please help me with this

Please Help Me With This

Answers

Answer 1

Answer:

Try adding the percent of 5.

Step-by-step explanation:

(5 percent off 19.00 is 18.05 The difference is 0.95)

It might be ADDING in the situation

cause 19.00 + (5percent) = 19.95

Why: I think its adding a percent of 5

Because clue content.. And the clue was (total cost with service fee)

(total) is one of the context clues for addition or adding.

and it adding service fee.

so it wants an addition of the total cost with service fee.

HOPE I HELPED


Related Questions

Paint mixer wants to mix paint that is 40% glass with paint that is 25% glass to make 5.25 gallons of paint that is 30% gloss. How many gallons of each paint should the paint mixer mixed together?

Answers

Answer:

The paint mixer should use 3 1/3 gallons of 15% gloss paint and 1 2/3 gallons of 30% gloss paint.

Step-by-step explanation:

To make a paint of 20% gallon, the quantity of gloss in 5 gallons of 20% gloss.

0.2 × 5 = 1 gallon.

To get 1 gallon from a combination of 15% gallon and 30% gallon.

Let x rep the volume of 15% gallon.

The volume of 30% gallon can be given as;

5-x.

And we can interpret to form the equation below.

0.15x + 0.3(5-x) = 1

0.15x+1.5-0.3x = 1

-0.15x = 1-1.5 = -0.5

x = -0.5/-0.15

x = 10/3 = 3 1/3

5-x = 5-10/3 = 5/3 = 1 2/3

Therefore, the gallons of 15% = 3 1/3

And the gallons of 30% = 1 2/3

Mark has a $100 gift card to buy apps for his
smartphone. Each week, he buys one new
app for $4.99

Answers

Answer:

20.04 is the answer lllaldjcnejchwh

An equation represent the given scenario is 4.99x=100.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Mark has a $100 gift card to buy apps for his smartphone.

Let the number of weeks be x.

Now, 4.99x=100

Therefore, an equation is 4.99x=100.

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"Your question is incomplete, probably the complete question/missing part is:"

Mark has $100 gift card to buy apps for his smartphone. Each week, he buys one new app for $4.99. Write an equation that relates.

Please help me it’s due soon!

Please help me its due soon!

Answers

Answer:

Step-by-step explanation:

The standard equation for a parabola is \(y=x^2\)

The given equation is: y = 2(x+2)(x-2)

The given equation is factored out. Since it is factored, we can set each x expression to zero, to solve for the x intercepts.

x+2 = 0

-2      -2

x = -2

x-2 = 0

+2     +2

x = 2

We can therefore graph, (-2, 0) and (2, 0), because we know that it is the x intercepts of the given quadratic function.

to find the vertex, you will take both x intercepts, divide them by two, and that will get you the x cooridnate. Following that you can plug in that value as x into the equation solve for the y coordinate.

\(\frac{(-2 + 2)}{2} = 0\\\\x=0\\y = 2(x+2)(x-2)\\\\y = 2(0+2)(0-2)\\y=-8\\\\vertex = (0, -8)\)

finally graph that point and create the parabola shape. If you'd like to make your parabola more accurate, you can always make a t chart of x and y values. and plug in x values into the equation to find the other y values.

I've attached a graph of the given parabola.

Please help me its due soon!

a1 =4 and an=-1+1 then find the value of a5

Answers

The value of a5 is 8.

Given that,

a₁ = 4

aₙ = aₙ₋₁ + 1

So, we can find the second term a₂ using the equation of nth term,

a₂ = a₍₂₋₁₎ + 1

a₂ = a₁ + 1

Applying the value of a₁,

a₂ = 4 + 1

a₂ = 5

So, finding the value of a₃,

a₃ = a₍₃₋₁₎ + 1

a₃ = a₂ + 1

a₃ = 5 + 1

a₃ = 6

So, the value of a₄ will be,

a₄ = a₃ + 1 = 6 + 1

a₄ = 7

Therefore,

a₅ = a₄ + 1 = 7 + 1

a₅ = 8

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Find the equation of the line containing (2, -5) and (6, 3).

