Using MATLAB, Plot Bode Diagrams Of G1(s) And G2(s) Given Below: G1(s)=1+s/1+2s G(s) = 1-s/1-2s Note (2024)

The unit rate for the speed of Runner A and B is 12 and 15 ft / sec respectively, where Rubber B is faster.

What is unit rate?

A unit rate means a rate for one of something.

Given that, Two runners are training for their next competitions. Each runner is able to run a certain distance in proportion to the time. The table displays the distance Runner A can run in relation to the time. Meanwhile, the graph on the right displays the distance Runner B can run in relation to time. We need to find the unit rates for both runners,

Runner A =

Unit rate = distance / time

= 54 / 4.5

= 12 ft / sec

Therefore, unit rate for the speed of Runner A is 12 ft / sec

Runner B =

According to graph, the Runner B can run 75 ft in seconds

Unit rate = distance / time

= 75 / 5

= 15 ft / sec

Therefore, unit rate for the speed of Runner B is 15 ft / sec

Since, the speed of Runner B is greater than Runner A therefore, Rubber B is faster.

Hence, the unit rate for the speed of Runner A and B is 12 and 15 ft / sec respectively, where Rubber B is faster.

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Finance amount: The amount you can finance for a new car with a monthly payment of $240, for 60 months (5 years), depends on several factors, including the loan interest rate, the down payment, and the value of the car.

Estimated percentage rate: The interest rate for a new car loan with a credit score between 601-660 typically ranges from 5% to 10%.

Amount of interest you will pay for the loan: The amount of interest you will pay for the loan can be calculated by multiplying the loan amount by the interest rate and the number of months.

How to calculate the total interest?

For example, if you finance $20,000 at a 7% interest rate for 60 months, the total interest paid over the life of the loan would be $3,140.

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Answer:

y = -110x + 1,600

Step-by-step explanation:

Zachary purchased a computer for $1,600 on a payment plan. Four months after he purchased the computer, his balance was $1,160. Five months after he purchased the computer, his balance was $1,050. What is an equation that models the balance y after x months?

1,160 - 1,050 = $110 change from month 5 to 4

Double check if the rate of decrease is steady over time:

1,600 - ($110 * 4 months) = 1,160

1,600 - ($110 * 5 months) = 1,050

This means, Zachary is paying $110 per month for his computer.

SO:

remaining payment plan balance = initial balance - 110 per month

This can be modeled by the algebraic equation:

y = 1,600 - 110x

rearrange right side:

y = -110x + 1,600

Answer:

[tex]y=-110x+1600[/tex]

Step-by-step explanation:

Given information:

Purchase price = $1,600Balance = $1,160 after 4 months.Balance = $1,050 after 5 months.

Define the variables:

Let x be the number of months.Let y be the balance of the payment plan (in dollars).

Therefore:

x = 0, y = 1600x = 4, y = 1160x = 5, y = 1050

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Determine if the equation is linear by calculating the slope between each pair of (x, y) points:

[tex]\implies \text{Slope}\;(m)=\dfrac{1050-1160}{5-4}=-110[/tex]

[tex]\implies \text{Slope}\;(m)=\dfrac{1160-1600}{4-0}=-110[/tex]

As the slope is the same, the equation is linear.

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

As the initial purchase price of the computer was $1,600, the y-intercept is 1600. We have already calculated the slope. Therefore, substitute the found slope and y-intercept into the slope-intercept formula to create an equation that models the balance y after x months:

[tex]y=-110x+1600[/tex]

Answer: V=144π cm³

Step-by-step explanation:

The given expression "4 divided by 2 left square brackets 2 plus 2 right square brackets equals" gives the solution one divided by 2.

How to solve expressions?

4 divided by 2 left square brackets 2 plus 2 right square brackets equals?

