a unity feedback control system is characterized by an open-loop transfer function
G(s)H(s)=k/s(s+10)
determine the system gain k so that the system will have a damping ratio of 0.5. for this value of k, find the rise time, settling time, and peak overshoot. assume that the system is subjected to a step input of 1v

Step-by-step explanation:

since we can officially use only one point (the given point), we need to start with the point-slope form :

y - y1 = m(x - x1)

with m being the slope, (x1, y1) being the point.

sadly, to get the slope, we need a second point anyway, because the slope is the ratio

y coordinate difference / x coordinate difference

when going from one point on the line to another.

I recommend to use (0, 50) for the "other" point, as there seems to be the smallest error in the coordinates.

so, when going from (0, 50) to the given point (6, -40) :

x changes by +6 (from 0 to 6).

y changes by -90 (from 50 to -40).

the slope m = -90/+6 = -15/1 = -15

y - -40 = -15(x - 6) = -15x + 90

y + 40 = -15x + 90

y = -15x + 50

that is the slope-intercept form.

m = -15

b = 50

y = -242

-242 = -15x + 50

-292 = -15x

x = -292/-15 = 292/15 = 19.46666666... ≈ 19

the best rule to describe this rotation is:

(x, y) → (-y, x)

Why it is?

The given rotation is a 270 degree clockwise rotation about the origin. This means that each point in Triangle ABC is rotated 270 degrees in a clockwise direction around the origin to produce the corresponding point in Triangle A'B'C'.

One possible rule to describe this rotation is:

(x, y) → (-y, x)

This rule represents a 90 degree clockwise rotation about the origin, which can be applied three times to achieve a 270 degree clockwise rotation.

So, if we apply this rule to each vertex of Triangle ABC, we get the corresponding vertices of Triangle A'B'C':

A = (a, b) → A' = (-b, a)

B = (c, d) → B' = (-d, c)

C = (e, f) → C' = (-f, e)

Therefore, the best rule to describe this rotation is:

(x, y) → (-y, x)

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the exponent of the product of 8.9 x 10¹² and 4.7 x 10⁻² in scientific notation is 11.

Exponential refers to a mathematical function or relationship in which a variable (such as x) is raised to a constant power (such as 2, 3, or e) to produce a result. The term "exponential" can also be used more broadly to describe any situation in which something grows or changes at an increasingly rapid rate over time, often with a compounding effect.

First, we multiply the two numbers:

(8.9 x 10¹²) x (4.7 x 10⁻²) = 41.83 x 10¹⁰

41.83 x 10¹⁰ = 4.183 x 10¹¹

Therefore, the exponent of the product of 8.9 x 10¹²and 4.7 x 10⁻² in scientific notation is 11.

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Answer:

Step-by-step explanation:

ur mom

Using trigonometric functions, the value of the side AC = 2.85 units.

The right triangle's angle serves as the domain input value for the six fundamental trigonometric operations, and the output is a range of numbers.

The angle, given in degrees or radians, is the domain of the trigonometric function, sometimes referred to as the "trig function," of  f(x) = sin, and the range is [-1, 1]. The other functions have a similar domain and scope. Trigonometric functions are widely used in algebra, geometry, and calculus.

Now in the given figure,

The angle is a right-angled triangle.

Now as per the trigonometric functions,

Sin 35° = AC/AB

⇒ 0.57 = x/5

⇒ x = 0.57 × 5

= 2.85.

The length of the opposite side AC is 2.85 units.

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As the banker at the Banco de los Trabajadores de Tegucigalpa, I greet Mr. Milton Escobar and thank him for choosing our bank for his fixed term deposit. I verify his identification and confirm the details of his deposit, which are:

Fixed Term Deposit number: #2250

Deposit amount: L100,000.00

Deposit term: 6 months

Interest rate: 10.5% per annum

I inform Mr. Escobar that the interest on his deposit will be calculated and credited to his account at the end of the deposit term. I also explain that he can choose to receive the interest in cash or reinvest it in the fixed term deposit.