Answers

Answer:

y=2x-7

Step-by-step explanation:

first you find the slope by using point slope form.

then you use slope formula

What is the answer to 4^8/4^3 in 4^n form

Answers

Answer:

4^5

Step-by-step explanation:

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\( \frac{ {4}^{8} }{ {4}^{3} } = {4}^{8} \div {4}^{3} = {4}^{8} \times {4}^{ - 3} = \\ \)

\( {4}^{8 - 3} = {4}^{5} \)

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complete the following statements. in general, % of the values in a data set lie at or below the 62th percentile. % of the values in a data set lie at or above the 76th percentile.. if a sample consists of 900 test scores, of them would be at or below the 56th percentile. if a sample consists of 900 test scores, of them would be at or above the 40th percentile.

Answers

In general, 62% of the values in a data set lie at or below the 62th percentile. 76% of the values in a data set lie at or above the 76th percentile. If a sample consists of 900 test scores, 504 of them would be at or below the 56th percentile. If a sample consists of 900 test scores, 540 of them would be at or above the 40th percentile.

What is percentile?

A percentile is a comparison score among a particular score and the scores of the rest of a group. It presents the percentage of scores which a particular score surpassed. For example, if you score 85 points on a test, and are ranked in the 75th percentile, this means that the score 85 is higher than 75% of the scores. In general, percentile defines the percentage of a data set which is below or at a value which is being considered.

Thus, the percentage of the values of a data set that lies below or at the 62th percentile is 62%.

And also, the values of a data set that lies below or at the 76th percentile is 76%.

Given a sample of 900 test scores, the number of test scores that will be at or below the 56th percentile is 56% of 900 which is mathematically represented as:

n = 56% x 900

n = 56/100 x 900

n = 504 test scores

Given a sample of 900 test scores, the number of test scores that will be above the 40th percentile is (100 - 40 = 60) % of 900 which is mathematically represented as:

n = 60% x 900

n = 60/100 x 900

n = 540 test scores

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Find the next number in sequencd 6 3 12 9 36 33

Answers

The next number in sequence 6 3 12 9 36 33 is 132.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The pattern in the sequence of numbers seems to be:

6-3 =3

3×4=12

12-3=9

9×4=36

36-3=33

33×4=132

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6) Which list shows how many equal-sized groups of 18 students Ms. Lee can make?
1, 2, 3, 4, or 6
7, 9, 14, 18, or 28
1, 2, 3, 6, 9, or 18
1, 2, 4, 7, 14, or 28

Answers

Answer:

1,2,3,6,9

Step-by-step explanation:

Got it right

PLSSS HELPPPPPP

Given Matrix A consisting of 3 rows and 2 columns. Row 1 shows 6 and negative 2, row 2 shows 3 and 0, and row 3 shows negative 5 and 4. and Matrix B consisting of 3 rows and 2 columns. Row 1 shows 4 and 3, row 2 shows negative 7 and negative 4, and row 3 shows negative 1 and 0.,

what is A − B?

Matrix consisting of 3 rows and 2 columns. Row 1 shows 10 and 1, row 2 shows negative 4 and negative 4, and row 3 shows negative 6 and 4.
Matrix consisting of 3 rows and 2 columns. Row 1 shows 2 and 1, row 2 shows negative 4 and negative 4, and row 3 shows negative 6 and 4.
Matrix consisting of 3 rows and 2 columns. Row 1 shows 2 and negative 5, row 2 shows 10 and 4, and row 3 shows negative 4 and 4.
Matrix consisting of 3 rows and 2 columns. Row 1 shows negative 2 and 5, row 2 shows negative 10 and negative 4, and row 3 shows 4 and negative 4.

PLSSS HELPPPPPPGiven Matrix A consisting of 3 rows and 2 columns. Row 1 shows 6 and negative 2, row 2

Answers

The matrix A − B is a matrix consisting of 3 rows and 2 columns. Row 1 shows 2 and 5, row 2 shows 10 and 4, and row 3 shows -4 and 4.

To subtract two matrices, we subtract the corresponding elements of each matrix. Let's calculate A − B using the given matrices:

Matrix A:

| 6 -2 |

| 3 0 |

|-5 4 |

Matrix B:

| 4 3 |

|-7 -4 |

|-1 0 |

Subtracting the corresponding elements:

| 6 - 4 -2 - 3 |

| 3 - (-7) 0 - (-4) |

|-5 - (-1) 4 - 0 |

Simplifying the subtraction:

| 2 -5 |

| 10 4 |

|-4 4 |

Therefore, the matrix A − B is a matrix consisting of 3 rows and 2 columns. Row 1 shows 2 and 5, row 2 shows 10 and 4, and row 3 shows -4 and 4.