4 ÷ 2(2 + 2)

based on the concept of PEMDAS

P = parenthesis

E = Exponent

M = Multiplication

D = Division

A = Addition

S = Subtraction

= 4 ÷ 2(4)

= 4 ÷ 8

= 4/8

= 1/2

Therefore, the correct answer is 1/2(one divided by two

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Answer: 35%

Explanation:

1 - 0.65 = 0.35

0.35 in percentage is 35%

Answer:

It might be "C"

Step-by-step explanation:

Answer:

Joe mum so gaeee

Step-by-step explanation:

your answer is 1000

Answer:

(3, -11)

Step-by-step explanation:

Rearranging the equation becomes a slope-intercept form:

[tex]y = 2 - 3x[/tex]

where m = slope of equation = [tex]-3[/tex]

and c = intercept = [tex]2[/tex]

Substitute any value of x into the above slope-intercept equation to determine it's corresponding y value. Together these x and y values will form an ordered pair.

For example:

Take x = 3 and substitute in the above mentioned equation:

[tex]y = 2 - 3(3)[/tex]

[tex]= 2 - 9[/tex]

y = [tex]-11[/tex]

∴ An ordered pair that is a solution to the equation: (3, -11)

The least squares regression line for the corrected data would be shifted upwards compared to the original data, indicating that increasing the amount of time spent studying would likely have a greater impact on a student's grades.

The least squares regression line for the corrected data would be shifted upwards compared to the least squares regression line for the original data, since the corrected data point has a higher value than the original data point. This shift in the regression line would indicate that, in general, increasing the amount of time spent studying would have a greater impact on the student's grades than the original data indicated.

The least squares regression line for the corrected data would be shifted upwards compared to the original data, indicating that increasing the amount of time spent studying would likely have a greater impact on a student's grades.

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The Coalition for Airline Passengers Rights, Health, and Safety averages 400 calls a day to help stranded travelers deal with airlines. The hotline is staffed for 16 hours a day.

To calculate the average number of calls in different time intervals and the probability of different events related to these calls.

Part 1:

a. 60-minute interval average number of calls: 400/16 = 25 calls

30-minute interval average number of calls: 25/2 = 12.5 calls

15-minute interval average number of calls: 12.5/2 = 6.25 calls

Part 2:

b. To find the probability of exactly 6 calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of exactly 6 calls in a 15-minute interval is:

P(6 calls) = (e^-6.25)*(6.25^6)/6! = 0.0686

c. To find the probability of no calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of no calls in a 15-minute interval is:

P(0 calls) = e^-6.25 = 0.0047

d. To find the probability of at least two calls in a 15-minute interval, we can use the cumulative distribution function of the Poisson distribution. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of at least two calls in a 15-minute interval is:

P(X >= 2) = 1 - P(0 calls) - P(1 call) = 1 - 0.0047 - (e^-6.25)*(6.25^1)/1! = 0.9906

Thus, the average number of calls in a 60-minute interval is 25, in a 30-minute interval is 12.5, and in a 15-minute interval is 6.25. The probability of exactly 6 calls in a 15-minute interval is 0.0686, the probability of no calls in a 15-minute interval is 0.0047, and the probability of at least two calls in a 15-minute interval is 0.9906.

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Answer: To calculate the total, we need to first calculate the discount and then the tip.

First, calculate the discount: $21.50 x 10% = $2.15

Then, subtract the discount from the subtotal: $21.50 - $2.15 = $19.35

Next, calculate the tip: $19.35 x 20% = $3.87

Finally, add the tip to the subtotal after the discount to find the total: $19.35 + $3.87 = $23.22

Therefore, Abdiel's total would be $23.22 if he uses a coupon for 10% off the subtotal and leaves a 20% tip before the discount.

Step-by-step explanation:

O D. x+16=60

The answer

For the given triangle the value of z = 1, y = 6, and x = 4.75.

What is geometry?

One of the earliest areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

The value of x,y, and z will be calculated by the property states that the ratio of the median line passing from the centroid of the triangle is divided into the ratio of 1: 2.

The value of x,

( 2x - 6 ) / 7 = 1 / 2

2 ( 2x - 6 ) = 7

4x - 12 = 7

4x = 19

x = 19 / 4

The value of y,

3 / y = 1 / 2

y = 3 x 2

y = 6

The value of z,

2z / 4 = 1 / 2

4z = 4

z = 1

Therefore, the values are z = 1, y = 6, and x = 4.75.

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Reliability refers to the consistency of measures, whereas validity refers to the truthfulness of a measurement.

What do we mean by measure?

