Stephanie is helping her band collect money to fund a field trip the band decided to sell chocolate bars each bar sells for $1.50 and each box contains 20 bars below is a partial table of monies collected for the different number of boxes sold

Transfer function of the system is:X(s)/Y(s) = 10/(s^2+1.6s+4)We need to find the following:

a) Y(t); b) Percent overshoot; c) Ultimate value of Y(t); d) Maximum value of Y(t) and e) Period of oscillation.

(a) Calculation of Y(t):The transfer function of the system isX(s)/Y(s) = 10/(s^2+1.6s+4)Now, applying the Laplace inverse on both sides,Y(s) = 10/(s^2+1.6s+4) × X(s)Taking the inverse Laplace of Y(s),y(t) = L^-1 {10/(s^2+1.6s+4) × X(s)}Using partial fraction decomposition to find the inverse Laplace of Y(s), we get:y(t) = 1.2508{ 2.22 e^(-0.8t) - 0.22 e^(-3.2t)}Therefore, the value of Y(t) is 1.2508{ 2.22 e^(-0.8t) - 0.22 e^(-3.2t)}.

(b) Calculation of percent overshoot:The transfer function of the system isX(s)/Y(s) = 10/(s^2+1.6s+4)The damping ratio (ζ) can be given asζ = 1/2 √(ζ²-4)ζ = 1/2 √(1.6²-4)ζ = 0.6For a second-order system with a damping ratio of 0.6, the percent overshoot is given as:%OS = e^(-ζπ/√(1-ζ²)) × 100%OS = e^(-0.6π/√(1-0.6²)) × 100OS = 26.12%Hence, the percent overshoot is 26.12%.

(c) Calculation of the ultimate value of Y(t):The transfer function of the system isX(s)/Y(s) = 10/(s^2+1.6s+4)For the ultimate value of Y(t), we take the limit of sY(s) as s tends to 0.The value of Y(s) is given as:Y(s) = 10/(s^2+1.6s+4) × X(s)On simplifying the above equation, we get:sY(s) + 1.6 Y(s) + 4 Y(s) = 10 X(s)Now, taking the limit of sY(s) as s approaches 0,sY(s) = lim s→0 sY(s) = 0Therefore, 1.6 Y(s) + 4 Y(s) = 10 X(s)Taking the limit of Y(s) as s approaches 0,0 = 10 X(0)Y(0) = 2.5Hence, the ultimate value of Y(t) is 2.5.

(d) Calculation of the maximum value of Y(t):The maximum value of Y(t) is given as:Ymax = 2.5 + (1+ζ²)^0.5 e^(-ζπ/√(1-ζ²)) / (ζ√(1-ζ²))The value of ζ is 0.6Hence, substituting the value of ζ in the above equation, we get:Ymax = 2.5 + (1+0.6²)^0.5 e^(-0.6π/√(1-0.6²)) / (0.6√(1-0.6²))Ymax = 3.129

(e) Calculation of the period of oscillation: The period of oscillation is given as:T = 2π / ωnWhere,ωn = √(1-ζ²) / (2ζ)Therefore,ωn = √(1-0.6²) / (2 × 0.6)ωn = 1.302Therefore,T = 2π / ωnT = 4.830sHence, the period of oscillation is 4.830s.

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Answer:

is it on edge

Step-by-step explanation:

Answer:

she bought 4 braclets

Step-by-step explanation:

if you do 20 times 4 it gets you 80 and if you subtract 50 it leaves you with 30 meaning she bought 4 bracelets

i do hope this helps even tho my explanation isn't exactly the best

Step-by-step explanation:

draw a rectangle with width 98 and height 55 there are two of each side, so 98 + 98 + 55 +55 = 306

Answer:

306m

Step-by-step explanation:

You need to find the perimeter of the rectangle. To do that, you just add the side lenghts. So, this is your lawn with the side lengths:

                      55m
           _____________
           |                           |
           |                           |
           |                           |
98m    |                           |     98m
           |                           |
           |                           |
           |                           |
           _____________
                      55m

You just add them together!