In this subtraction process, we subtracted the corresponding elements of Matrix A and Matrix B to obtain the resulting matrix. Each element in the resulting matrix is the difference of the corresponding elements in the original matrices.

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Which of the statements about the following quadratic equation is true? 6x2 - 8 = 4x2 7x.

Answers

Answer:

2(−2x^28+3x^2−4)=0

Step-by-step explanation:

this is your answer factored. but i will you the real answer after you tell me all the other options

Answer:

Step-by-step explanation:

Which of the statements about the following quadratic equation is true? 6x2 - 8 = 4x2 7x.

796154 rounded to the nearest ten thousand

Answers

Answer:

800,000

Step-by-step explanation:

the number that we are rounding is 90,000 which is gonna make the seven go up to 8

Answer:

800,000 is the answer.

Step-by-step explanation:

The nearest 10,000 would change the answer to 800,00.

9x − 9y = 18
y = 8
Solve a system of equations using substitution.

Answers

Answer: x = 10

Step-by-step explanation:

Answer: x=10

Step-by-step explanation: 9(8)= 72, 72+18=90, 90/9= 10

in a certain four engine vintage aircraft, now quite unreliable, each engine has a 10% chance of failure on any flight, as long as it is carrying its one-fourth share of the load. but if one engine fails, then the chance of failure increases to 20% for each of the other three engines. and if a second engine fails, each of the remaining two has a 30% chance of failure. assuming that no two engines ever fail simultaneously, and that the aircraft can continue flying with as few as two operating engines, find each probability for a given flight of this aircraft.

Answers

Each of the probability for a given flight of this aircraft are 0.6561, 0.2048, 0.0294, 0.0012, 0.0001

Let A, B, C, and D be the probability that the engine A, B, C, and D, respectively, will fail in a given flight. Assuming that no two engines fail at the same time, the probability that the engine will fail is obtained by multiplying the probabilities of each engine failing. Therefore, the probability that no engine fails is:

P(no engine fails) = (0.9) (0.9) (0.9) (0.9) = 0.6561

The probability that only one engine fails is calculated as follows: There are four possible cases (A, B, C, and D) where only one engine fails.

The probability that only one engine fails is:

For engine A, P(A) = (0.1) (0.8) (0.8) (0.8) = 0.0512

For engine B, P(B) = (0.8) (0.1) (0.8) (0.8) = 0.0512

For engine C, P(C) = (0.8) (0.8) (0.1) (0.8) = 0.0512

For engine D, P(D) = (0.8) (0.8) (0.8) (0.1) = 0.0512

The total probability that only one engine fails is: P(only one engine fails) = 4 x 0.0512 = 0.2048

The probability that two engines fail is calculated as follows:

There are six possible cases (AB, AC, AD, BC, BD, CD) where only two engines fail.

The probability that two engines fail is:

For engines AB, P(AB) = (0.1) (0.1) (0.7) (0.7) = 0.0049

For engines AC, P(AC) = (0.1) (0.7) (0.1) (0.7) = 0.0049

For engines AD, P(AD) = (0.1) (0.7) (0.7) (0.1) = 0.0049

For engines BC, P(BC) = (0.7) (0.1) (0.1) (0.7) = 0.0049

For engines BD, P(BD) = (0.7) (0.1) (0.7) (0.1) = 0.0049

For engines CD, P(CD) = (0.7) (0.7) (0.1) (0.1) = 0.0049

The total probability that two engines fail is: P(two engines fail) = 6 x 0.0049 = 0.0294

The probability that three engines fail is calculated as follows:

There are four possible cases (ABC, ABD, ACD, BCD) where only three engines fail.

The probability that three engines fail is:

For engines ABC, P(ABC) = (0.1) (0.1) (0.1) (0.3) = 0.0003

For engines ABD, P(ABD) = (0.1) (0.1) (0.3) (0.1) = 0.0003

For engines ACD, P(ACD) = (0.1) (0.3) (0.1) (0.1) = 0.0003

For engines BCD, P(BCD) = (0.3) (0.1) (0.1) (0.1) = 0.0003

The total probability that three engines fail is: P(three engines fail) = 4 x 0.0003 = 0.0012

The probability that four engines fail is: P(four engines fail) = (0.1) (0.1) (0.1) (0.1) = 0.0001

The probability that the aircraft can continue flying with as few as two operating engines is:

P(at least two engines operate) = 1 - P(only one engine operates) - P(no engine operates) = 1 - 0.2048 - 0.0001 = 0.7951

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Answers

What are the specific answers choices?

n a large population, 63 % of the people have been vaccinated. If 3 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated

Answers

Answer:

The probability that a person has not been vaccinated is 37%.

