Which is the correct choice.

Answer:

The vertex is option C: (-6, -2)

Step-by-step explanation:

The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)

Pls mark brainliest.

Answer:

Dilation. a transformation in which a figure grows larger. Dilation may be with respect to a point (dilation of a geometric figure) or with respect to the axis of a graph (dilation of a graph). Center of Dilation. the center of dilation is a fixed point in the plane.

Step-by-step explanation:

Answer:

The vertical line test can be used to determine whether a graph represents a function. ... If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x value has more than one output. A function has only one output value for each input value.

True. Exception reports show a greater level of detail than is included in routine reports.

Exception reports are reports that help in identifying data that does not conform to expected patterns. Exception reports show information about an exception in the data set.

This helps to identify irregularities or anomalies in data or system operations.Exception reports are used to analyze system performance, monitor resource consumption, and to detect unusual activity.

This type of report is important to identify issues or errors, where the routine reports or standard reports would not provide enough detail or insight to do so.

It provides detailed information on any unusual event or anomaly that occurred beyond the usual course of events or processes.Exception reports are generated and distributed when the data is not expected or when an event occurs that is outside of what is considered typical.

For example, a financial system might generate an exception report if a transaction is entered that exceeds the maximum allowed amount. This report would show the details of the transaction and highlight the exception.

The purpose of exception reports is to provide users with a higher level of detail than they would find in routine reports. Exception reports are used to highlight significant data, which will be used for further analysis or action.

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The weight that separates the bottom 5% is approximately 5.02 ounces.

To find the weights that separate the top 5% and the bottom 5%, we need to use the z-score formula and the standard normal distribution table.

First, let's find the z-score for the top 5%. Using the standard normal distribution table, we find that the z-score for the top 5% is approximately 1.645.

Next, we can use the formula z = (x - μ) / σ, where z is the z-score, x is the weight we're trying to find, μ is the mean, and σ is the standard deviation.

For the top 5%, we have:

1.645 = (x - 5.12) / 0.07

Solving for x, we get:

x = 5.12 + 1.645 * 0.07

x ≈ 5.22 ounces

Therefore, the weight that separates the top 5% is approximately 5.22 ounces.

To find the weight that separates the bottom 5%, we use the same process but with a negative z-score. The z-score for the bottom 5% is approximately -1.645.

-1.645 = (x - 5.12) / 0.07

Solving for x, we get:

x = 5.12 - 1.645 * 0.07

x ≈ 5.02 ounces

Therefore, the weight that separates the bottom 5% is approximately 5.02 ounces.

These weights could serve as limits used to identify which components should be rejected. Any component with a weight less than 5.02 ounces or greater than 5.22 ounces should be rejected.

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The Matlab & Simulink model consists of a Clock block to generate a time signal, a Gain block to multiply the time signal by 2, and a Differential Equation block to solve the given differential equation. The Scope block is used to visualize the behavior of the variable x over time.

To construct a Matlab & Simulink model for the given mathematical model, we can use Simulink's Differential Equation block and a Clock and Gain block. Here's a step-by-step guide:

1. Open Simulink in Matlab.

2. Drag and drop a Clock block from the Simulink Library Browser into the model.

3. Drag and drop a Gain block from the Simulink Library Browser into the model.

4. Double-click on the Gain block and set the Gain value to 2.

5. Drag and drop a Differential Equation block from the Simulink Library Browser into the model.

6. Double-click on the Differential Equation block and enter the equation `d²x + 3 + 4*x + 6 = 5*cos(2*t)`.

7. Connect the output of the Clock block to the input of the Gain block, and the output of the Gain block to the input of the Differential Equation block.

8. Connect the output of the Differential Equation block to a Scope block from the Simulink Library Browser.

9. Run the simulation.

The Scope block will show the behavior of the value of x over time according to the given mathematical model.

In conclusion, The Clock block provides the independent variable t, and the Differential Equation block evaluates the given equation to compute the value of x. The simulation shows the dynamic response of x as influenced by the equation and the time signal.

