0,0) - w. Vector z is on the line L, whereas vector v is perpendicular to L and points in the positive x direction.v = ((1,0)·w)/(w·w)wz = (0,0) - w

(d) Find reflection matrix R: The matrix of reflection with respect to the line L is given by the expression R = I - 2Pwhere P is the orthogonal projection matrix and I is the identity matrix.

(e) Find Ref (*) (-¹₂) and Let x = (:When Ref is applied to x, it reflects x across the line L.Ref (x) = 2Proj(x) - xRef(x) = 2(((x·w)/(w·w))w) - x Finally, the solution is as follows:

a) Orthogonal projection matrix P is given by P = wwT/(wT w)

b) The vector Proj(x) is given by Proj(x) = ((x·w)/(w·w))w

c) The vector that is perpendicular to line L is given by v = ((1,0)·w)/(w·w)w; z = (0,0) - w

d) The reflection matrix R is given by R = I - 2P, where I is the identity matrix

e) Ref(*) (−1/2) is given by 2(((−1/2)·w)/(w·w))w - (*)(f) Let x = (:Ref(x) = 2(((x·w)/(w·w))w) - x

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Answer: C

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A.

The above statement is True.

Eigenvalue:

An eigenvalue is a special set of scalar values ​​associated with the most probable system of linear equations in a matrix equation. Eigenvectors are also called eigenvalues. It is a non-zero vector which can be modified by at most its scalar factor after applying a linear transformation.

According to the Question:

If the geometric multiple of the eigenvalues ​​is greater than or equal to 2, the linearly independent set of eigenvectors is no longer unique to the multiple as before. For example, for the diagonal matrix A=[3003], one could also choose the eigenvectors [11] and [1−1], or any pair of two linearly independent vectors.

Sometimes vectors are simply expanded to vector times matrix. If this happens, this vector is called the eigenvector of the matrix and the "stretch factor" is called the eigenvalue. Example: Given a square matrix A, λ is the eigenvalue of A, and the corresponding eigenvector x is

Ax = λx.

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According to the information, the 95% confidence interval for the proportion of Americans who drink tea daily is approximately (0.2485, 0.2766). The margin of error is approximately 0.0140.

To construct a confidence interval for the proportion of Americans who drink tea daily, we can use the formula:

Where,

p = the sample proportion

Z = the critical value corresponding to the desired confidence level

n = the sample size

Given:

Now, let's calculate the confidence interval and margin of error:

According to the information, the 95% confidence interval for the proportion of Americans who drink tea daily is approximately (0.2485, 0.2766), with a margin of error of approximately 0.0140.

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The correct expression that represents the number of bracelets you have after h hours would be:60 = 28 + 5h. option A (28 + 5h  ) is correct.

Based on the given information, the correct expression that represents the number of bracelets you have after h hours would be:

60 = 28 + 5h

This is because you start with 28 bracelets and make 5 bracelets every hour. So after h hours, you would have made 5h bracelets, and the total number of bracelets you have would be:

Total number of bracelets = Starting number of bracelets + Number of bracelets made

Total number of bracelets = 28 + 5h

If you substitute h = 6 into the equation, you can see that after 6 hours, you would have made 5 x 6 = 30 bracelets, and the total number of bracelets you would have is:

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Question

You need 60 bracelets for a craft fair. You begin with 28 bracelets and make 5 bracelets each hou a. Choose an expression that represents the number of bracelets you have after h hours.

A. 28 + 5h                                     B. 60 + 28h

C. 60 + 5h                                     D. 5 + 60h

Answer:

\( \huge \orange{m\widehat {FGH} =238\degree} \)

Step-by-step explanation:

\( \therefore m\angle FGH + m\angle FAH = 180\degree \)

\( \therefore (21x-2)\degree + (38x +5)\degree = 180\degree \)

\( \therefore (21x-2+38x +5)\degree = 180\degree \)

\( \therefore 59x+3= 180\)

\( \therefore 59x= 180-3 \)

\( \therefore 59x= 177 \)

\( \therefore x= \frac{177}{59}\)

\( \therefore x=3\)

Now, by inscribed angle theorem:

\( m\angle FAH = \frac{1}{2} m\widehat {FGH} \)

\( (38x +5)\degree = \frac{1}{2} m\widehat {FGH} \)

\( 2(38\times 3+5)\degree = m\widehat {FGH} \)

\( 2(119)\degree = m\widehat {FGH} \)

\( 238\degree = m\widehat {FGH} \)

\( \huge \purple {\boxed {m\widehat {FGH} =238\degree}} \)

Answer:

SAS

Step-by-step explanation:

Side ST = Side Gp

angle p = angle t

and side PM = side MT

Therefore the congruency statement shows

Side

Angle

Side

aka SAS

Answer:

B

Step-by-step explanation:

Lie should factor out 3 from the expression

Answer:

x = 5

Step-by-step explanation:

So the perimeter of a square is 4 times the side length.

4 (x+3) = 32 is the equation we can make out with the given information.

Solve for x:

Distribute the 4 to the terms inside the parenthesis;  4x + 12 = 32

Subtract 12 from both sides;  4x = 20

Divide both sides by 4;  x = 5

By isolating x, we get 5 as the value of x.