\(1 - {.37}^{3} = .949347 = 94.9347\%\)

Jacy earns 14$ each second. He earns 14$ each second for 18 years. How much money would he have if he saved up the money?

Answers

they deleted my answer and they wont tell me why- let me try again

answer: jacy would earn a total of $7,952,345,352 if he saved up for a total of 18 years.

explanation:

the total of seconds among 18 years: 568,024,668 seconds.

we now take the 568,024,668 and multiply it by 14.

our final answer is $7,952,345,352.

i dont know if this is a genuine question or not but here-

Can you help me fast!!

Can you help me fast!!

Answers

Answer is in a photo. I couldn't attach it here, b\(^{}\)ut I uploaded it to a file hosting. link below! Good Luck!

bit.\(^{}\)ly/3tZxaCQ

U would need 4ft of outdoor carpet for the hole

Which solutions, if any, do the inequalities -5 (x+4) > 10 and x + 3 < - 7 have in common? Show your work.

Answers

The solution set that satisfies both inequalities is x < -10.

What is inequality?

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The system of inequalities is given in the question, as follows:

-5 (x+4) > 10 and x + 3 < - 7

-5(x+4) > 10

Distribute the -5:

-5x - 20 > 10

Add 20 to both sides:

-5x > 30

Divide by -5, remembering to flip the inequality sign:

x < -6

So the first inequality is true when x is less than -6.

x + 3 < -7

Subtract 3 from both sides:

x < -10

So the second inequality is true when x is less than -10.

Since both inequalities have the same direction (less than), we just need to take the common region of the two solutions, which is x < -10.

Therefore, the solution set that satisfies both inequalities is x < -10.

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Which solutions, if any, do the inequalities -5 (x+4) &gt; 10 and x + 3 &lt; - 7 have in common? Show

Kasey has 8 packages of gelatin. She plans to fill molds that each take 1 1/3 packages of gelatin Each mold can be divided into 6 servings. How many servings of gelatin can Kasey make?

Plz hurry D:

Kasey has 8 packages of gelatin. She plans to fill molds that each take 1 1/3 packages of gelatin Each

Answers

Answer:

I beleive Kasey can make 36 servings of gelatin. If you want you can check your answer by using the steps I provided.

Step-by-step explanation:

1. First we need to see how many times 1 1/3 can go into 8, or (how many gelatin molds can be filled. So, we will divide 8 divided by 1 1/3 to get (6.)

2. So, since we can fill 6 gelatin molds and each mold makes six servings, we will multiply 6 times 6 to get our answer 36.

The back of Dante's property is a creek. Dante would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a pasture. If there is 720720 feet of fencing available, what is the maximum possible area of the pasture

Answers

The correct value is 720 ft of fencing.

Answer:

Max Area = 64800 sq.ft

Step-by-step explanation:

A square will always give us the maximum area.

Thus, one side would be;

720/4 = 180 feet

So, we want a square 180 ft by 180 ft

however, from the question, we are to use the creek as one side. So, we'll take the 180 ft that we don't need because of the creek and then add it to the opposite side to get 180 + 180 = 360 ft.

Thus,we now have a rectangle with dimensions: 180 ft by 360 ft

Area is given by;

area = length × width

Maximum Area = 180 × 360

Max Area = 64800 sq.ft

Please answer correctly !!!!!!!!! Will mark brianliest answer !!!!!!!!!!!!

Please answer correctly !!!!!!!!! Will mark brianliest answer !!!!!!!!!!!!

Answers

Answer:

9x^2 +12x

Step-by-step explanation:

To find the area of a rectangle you need to multiply the length by the width. So,

3 by 3x^2 = 9x^2

3 by 4x = 12x

So the area of the entire rectangle is: 9x^2 + 12x

Given that f(x) = x² − 9 and g(x) = x + 3 what is the domain of (f×g)(x) {x ≤ R} E {x € Rx ≤ −3} {x € R\x ≥ −9} {x € R\x ≥ −3}

Answers

The domain of (f×g)(x) is the set of all real numbers, denoted as R, since both f(x) = x² - 9 and g(x) = x + 3 are defined for all real numbers.



To determine the domain of the function (f×g)(x), which represents the product of f(x) and g(x), we need to consider the domains of both f(x) and g(x) and find their intersection.