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Answer:

27,29,38,39,42,52,53

Step-by-step explanation:

The expressions are different, one is fixed and the other depends on the value of y.

a) To evaluate 869 - 14 for y = 20, we simply substitute y = 20 into the expression:

869 - 14 = 855

Therefore, the value of the expression 869 - 14 when y = 20 is 855.

b) To evaluate 8y - 14 for y = 20, we substitute y = 20 into the expression:

8y - 14 = 8(20) - 14 = 160 - 14 = 146

Therefore, the value of the expression 8y - 14 when y = 20 is 146.

The answers are not the same because the expressions are different. In part (a), we are subtracting 14 from 869, which gives us a fixed value of 855. In part (b), we are multiplying 8 by y and then subtracting 14, which gives us a value that depends on the value of y. When y = 20, the value of 8y - 14 is 146, which is different from the fixed value of 855 we obtained in part (a).

In other words, the expression 869 - 14 is a constant expression that always evaluates to 855, regardless of the value of y. On the other hand, the expression 8y - 14 is a variable expression that evaluates to different values depending on the value of y.

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Answer:

$12,150

Step-by-step explanation:

I = Prt

I = (40500)(0.03)(10)

I = 12150

Solve for q

-----------------

\((8q-5)^o+81=180^o\)

\(8q-5+81=180\)

\(8q+76=180\)

\(8q=180-76\)

\(8y=104\)

\(q=13\)

---------------

(a) The probability that both Anderson and Box will be selected is 0.1

(b) The probability that at least one of the two members whose name begins with C is selected is 0.7

(c) The probability that the two chosen representatives have a total of at least 17 years teaching experience there is 0.6

(a) You will have to consider the 10 different outcomes. Each combination of "A−B","B−Cox", "B−Cramer",... is equally likely to be drawn.

There are \(\left \{ {{5} \atop {2}} \right. =10\)

10 ways to choose 2 people from a group of 5. Since we are only considering 1 possibility, the answer will be 1/10=0.1

(b), there are a few possibilities where at least 1 "C" member gets selected. Consider

"Cox−A", "Cox−B", "Cox−Cramer", "Cox−F"

and

"Cramer−A", "Cramer−B", "Cramer−Cox", "Cramer−F"

Notice that "Cox−Cramer" appears twice, so one needs to be eliminated. Turns out there are 7 different possibilities out of 10...so we have 0.7

(c), I'd personally recommend taking the "compliment" of events. ie, how many combinations have LESS than 17 years? Turns out there are 4 combinations - (3,6),(3,7),(3,10),(6,7).

You can use the answer from (a) and evaluate this to become

1−4/10=0.6.

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The asymptotic notation relationship between the functions \(f(n) = n^3 (8 + 2 cos 2n)\) and \(g(n) = n^2 + 2n^3 + 3n\) is f(n) ∈ Θ(g(n)). Therefore, the growth rates of f(n) and g(n) are primarily determined by the cubic terms, and they grow at the same rate within a constant factor.

To determine the asymptotic notation relationship between the functions \(f(n) = n^3 (8 + 2 cos 2n)\) and \(g(n) = n^2 + 2n^3 + 3n\), we need to compare their growth rates as n approaches infinity.

Θ (Theta) Notation: f(n) ∈ Θ(g(n)) means that f(n) grows at the same rate as g(n) within a constant factor. In other words, there exists positive constants c1 and c2 such that c1 * g(n) ≤ f(n) ≤ c2 * g(n) for sufficiently large n.

o (Little-o) Notation: f(n) ∈ o(g(n)) means that f(n) grows strictly slower than g(n). In other words, for any positive constant c, there exists a positive constant n0 such that f(n) < c * g(n) for all n > n0.

ω (Omega) Notation: f(n) ∈ ω(g(n)) means that f(n) grows strictly faster than g(n). In other words, for any positive constant c, there exists a positive constant n0 such that f(n) > c * g(n) for all n > n0.

Now let's analyze the given functions:

\(f(n) = n^3 (8 + 2 cos 2n)\\g(n) = n^2 + 2n^3 + 3n\)

Since both functions have the same dominant term, we can say that f(n) ∈ Θ(g(n)) because they grow at the same rate within a constant factor. The other notations, o and ω, are not applicable here because neither function grows strictly faster nor slower than the other.