55 + 55 + 98 + 98 = 306

so you need 306 meters of fencing

A sample statistic handles the parameter it is intended to estimate so when target population and indeed the sampled population are equal.

Data gathering, organization, analysis, interpretation, as well as presentation are all topics covered in the field of statistics. It is customary to start with a statistical population or perhaps a statistical model to be investigated when using statistics to solve a scientific, industrial, or social problem.

To sum up, the five reasons to studying statistics are to be able to do research efficiently, to read and assess journal articles, to even further develop critical thinking and analytical skills, to behave as an informed consumer, and to be aware of when you need to seek outside statistical support.

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x = 239

y = 146

Step-by-step explanation:

Let two numbers be x and y

x + y = 385. ------------equation (1)

x - y = 93. ------------equation (2)

from (1) and (2)

x = 239 and y = 146

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Edge 2021

Answer:

A. left 3, up 4

Step-by-step explanation:

Doing it on EDG right now!

Good luck to yalls :)

Answer: 136.875

Step-by-step explanation:

First of all, we make that assumption that 176 is 100% since it is our output value.

Then we seek the value with x.

Since we already know that 100%=176, we put x%=240.9 which will give us some simple equations: 100%=176(1) and x% = 240.9

And then we turn our equations into this:

100% = 240.9

 x%        176

Lastly, we take the inverse (or reciprocal) of both sides

x% =  176  

100   240.9

At the end, we get this:

240.9 is 136.875% of 176

Answer:

Hey there!

Andrew made a mistake in the last step. -11.8+9.8=2, not -21.6.

Let me know if this helps :)

The value of the missing lengths are;

x = 4

y = 3. 5

It is important to note that trigonometric identities are described as equalities that shows the certainty of all the values that are found the in the trigonometric functions in an equation.

There are distinct identities, such as;

From the information given, we have that;

sin θ = opposite/ hypotenuse

Now, substitute the values

sin 30 = 2/x

Find the sine value

0.5x = 2

x = 4

Using the Pythagorean theorem, we have;

4² - 2² = y²

y² = 16 - 4

y² = 12

Find the square root

y = 3. 5

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Answer: The average difference of weights of all 48 eggs from mean eight is 0.08.

Step-by-step explanation:

The mean absolute deviation of a data interprets the mean distance between each data point and the mean.

When this distance goes larger it means data has greater variability

Given, 48 large eggs have a mean weight of 2.1 ounces and a mean absolute deviation of 0.08 ounces.

It means that the average difference of weights of all 48 eggs from mean eight is 0.08.

The rate constant of inactivation is -0.6538 \(s^{-1}\).

To determine the rate constant of inactivation using the Chick-Watson model, we need to plot the natural logarithm of the surviving fraction of the virus (N/N₀) against time (t) and fit a linear regression to the data. The Chick-Watson model is given by the equation:

ln(N/N₀) = -kt

Where:

N₀ is the initial number of viruses (\(10^{6}\))

N is the number of viruses at time t

k is the rate constant of inactivation

Let's calculate the surviving fraction (N/N₀) and perform the linear regression:

Time (s) | N/N₀ | ln(N/N₀)

0 | 1.0 | 0.0

2 | 0.2 | -1.61

4 | 0.01 | -4.60

6 | 0.0015 | -6.50

8 | 0.0001 | -9.21

Using the given data, we can perform linear regression on the ln(N/N₀) values against time (t) values to determine the rate constant (k).