Next, I ask Mr. Escobar to provide me with a check for the full deposit amount, payable by the Banco de los Trabajadores de Tegucigalpa, and I confirm that the check number is #0045. I inform him that the check will be deposited in his account and that he will receive a deposit confirmation letter.

Finally, I thank Mr. Escobar for his business and remind him to keep his deposit confirmation letter in a safe place, as it is a crucial document that he will need to produce at the time of maturity to withdraw his funds. I assure him that our bank will provide him with the highest quality service and look forward to his continued patronage.

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Translated Question ;

Mr. Milton Escobar appears at the Banco de los Trabajadores de Tegucigalpa to set up a Fixed Term Deposit #2250 for 6 months for L100,000. 00 to 10.5% annual interest, delivering the total amount by check #0045 payable by the same bank. Play the opening game

(a) The probability that exactly two cars finish the race is 0.0512.

(b) The probability that at most two cars finish the race is 0.05792.

(c) The probability that at least three cars finish the race is 0.94208.

(a) To determine the probability that exactly two cars finish the race, we have to use binomial distribution. In this case, we have n = 5 trials, and p = 0.8 is the probability that a car finishes the race (1 - 0.2). Using the binomial distribution formula:

P(X = k) = (nCk)(p^k)(1 - p)^(n - k)

Where X is the number of cars that finish the race, we get:

P(X = 2) = (5C2)(0.8²)(0.2)³= (10)(0.64)(0.008)= 0.0512

Therefore, the probability that exactly two cars finish the race is 0.0512.

(b) To determine the probability that at most two cars finish the race, we have to calculate the probabilities of 0, 1, and 2 cars finishing the race and add them up.

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)= (5C0)(0.8⁰)(0.2)⁵ + (5C1)(0.8¹)(0.2)⁴ + (5C2)(0.8²)(0.2)³= 0.00032 + 0.0064 + 0.0512= 0.05792

Therefore, the probability that at most two cars finish the race is 0.05792.

(c) To determine the probability that at least three cars finish the race, we can calculate the probability of 0, 1, and 2 cars finishing the race and subtract it from 1, which gives us the probability of at least three cars finishing the race.

P(X ≥ 3) = 1 - [P(X = 0) + P(X = 1) + P(X = 2)]= 1 - (0.00032 + 0.0064 + 0.0512)= 0.94208

Therefore, the probability that at least three cars finish the race is 0.94208.

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A random sample is called a representative sample.

It is a subset of a larger population that is selected in a way that ensures every individual in the population has an equal chance of being included in the sample. By ensuring randomness in the selection process, a representative sample is more likely to accurately reflect the characteristics and diversity of the larger population.

Representative samples are important in research and statistical analysis because they allow for more generalizable conclusions to be drawn about the population as a whole.

Without a representative sample, research findings may be biased and not applicable to the entire population. Therefore, a representative sample is crucial for ensuring the validity and reliability of research results.

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Answer:

same

Step-by-step explanation:

They are the same since

1/2÷4=1/2×1/4(reciprocal)

Answer:

dfgdfvdfvthtybg f cv v  

Step-by-step explanation:

Answer:

Find the numerical values of the following expressions. -3|x|+2x-1 if x=-5

Step-by-step explanation:

Substituting x=-5, we get:

-3|x| + 2x - 1 = -3|-5| + 2(-5) - 1

= -3(5) - 10 - 1

= -15 - 10 - 1

= -26

Therefore, -3|x| + 2x - 1 = -26 when x=-5.

Answer:

$2.235

Step-by-step explanation:

15% = 0.15

We Take

15.50 x 0.15 = $2.235

So, the tip for this bill is $2.235

Answer:

2 hours

Hope its right

Answer:

CP of computer = 27000 rs.

Step-by-step explanation:

D% = Dis/MP*100

We know, Dis = MP-SP

Given Profit= 1160 rs.

So,CP = 27000 rs.

Answer: $8

Step-by-step explanation:

To find how much he saved over the course of 6 weeks, subtract 62 from 110.