The size, capacity, or amount of something determined by measurement. Use equal amounts of ingredients. Something used for measurement (such as a ruler or cup).A unit used to measure. A foot is a measure of length.

What is statistics in mathematics?

Statistics is a science concerned with developing and studying methods for measure, collecting, analyzing, interpreting, and presenting empirical data.

Significance of statistics:

Statistics is the branch of mathematics for collecting, analyzing and interpreting data. Statistics can be used to predict the future, determine the likelihood of certain events occurring, and answer research questions.

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The implicit cost of Jack's education is $77,000, which is the amount of foregone income he gave up in order to attend college.

The implicit cost of Jack's education refers to the opportunity cost or the foregone income he gave up in order to attend college. It is a measure of the value of the next best alternative that he had to sacrifice.

First, let's find the total cost of tuition and books. Jack pays $17,000 per year, so the total cost will be 17,000 * 4 = $68,000 over 4 years of college.

Next, let's find the total cost of rent and food. Jack pays $600 per month for rent and $400 per month for food, so the total cost will be 600 + 400 = $1,000 per month. Over 4 years of college, this comes to 1,000 * 12 * 4 = $48,000.

Finally, Jack also pays $125 per month for on-campus parking, so the total cost will be 125 * 12 * 4 = $6,000.

Putting it all together, we can write the equation for the implicit cost of Jack's education as follows:

Implicit Cost = Foregone Income - Total Cost of Tuition, Rent, Food and Parking

Implicit Cost = 45,000 - (68,000 + 48,000 + 6,000)

Implicit Cost = 45,000 - 122,000

Implicit Cost = -77,000

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The value of variables are,

⇒ a = 3100

⇒ b = 0.7

What is exponential decay?

An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time.

The exponential decay function:

Aₙ = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.

Given that;

Wellington Elementary School bought a printer one year ago for $3,100.

And, Today, the value of the printer has decreased to $2,170 and is expected to continue decreasing each year.

Now, An equation in the required exponential form,

A = A₀(1 - r)ˣ

Substituting the values,

A = 3100(1-r)ˣ.

To find the r:

2170 = 3100(1-r)

r = 0.3

So, The equation is,

Aₙ = 3100(1-0.3)ˣ.

y = 3100(0.7)ˣ.

Therefore, The value of variables are,

⇒ a = 3100

⇒ b = 0.7

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Using the drop-down menu below to write an inequality is V ≥ 10. The number of visits she needs to make in order to get a free movie ticket is 10.

We have,

75 rewards points just for signing up.

earns 13.5 points for each visit to the movie theater

she needs at least 210 points for a free movie ticket

To write the inequality representing v is,

75 + 13.5v ≥ 210

13.5v ≥ 210 - 75

13.5 v ≥ 135

v ≥ 10

Therefore, by solving inequality the number of visits she needs to make in order to get a free movie ticket is 10.

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Step-by-step explanation:

x÷12

2/3/12

2×12/3

24/3

8

For a set of data in which the sample mean is 83.3 and the sample standard deviation is 6.3 the z-score given that x = 79.8 would be -0.555

We know that the formula for calculating a z-score is :

z = (x - μ) / σ

where z is the standard z - score

x is the observed value

μ is the mean of the sample

σis the standard deviation of the sample

here, set of data in which the sample mean is 83.3 and the sample standard deviation is 6.3

i.e., μ = 83.3, σ = 6.3

We calculate the z-score for x = 79.8

Using above formula,

z = (x - μ) / σ

z = (79.8 - 83.3) / (6.3)

z = (-3.5) / (6.3)

z = -0.555

Therefore, the z-score is: -0.555

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The linear function that models this scenario is given as follows:

y = -0.25x + 13.

How to define the linear function?

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The slope m represents the rate of change.The intercept b represents the initial amount.

Bridget has 13 gallons of gasoline to use for her lawnmowing business, hence the intercept b is given as follows:

b = 13.

From the graph, when x increases by 20, y decays by 5, hence the slope m is given as follows:

m = -5/20

m = -0.25.

Hence the function is given as follows:

y = -0.25x + 13.

Missing Information

The problem is given by the image presented at the end of the answer.