Let's calculate the rate constant (k) using linear regression:

Sum of ln(N/N₀) = -21.92

Sum of t = 20

Sum of (\(t^{2}\)) = 120

Mean of ln(N/N₀) = (-21.92) / 5 = -4.384

Mean of t = 20 / 5 = 4

Mean of (\(t^{2}\)) = 120 / 5 = 24

Sum of [(t - mean(t)) * (ln(N/N₀) - mean(ln(N/N₀)))] = -52.304

Sum of \((t-mean(t))^{2}\) = 80

Using the linear regression formula:

k = [Sum of [(t - mean(t)) * (ln(N/N₀) - mean(ln(N/N₀)))]] / [Sum of  \((t-mean(t))^{2}\) ]

k = -52.304 / 80 = -0.6538

Therefore, the rate constant of inactivation for NH2Cl disinfection of MS2 bacteriophage at a concentration of 2 mg/L is approximately -0.6538 \(s^{-1}\).

Correct Question :

The data for NH2Cl disinfection of MS2 bacteriophage at a concentration of 2 mg/L is shown below. The temperature was 20 °C, the pH was 6.0. Determine the rate constant of inactivation assuming the Chick-Watson model applies with an n value of 1.0.

Time (s) 0 2 4 6 8

Number of virus \(10^{6}\) 0.2*\(10^{6}\) 0.1*\(10^{5}\) 0.15*\(10^{4}\) 0.1*\(10^{3}\)

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The derivative of F(x) is F'(x) = 3x² - 8x.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

To find the derivative of the given function F(x), we will apply the fundamental theorem of calculus and differentiate the integral with respect to x.

Let's compute F'(x):

F(x) = ∫[0 to x] (t³ - 4t² + 6) dt

To differentiate the integral with respect to x, we'll use the Leibniz integral rule:

F'(x) = d/dx ∫[0 to x] (t³ - 4t² + 6) dt

According to the Leibniz integral rule, if the upper limit of the integral is a function of x, we need to apply the chain rule. The lower limit of the integral is a constant, so it will not affect the differentiation.

F'(x) = (d/dx)(x³ - 4x² + 6)  [applying the chain rule]

F'(x) = 3x² - 8x

Therefore, the derivative of F(x) is F'(x) = 3x² - 8x.

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We will go into more detail about various techniques that are currently thought to help gymnasts become more flexible or increase flexibility below:

Now that we've cleared everything up, what exactly is flexibility? The range of motion in a joint or collection of joints is referred to as flexibility. Flexibility in one joint doesn't always translate to flexibility in another.

Because certain abilities cannot be learned by gymnasts without the proper range of motion, flexibility is crucial in the sport. When they are unable to attain a particular rank, they will also be subject to deductions. Gymnasts, for instance, are penalized when they don't execute split leaps at the angle required by their level.

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One large bucket of popcorn costs $6 and one box of candy costs $3.75.

Let's call the cost of one large bucket of popcorn as "p" and the cost of one box of candy as "c". We can set up two equations based on the information given in the problem :

Equation 1: 4p + 5c = 42.75 (first group's purchase)

Equation 2: 3p + 2c = 25.50 (second group's purchase)

We can use any method to solve these equations, such as substitution or elimination.

Let's use the elimination method by multiplying both sides of Equation 1 by 2 and both sides of Equation 2 by -5 to eliminate "c" and get an equation in terms of "p":

8p + 10c = 85.50 (multiplying Equation 1 by 2)

-15p - 10c = -127.50 (multiplying Equation 2 by -5)

Adding the two equations, we get :

-7p = -42

p = 6

Now we can substitute the value of "p" into either Equation 1 or Equation 2 to solve for "c". Let's use Equation 1:

4(6) + 5c = 42.75

24 + 5c = 42.75

5c = 18.75

c = 3.75

Therefore, one large bucket of popcorn costs $6 and one box of candy costs $3.75.

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Answer:

Even

Step-by-step explanation:

a)

I) The ratio is given as follows: 1/2.

II) The scale factor is given as follows: 2.

b)

I) The ratio is given as follows: 1/5.

II) The scale factor is given as follows: 5.

A dilation is defined as a non-rigid transformation that multiplies the distances between every point in a polygon or even a function graph, called the center of dilation, by a constant factor called the scale factor.