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Answer:

a = 8 cm

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Geometry

Volume of a Cube Formula: V = a³

Step-by-step explanation:

Step 1: Define

Identify variables

V = 512 cm³

Step 2: Find a

Answer:

$23780

Step-by-step explanation:

Given data

Let the original price be x

discount= 20%

price= $19,024

so that

20/100*x=x-19,024

0.2x= x-19,024

19,024=x-0.2x

19,024=0.8x

x= 19,024/0.8

x=23780

Hence the original price is $23780

The expansion of  (z+1)⁶ = z⁶ + 6z⁵+ 15z⁴ + 20z³+ 15z² + 6z + 1

A type of number pattern is Pascal's Triangle. The triangle-shaped arrangement of integers known as Pascal's Triangle provides the coefficients for the expansion of any binomial statement.

The arrangement of the numerals creates a triangle when they are reflected. The number 1 is first placed at the top, and then the numbers are arranged in a triangle design.

The expansion of (x + y)ⁿ is is given by

(x + y)ⁿ = a₀xⁿ + a₁xⁿ⁻¹y + a₂xⁿ⁻²y² + … + a\(_{n -1}\) xyⁿ⁻¹ + a\(_{n}\)yⁿ  

Here we have (z+1)⁶

Write out Pascal's triangle starting from 1 and up to 6 rows

                                1

                           1         1    

                      1         2         1      

                 1         3         3        1          

            1        4          6         4       1    

      1         5        10         10      5        1  

1          6         15         20      15      6        1    

So coefficients of expansion are 1, 6, 15, 20, 15, 6, and 1  

(z+1)⁶ =  (1)z⁶ + (6)z⁵(1)+ (15)z⁴(1)² + 20z³(1)³ + 15z²(1)⁴ + 6z¹(1)⁵ + (1)z⁰(1)⁶

=> (z+1)⁶ = z⁶ + 6z⁵+ 15z⁴ + 20z³+ 15z² + 6z¹ + 1

Therefore,

The expansion of  (z+1)⁶ = z⁶ + 6z⁵+ 15z⁴ + 20z³+ 15z² + 6z + 1

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Answer:

The correct option is b) 0.0593.

Given that a single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 12 customers per hour and an average service rate of 16 customers per hour.

The probability of 5 customers in the system is to be calculated.

Probability that there are n customers in the system is given by:

                    Pn= λ/μ

λ = average arrival rate = 12 customers per hour

μ = average service rate = 16 customers per hour

                   P5 =  λ/μ * (λ/μ)^n−1 / n!

                         = 12/16 * (12/16)^4 / 5!

                         ≈ 0.0593

Therefore, the probability of 5 customers in the system is approximately 0.0593.

Hence, the correct option is b) 0.0593.

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The expression can be rewritten as:

2*(n - 3)

This is twice an integer number, so this is an even number

Here we know that n is an integer larger than 1, and we have the expression:

n² - (n - 2)² - 2

Now, remember that for any integer m, 2m is always an even number.

Expanding the term in the middle of the expression we get:

n² - (n - 2)² - 2

n² - (n² - 4n + 4) - 2

4n - 4 - 2 = 4n - 6 = 2*(n - 3)

Integer numbers are closed under addition, then n - 3 is an integer, so we have:

2*(n - 3)

This is twice an integer, so this is an even number.

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The sentence "If it is a dog (d), it has fleas (f)" can be represented in symbolic form as d → f.

In symbolic logic, we represent the components of a sentence using letters or symbols. In this case, the given sentence has two components: "it is a dog" and "it has fleas." To represent these components, we assign the letter 'd' to "it is a dog" and the letter 'f' to "it has fleas."

The sentence "If it is a dog, it has fleas" implies a conditional relationship between the two components. It states that if something is a dog (d), then it has fleas (f). This can be symbolically represented as d → f, where the arrow (→) denotes the conditional relationship.

The given sentence, "If it is a dog (d), it has fleas (f)," can be represented in symbolic form as d → f. The arrow (→) in symbolic logic represents the conditional relationship. It indicates that if something is a dog (d), then it has fleas (f). In this symbolic representation, 'd' stands for "it is a dog," and 'f' represents "it has fleas."

The sentence is a conditional statement because it presents a hypothetical relationship between the two components. The truth value of the sentence depends on whether the antecedent (d) is true or false. If something is indeed a dog, then it implies that it has fleas. However, if it is not a dog, the statement does not make any specific claim about fleas.