110 - 62 = 48

To find how much he saved each week, divide 48 by 6.

48 ÷ 6 = 8

Liam saved $8 each week.

The given example of f(1011) = 1110 illustrates how a one-to-one function operates, in that the same bitstring is not mapped to multiple elements in the range.

For the given functions f: A -> A and g: A -> A which are one-to-one functions, the following statements are true:

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a. the mean is 200.31 cm. b. The height of the new player is 210 cm.

The mean, commonly referred to as the average, is a statistic that depicts the usual value of a group of data and measures central tendency. It is calculated by adding up all of the data set's values and dividing the result by the total number of values. Since it offers a single value that summarises the complete set of data, the mean is an effective statistical tool. It may, however, be vulnerable to outliers or extremely high or low values that affect the mean's value. As a result, while examining data, it is crucial to take additional measures of central tendency into account, such as the median or mode.

The mean or average is given as:

mean = (sum of all heights) / (number of players)

The total number of players are:

1 + 3 + 2 + 5 + 2 = 13

Sum of heights is:

(198 x 1) + (199 x 3) + (200 x 2) + (201 x 5) + (202 x 2) = 198 + 597 + 400 + 1005 + 404 = 2604

Thus,

mean = 2604 / 13 = 200.31 cm

b. For the new player the number of players are 14:

201 = (2604 + height of new player) / 14

201 x 14 = 2604 + height of new player

2814 = 2604 + height of new player

height of new player = 2814 - 2604 = 210 cm

Hence, a. the mean is 200.31 cm. b. The height of the new player is 210 cm.

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Answer:

Step-by-step explanation:

To solve this problem, we can use the formula for calculating compound interest:

A = P * (1 + r/n)^(n*t)

where:

A = the final amount

P = the principal (initial amount of money)

r = the annual interest rate (as a decimal)

n = the number of times interest is compounded per year

t = the time (in years)

In this problem, we know that the interest rate is 4.5% per year, or 0.045 as a decimal. The money is deposited for 48 months, or 4 years.

Let's assume that the principal deposited is P. Then we can use the formula to calculate the final amount:

A = P * (1 + r/n)^(nt)

80,000 = P * (1 + 0.045/12)^(124)

Simplifying the equation, we get:

80,000 = P * (1.00375)^48

80,000 = P * 1.21169

Dividing both sides by 1.21169, we get:

P = 80,000 / 1.21169

P = 66,000

Therefore, the initial amount deposited by the person was Rs. 66,000.

The average number of hours of sleep for working college students is between 6.28 and 6.72 hours of sleep each night

According to the given data,

Sample size n = 101

Sample mean x = 6.5

Standard deviation s = 2.14

Level of confidence C = 96%

Using a 96% confidence level, the value of t* for 100 degrees of freedom is 2.081, as given in the question.

Now, the formula for the confidence interval is:x ± (t* × s/√n)Here, x = 6.5, s = 2.14, n = 101, and t* = 2.081

Substituting the values in the above formula, we get:

Lower limit = x - (t* × s/√n) = 6.5 - (2.081 × 2.14/√101) = 6.28

Upper limit = x + (t* × s/√n) = 6.5 + (2.081 × 2.14/√101) = 6.72

Therefore, the 96% confidence interval for the average number of hours of sleep for working college students is between 6.28 and 6.72 hours of sleep each night.

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As Masons backyard deck is rectangular, the length of the deck is 22 feet.

Let's start by using algebra to solve for the length of the rectangular deck.

Let L be the length of the deck.

Then, the width of the deck is L - 12.

The perimeter is the sum of all four sides, so we have:

Perimeter = 2L + 2(L - 12) = 64

Simplifying the equation, we get:

2L + 2L - 24 = 64

Combining like terms, we get:

4L - 24 = 64

Adding 24 to both sides, we get:

4L = 88

Dividing both sides by 4, we get:

L = 22

Therefore, the length of the deck is 22 feet.

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(a) The present value of an annuity formula can be used to calculate the monthly payment: Payment is equal to (PV x I / (1 - (1 + i)(-n)).