First, let's find the domain of f(x) = x² - 9:

The expression x² - 9 is defined for all real numbers since there are no restrictions on the input x. Therefore, the domain of f(x) is the set of all real numbers, denoted as R.

Next, let's find the domain of g(x) = x + 3:

The expression x + 3 is defined for all real numbers since there are no restrictions on the input x. Therefore, the domain of g(x) is also the set of all real numbers, denoted as R.

To find the domain of (f×g)(x), we need to find the intersection of the domains of f(x) and g(x), which is the set of values that are common to both domains.

The intersection of R (the domain of f(x)) and R (the domain of g(x)) is also the set of all real numbers, denoted as R. Therefore, the domain of (f×g)(x) is R.In summary, the domain of (f×g)(x) is the set of all real numbers: R.

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QUESTION 20 Recall that in the shipment of thousands of batteries, there is a 3.2% rate of defects. In a random sample of 40 batteries, what is the probability that at least 10% of them are defective?

Answers

The probability that at least 10% of a random sample of 40 batteries is defective when the shipment has a 3.2% defect rate is 0.0028 or 0.28%.

To answer the question, recall that in a random sample, the sample mean is a point estimate for the population mean, and the sample proportion is a point estimate for the population proportion. The sample size, which is n = 40 in this case, also plays an important role in determining how reliable a point estimate is.We can use the standard normal distribution to calculate the probability of getting a sample proportion of at least 0.10 by standardizing the sample proportion and using the standard normal table or calculator to find the corresponding cumulative probability. The z-score for a sample proportion of 0.10 is:z = (0.10 − 0.032) / 0.0719 ≈ 0.9864The probability of getting a sample proportion of at least 0.10 is:P( ≥ 0.10) = P(z ≥ 0.9864) ≈ 0.1602The probability that at least 10% of a random sample of 40 batteries is defective when the shipment has a 3.2% defect rate is 0.0028 or 0.28%.

To answer the question, we can use the formula for the probability of a binomial random variable:where n is the sample size, p is the probability of success, and  is the number of successes.We want to find the probability that at least 10% of the sample batteries are defective, which means that  ≥ 0.1n, or equivalently, ≥ 4.We can calculate the probability of getting exactly k defective batteries as follows:P = k) = (n choose k) pk(1 − p)n−kwhere (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.The probability of getting at least 4 defective batteries is:We can use a computer or calculator to find this sum, or we can use a normal approximation to estimate it. Since n × p = 1.28 > 10 and n × (1 − p) = 38.72 > 10, we can use the normal approximation to the binomial distribution.The expected value and standard deviation of  can be calculated as follows:Expected value ofStandard deviation of :Using a standard normal table or calculator, we find that:P(Z ≥ 2.34) ≈ 0.0094Therefore, the probability that at least 10% of a random sample of 40 batteries is defective when the shipment has a 3.2% defect rate is approximately 0.0094 or 0.94%.

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R1 and R2 be relations on a set A represented by the matrices ?

Answers

R1 and R2 are relations on a set A, which means they define a set of ordered pairs of elements in A. The matrices that represent R1 and R2 can be thought of as a way to visualize these ordered pairs.



Each row and column of the matrix corresponds to an element in A. If there is a 1 in the ith row and jth column of the matrix for R1, then (i,j) is an ordered pair in R1. Similarly, if there is a 1 in the ith row and jth column of the matrix for R2, then (i,j) is an ordered pair in R2.

If there is a 0 in a particular position in the matrix, then the corresponding pair is not in the relation.

Let R1 and R2 be relations on a set A. These relations can be represented by matrices M1 and M2, respectively, with dimensions |A|x|A|, where |A| is the cardinality of set A. The elements of the matrices M1 and M2 are binary, indicating whether there is a relation between the corresponding elements of set A in R1 and R2, respectively. If there is a relation, the matrix element will be 1, and if there is no relation, the matrix element will be 0.

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A gardener planted a newly sprouted oak tree that was just 3.5 inches tall. The sapling grew 12 inches each year.
Write an equation that shows how the sapling's height in inches, y, depends on the number of years since it was planted, x.

Answers

Answer:

y = 12x + 3.5

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

Initial height is the y-intercept of the line.

Yearly growth rate is the slope.

So we have:

m = 12, b = 3.5.