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Formula :

Perimeter of Trapezium = sum of all sides

AB + BD + EC + BC [Refer to the attachment]

AB = 14 cm

EC = 6 cm

BD = 8 cm

Let's find the length of side BC

In right angle triangle , BDC

EC = 14 cm

AB = 6 cm

DC = EC - AB

= 14 - 6

= 8 cm

According to Pythagoras theorem,

BC² = DC² + BD²

BC² = 8² + 8²

BC² = 64 + 64

BC = √128

Perimeter = sum of all sides

= 14 + 6 + 8 +11.31

= 20 + 8 + 11.31

= 28 + 11.31

Answer:

180 eggs is the correct amount.

The maximum number of possible different eigenvalues is 2 when

det(A-I×λ)=0.

Given that,

We have to describe the reason why a 2x2 matrix can only have two different eigenvalues.

We know that,

Checking this out with straight calculations

Keep in mind that the eigenvalues of a matrix A are determined by:

det(A-I×λ)=0

Where I is the identity matrix, whose diagonal exclusively contains ones.

As a result, the size of the matrix determines the maximum number of eigenvalues. For instance, a 2x2 matrix corresponds to an identity matrix with just two members on the diagonal.

Therefore, The maximum number of possible different eigenvalues is 2 when det(A-I×λ)=0.

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Answer:

x = 45°, y= 5°

Step-by-step explanation:

x = 9y

90+2x = 180

2x = 90

x = 45

so x = 45

9y = 45

y = 5

Answer:

  see attached

Step-by-step explanation:

We followed instructions to create the attached graph of the two triangles.

Each mid-segment is parallel to the side of the triangle whose midpoint is the vertex opposite that segment. So, we used a graphing tool to draw, for example, a line parallel to PQ through point R. The vertices of the original triangle are at the intersection points of these lines (or 1 mid-segment length from the midpoint).

__

Analytically, we can make use of the fact that each mid-segment is effectively a diagonal of a parallelogram. For example, PQ is a diagonal of APRQ. The other diagonal is AR. The two diagonals cross at the midpoint of each. This means we can find point A using the midpoint relation:

  midpoint AR = midpoint PQ

  (A +R)/2 = (P +Q)/2 . . . use the midpoint formula

  A +R = P +Q . . . . . . . . multiply by 2

  A = P +Q -R . . . . . . . . subtract R to get an expression for A

  A = (2, 1) +(4, 5) -(7, 4) = (2+4-7, 1+5-4) = (-1, 2)

The other vertices of ΔABC can be found in similar fashion:

  B = R +P -Q = (7, 4) +(2, 1) -(4, 5) = (7+2-4, 4+1-5) = (5, 0)

  C = Q +R -P = (4, 5) +(7, 4) -(2, 1) = (4+7-2, 5+4-1) = (9, 8)

So, the original triangle's vertices are ...

  A(-1, 2), B(5, 0), C(9, 8)

Answer:

It is 1 cent cheaper  to pay 5.46 for 7 apples.

Step-by-step explanation:

Find the unit rate:

5.46 /7 = 0.78

This is the cost for 1 apple

3.95/5 = 0.79

This is the cost for 1 apple

Answer:

5 apples for 3.95 is the better deal

Step-by-step explanation:

If you divide 7 by 5.46 you should get roughly 1.28, so $1.28 per apple

and if you divide 5 by 3.95 you should get roughly 1.26, meaning $1.26 per apple. You can verify this by multiplying 1.26 by 5 and 1.28 by 7

Answer:

400

Step-by-step explanation:

Answer:

44.0925 pounds

Step-by-step explanation:

Answer:

The slope intercept is

Y = mx + b

Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.

Answer:  The amount of white fabric to coloured fabric as a ratio in its simplest form is \(\frac{10}{11}\)

Step-by-step explanation:

Given :

Amount of coloured fabric used by June = 11 mm = 1.1 cm    (1 mm=0.1 cm)

Amount of white fabric used by June = 1 cm

To find : amount of white fabric to coloured fabric as a ratio in its simplest form

To find the ratio in simplest form , the units of both measurements should be same

Thus \(\frac{\text {amount of white fabric}}{\text {amount of coloured fabric}}=\frac{1cm}{1.1cm}=\frac{10}{11}\)

The amount of white fabric to coloured fabric as a ratio in its simplest form is \(\frac{10}{11}\)