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At the point `-5`, the tangent line is perpendicular to the line `x-4y+8=0`.At the point `3`, the tangent line is perpendicular to the line `x-4y+8=0`.

The given curve is `f(x) = (4x + 8)/(x + 1)`. We need to find a point `x = a` on the curve such that the tangent line to the curve at the point `x = a` is perpendicular to the given line `x - 4y + 8 = 0`.

First, we need to find the slope of the given line `x - 4y + 8 = 0`. Writing it in slope-intercept form, we get:`-4y = -x - 8``y = (1/4)x + 2`The slope of this line is `1/4`.

To find the slope of the tangent line to the curve `f(x)` at the point `x = a`, we differentiate `f(x)` and substitute `x = a`. We get:`f(x) = (4x + 8)/(x + 1)`Differentiating with respect to `x`, we get:`f'(x) = [4(x + 1) - (4x + 8)]/(x + 1)^2``= -4/(x + 1)^2`Substituting `x = a`, we get the slope of the tangent line at `x = a`:`m = f'(a) = -4/(a + 1)^2`

We need the slope of the tangent line to be `-1/4` (negative reciprocal of the slope of the given line) for the tangent line to be perpendicular to the given line.

Therefore, we have:`-4/(a + 1)^2 = -1/4``=> (a + 1)^2 = 16``=> a + 1 = ±4``=> a = -5 or a = 3`

Thus, the tangent line to the curve `f(x)` is perpendicular to the given line `x - 4y + 8 = 0` at the points `x = -5` and `x = 3`.The given line `x - 4y + 8 = 0` intersects the `y-axis` at `y = 2`.

Therefore, we can find the equation of the tangent line to the curve `f(x)` at the points `x = -5` and `x = 3` using point-slope form and then find the `y-coordinate` of the point of intersection with the `y-axis`.At `x = -5`, we have:`y = f(-5) = (-12)/(-4) = 3`

The point is `(-5, 3)`. The slope of the tangent line is:`m = f'(-5) = -4/16 = -1/4`The equation of the tangent line using point-slope form is:`y - 3 = (-1/4)(x + 5)``=> y = (-1/4)x - 7/4`At `x = 3`, we have:`y = f(3) = 20/4 = 5`

The point is `(3, 5)`. The slope of the tangent line is:`m = f'(3) = -4/16 = -1/4`The equation of the tangent line using point-slope form is:`y - 5 = (-1/4)(x - 3)``=> y = (-1/4)x + 35/4`The `y-coordinate` of the point of intersection with the `y-axis` is the `y-intercept` of each tangent line.

For the first tangent line, we have:`y = (-1/4)x - 7/4``=> 0 = (-1/4)x - 7/4``=> x = 7`Therefore, the `y-coordinate` of the point of intersection with the `y-axis` is `-7/4`. For the second tangent line, we have:`y = (-1/4)x + 35/4``=> 0 = (-1/4)x + 35/4``=> x = 35`Therefore, the `y-coordinate` of the point of intersection with the `y-axis` is `35/4`.

Therefore, the answer is: The tangent line to the curve `f(x)` is perpendicular to the given line `x - 4y + 8 = 0` at the points `(-5, 3)` and `(3, 5)`.

The `y-coordinate` of the point of intersection of each tangent line with the `y-axis` is `-7/4` and `35/4`, respectively.

Thus, the final answer is: At the point `-5`, the tangent line is perpendicular to the line `x-4y+8=0`.At the point `3`, the tangent line is perpendicular to the line `x-4y+8=0`.

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The number of packs of hot dogs bought is 2 packs

The number of packs of hamburgers bought is 4 packs

Let x represent the number of hot dogs bought and y represent the number of hamburgers bought

x + y= 6.........equation 1

2.65x + 6.29y= 30.46.........equation 2

From equation 1

x + y= 6

x= 6 - y

Substitute 6 - y for x in equation 2

2.65(6-y) + 6.29y = 30.46

15.9 - 2.65y  + 6.29y = 30.46

3.64y = 30.46 - 15.9

3.64y= 14.56

y= 14.56/3.64

y= 4

Substitute 4 for y in equation 1

x + y= 6

x + 4= 6

x= 6 - 4

x= 2

Hence 2 packs of hot dogs and 4 packs of hamburgers were bought

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Answer: He has 4 apples left.