Where PV is the loan's present value, I is its monthly interest rate (0.035 / 12), and n is the number of payments (15 years multiplied by 12 months every year = 180 months).

Applying the values provided, we obtain:

(136,000 x 0.002917) / (1 - (1 + 0.002917)(-180)) is the amount to be paid.

Amount paid: $1,054.63

Hence, the installment will be $1,054.63 per month.

(b) By deducting the loan amount (PV) from the total amount paid over the loan's lifetime, it is possible to get the total interest payment:

Total interest equals PV minus (Payment x n)

Applying the values provided, we obtain:

$1,054.63 multiplied by 180 equals $136,000 in interest.

Interest totaled $88,833.40.

The total interest payment will therefore be $88,833.40.

(c) The Turners will have paid 120 times over the course of 10 years (10 years x 12 months/year). To determine their equity, we can apply the formula for calculating a loan's remaining balance:

The remaining balance is calculated as follows: PV x (1 + i)n - Payment x (1 + i)n - 1)/i

Where n denotes how many payments are still due (180 - 120 = 60).

Applying the values provided, we obtain:

The remaining balance is calculated as follows: $136,000 x (1 + 0.002917)60 - $1,054.63 x (1 + 0.002917)60 - 0.002917

Balance remaining: $71,587.90

As a result, their equity will be $170,000 (the original purchase price) less $71,587.90 (the outstanding balance) = $98,412.10 after ten years.

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A The amount of money in a savings account with an annual interest rate of 1.5%

Answer:

  C, E

Step-by-step explanation:

You want the equations that represent 2 boys for every 5 girls in a class.

The number of boys is represented by x, and the number of girls is represented by y, so you have ...

  x : y = 2 : 5

As fractions, this is ...

  x/y = 2/5

Multiplying by 5y gives ...

  5x = 2y . . . . . . matches equation C

Dividing by 5, we have ...

  x = 2/5y . . . . . . matches equation E

The compass directions that are given to A, B and C. are East, South-East and North-west respectively.

North, South, East, and West are the four cardinal directions. The sun's rising and setting serve as a point of reference for these instructions.

Thus, the compass directions that are given to A, B and C. are East, South-East and North-west respectively.

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If the probability an American will die from falling is 0.41%, the probability a American will not die from falling is 100% - 0.41% = 99.59%.

Answer: 99.59%.

The measures of central tendency include mean and mode, which include a third measure called median.

The three measures for determining central tendency are mean, median, and mode. The mean, also known as average, is the result of dividing the total number of observations by the number of observations. The mode is the value that occurs the most frequently, whereas the median is the midpoint value in the ordered set of observations.

The average or middle of a dataset can be discovered with the aid of central tendency measures. The most frequent value is the mode. The median is the midpoint of an ordered dataset. Mean: the product of the total number of values and their sum.

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Correct question is:

The measures of _________ include mean and mode. The third of those measures is ________.

Dividing the sum of all data values by the total frequency will give us the_____.

This principle is validated by the data shown in the table.

Tests and measurements is an essential aspect of the education process as it enables educators to gauge the level of knowledge and skills their students have acquired. The principle that longer tests tend to be more reliable than shorter ones has some merit because it allows educators to assess a broader range of skills and knowledge, which increases the validity of their assessments.In my opinion, the principle that longer tests tend to be more reliable than shorter ones is illustrated in the reliability coefficients shown in the table. This is because the data shows that the reliability coefficients for longer tests are consistently higher than those for shorter tests. Additionally, the results for the 10-item test indicate a higher reliability coefficient compared to the 5-item test, which supports the notion that longer tests are more reliable than shorter ones.The table displays that the longer tests have higher reliability coefficients compared to the shorter tests. For example, in the 5-item test, the reliability coefficient is .45, while the 10-item test's reliability coefficient is .73. This shows that the 10-item test is more reliable than the 5-item test, as the higher reliability coefficient indicates that the assessment is consistent in measuring the skill or knowledge it is intended to measure. As a result, this principle is validated by the data shown in the table.

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