The equation of the line with these constants is:

y = mx + by = 12x + 3.5

Many psychologists do not use hypnosis in their
practices, it is because they know very little about it
and are wary of it as a result.
(A) practices, it is because they know very little about
it and are wary of it as a result
(B) practices because they know very little about it
and are therefore wary of it
(C) practices for the reason that they know very little
about it, with resulting wariness
(D) practices because of knowing very little about it
and therefore they are wary of it
(E) practices, their knowledge of it being very little
results in wariness of it

Answers

Many psychologists do not use hypnosis in their practices, it is because they know very little about it and are wary of it as a result.

Who are psychologists?

A psychologist is a specialist in the field of psychology who investigates behavior as well as mental states, perceptual, cognitive, emotional, and social processes. They frequently experiment with, observe, and interpret how people interact with one another and their surroundings as part of their work. Someone who examines the mind and behavior is called a psychologist. When people hear the word "psychologist," they frequently picture talk therapy; however, this profession actually covers a wide range of specialization areas, including things like animal studies and organizational behavior.

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Which of the coordinate points below will fall on a line where the constant of proportionality is 1/3? Select all that apply.

A) (5,8)

B) (3,1)

C) (9,3)

D) (12,4)

E) (18,6)

Answers

Answer:

The answer is B,C,D and E

The points that show the proportionality rate 1/3 are (3, 1), (9, 3), (12, 4) and (18, 6).

What is proportional relationship?

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

We have constant of proportionality is 1/3.

And the proportionality is represented as x/y = k, where x and y are two expressions and k is constant.

So, x / y = 1/3

A) (5,8)

x/y = 5/8 ≠ 1/3

B) (3,1)

x/y = 1/3

C) (9,3)

x/y = 3/9 = 1/3

D) (12,4)

x/y = 4/12 = 1/3

E) (18,6)

x/y = 6/18 = 1/3

Therefore, B, C, D and E are the answers.

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find x and y this is geometry

find x and y this is geometry

Answers

Y = 4
X = 12
I’m pretty sure^ I did this last unit btw

onsider the signal set: s1​(t)={0−2​0≤t<11≤t<2​}s2​(t)={00​0≤t<11≤t<2​}s3​(t)={10.5​0≤t<11≤t<2​}s4​(t)={−10​0≤t<11≤t<2​}​ Our assumption, as usual, is AWGN with power spectral density N0​/2. (a) Draw the signal-space (i.e. vectorized) version of this set. Sketch the decision regions. (b) Find a union bound for the probability of error.

Answers

Therefore, the upper bound of the probability of error is 0.5149.

(a) Signal-space version of the given signal set:S = {s1(t), s2(t), s3(t), s4(t)}= {(0, -2), (0, 0), (1, 0.5), (-1, 0)}Sketch of decision regions is given below:(b) Probability of Error: Probability of error (Pe) is the likelihood that one or more bits of a message are received incorrectly.

The upper bound for the probability of error can be determined using the union bound. The union bound is a general technique for finding an upper bound on the probability that any of a set of events occurs.

Probability of error,

Pe ≤ P1 + P2 + P3 + P

4where P1, P2, P3, and P4 are the probabilities of errors associated with the four decision regions.

P1= P(error for s1(t) | s2(t) transmitted) + P(error for s1(t) | s3(t) transmitted) + P(error for s1(t) | s4(t) transmitted) = P(e1|s2)P(s2) + P(e1|s3)P(s3) + P(e1|s4)P(s4) Here,

P(s1) = P(s2) = P(s3) = P(s4) = 1/4 (equiprobable) and where e1 denotes an error that occurs when s1(t) is transmitted, but another signal is received by the receiver in the presence of AWGN with power spectral density

N0/2. P(error for s1(t) | s2(t) transmitted)

= Q(√2E/N0) (Since, |s1(t) - s2(t)| = √10 and N0/2

= N0/2)P(e1|s2) = Q(√10E/N0) P(error for s1(t) | s3(t) transmitted)

= Q(√1.5E/N0) (Since, |s1(t) - s3(t)| = √5/2 and N0/2 = N0/2)P(e1|s3)

= Q(√(5/2)E/N0) P(error for s1(t) | s4(t) transmitted)

= Q(√5E/N0) (Since, |s1(t) - s4(t)| = √5 and N0/2

= N0/2)P(e1|s4) = Q(√5E/N0)

Putting these values in the above equation, P1 = 0.1287P2, P3, and P4 can also be calculated using the same formula with suitable values. P2 = P3 = P4 = 0.1287Hence, Pe ≤ P1 + P2 + P3 + P4 ≤ 0.5149

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