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Answer: 172.0 degrees

Step-by-step explanation:

In 180 degrees, there are [tex]\pi[/tex] radians. That means each radian is equal to:

[tex]\frac{180}{\pi }[/tex]

= 57.3248408

Then we simply multiply that by 3 to get:

3 * 57.3248408

= 171.974522

Rounded to the nearest tenth is 172.0

Answer:

172

Step-by-step explanation

180 degrees is equal to one pi.

That means each radian is equal to:= 57.3248408

Then multiply that number by 3

Written out is: 3 x 57.3248408= 171.97452

When rounded to the nearest tenth is 172.0

Answer: Yes, I can solve this problem using a system of equations. Let n be the number of nickels and q be the number of quarters. Then we can write two equations:

The total number of coins is 25: n + q = 25.

The total value is $3.85: 0.05n + 0.25q = 3.85

We can solve this system of equations using substitution or elimination. Let's use substitution:

From equation (2), we can solve for n: n = (3.85 - 0.25q)/0.05.

Substitute this expression for n into equation (1): (3.85 - 0.25q)/0.05 + q = 25.

Multiply both sides by 0.05 to clear the denominators: 3.85 - 0.25q + 0.05q = 25 * 0.05.

Simplify the left side: 3.85 = 1.25q.

Divide both sides by 1.25 to solve for q: q = 3.08

Substitute this value for q into equation (1) or the expression for n from step (1) to find n: n = 25 - q = 25 - 3.08 = 21.92

Since n and q represent the number of coins, we round them down to the nearest whole number. So, there are 21 nickels and 3 quarters.

Step-by-step explanation:

Kerys should substitute the values of k from 0 to 4 (inclusive) in the binomial theorem expression to expand the binomial (2x + y)⁴.

What is the Binomial Theorem?

The binomial theorem states the principle for expanding the algebraic expression (x + y)ⁿ and describes it as the total of the phrases involving the unique exponents of the x and y variables. Each word in a binomial expansion has a coefficient, which is a numerical value.

here, we have,

The binomial theorem states that the expansion of the binomial (x+y)^n is given by the formula:

(x+y)n = ∑nk=0nCk xn-kyk = ∑nk=0nCk xkyn-k

The variable n represents the power to which the binomial is raised, in this case n = 4.

The variable k is the exponent of the second term in the binomial (b), in this case y.

So, with k = 0, the term will be aⁿ = (2x)⁴, with k = 1, the term will be

a^(n-1) *b = (2x)³y , and so on.

Therefore, he should substitute the values of k from 0 to 4 (inclusive) in the binomial theorem expression to expand the binomial (2x + y)⁴.

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Using proportional relationships, it is found that:

1. A = 15.8, B = 5, C = 63.2.

2. A table with a rate of 0.82 represents the data.

3. Candidate B received 54 votes.

What is a direct proportional relationship?

A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, also called unit rate, as follows:

y = kx

here, we have,

For item 1, the constant is given as follows:

k = 31.6/4 = 7.9.

Hence the equation is:

y = 7.9x.

Then the value of A is found as follows:

A = 7.9(2)

= 15.8.

The value of B is found as follows:

7.9B = 39.5

B = 39.5/7.9

B = 5.

The value of C is:

C = 7.9(8) = 63.2.

For item 2, the rate is given as follows:

k = 35/42.5 = 0.82.

Hence a table with a rate of 0.82 represents the data.

For item 3, we have that the relation is:

B = kA.

Hence the constant is:

k = 18/15

k = 1.2.

Then the number of votes received by Candidate B is:

B = 1.2 x 45 = 54 votes.

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Answer:

3

28

Step-by-step explanation:

The expression (f/g) (4) is equal to f(4) / g(4).

f(4) = 4^2 + 2*4 - 3 = 16 + 8 - 3 = 21

g(4) = 4^2 - 9 = 16 - 9 = 7

So, (f/g) (4) = 21 / 7 = 3.

The expression (f + g) (4) is equal to f(4) + g(4).

f(4) = 4^2 + 2*4 - 3 = 16 + 8 - 3 = 21

g(4) = 4^2 - 9 = 16 - 9 = 7

So, (f + g) (4) = 21 + 7 = 28.