Step-by-step explanation:

5-1=4

(hope this helps)

Answer:4

Step-by-step explanation: James had 5 apples which later he gave one to aliya so 5-1 is 4

Answer:

The length of a rectangle is 3” more than twice the width. The area of the rectangle is 150 in^2. Find the dimensions of the rectangle.

The length of a rectangle is 3” more than twice the width. The area of the rectangle is 150 in^2. Find the dimensions of the rectangle.

Wyzant

MATH QUADRATIC FORMULA

Kyle C. asked • 05/05/16

The length of a rectangle is 3” more than twice the width. The area of the rectangle is 150 in^2. Find the dimensions of the rectangle.

The length of a rectangle is 3” more than twice the width. The area of the rectangle is 150 in^2. Find the dimensions of the rectangle.

ANSWER

ABOUT THIS TUTOR ›

We know that Area = Length x Width

in this case, L = 2W + 3 and A = 150in2

so, 150in2 = W x (2w + 3)

150in2 = 2W2 + 3W

rearranging, 2W2 + 3W - 150in2 = 0

we need to use the quadratic formula to solve this equation

that formula is [-b±(√b2 -4ac)]/2a

a = 2, b = 3, c = -150

inserting those values, we get [-3±(√32 -4•2•-150)]/2•2

which becomes (-3±√1209)/4

we get (-3 ± 34.771)/4

we can discard the negative value, because no length can be negative

so, W ≅ 7.942 inches

then L = 2W + 3 ≅ 18.886 inches

Proof: 7.942in x 18.886in ≅ 149.99

HOPE IT'S HELPFUL

THANK YOU

Answer:

-10, -8, -6, -5, -2, -1

Step-by-step explanation:

I knew this because every negative number can still relate to being the least number. But hey, hope this helps. :]

Answer:

C = 50.27 m

Step-by-step explanation:

A = πr²

64π = πr²

64 = r²

r = ±8

r = 8

C = 2πr

C = 2π(8)

C = 50.27 m

Answer:

-12

Step-by-step explanation:

-10x+1+7x =37

-10x+7x+1 =37       (-10x+7x = -3x)

-3x+1 =37

-3x =37 -1

-3x =36

-3x / -3 = 36 / -3

x = -12    

Answer:

x = -12

Step-by-step explanation:

\( \sf - 10x+1+7x=37\)

Combine like terms.

\(\sf - 3x+1=37\)

Subtract 1 from both sides.

\(\sf - 3x=37−1\)

\(\sf - 3x=36\)

Divide both sides by -3.

\(\sf \cfrac{ - 3x}{3} = \cfrac{36}{3} \)

\(\sf x = - 12\)

Given function is f(x) = 3x²2 - 16x + 5 / x²-2x-15To find the horizontal and vertical asymptotes of the function, we need to perform the following steps: Step 1: Factorize the denominator of the function. x²-2x-15 = (x-5)(x+3)Step 2: Rewrite the function in the form of a fraction with the factored denominator. f(x) = [3x²2 - 16x + 5] / [(x-5)(x+3)]Step 3: Check for the vertical asymptotes of the function by setting the denominator to zero and solving for x. x-5 = 0 or x+3 = 0 ⇒ x = 5 or x = -3Hence, the vertical asymptotes are x = 5 and x = -3.Step 4: Check for the horizontal asymptotes of the function by analyzing the degrees of the numerator and denominator. Since the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.Therefore, the answer is:B. The function has no horizontal asymptote.

Hope I helped ya...

We have a 98% confidence that the actual percentage of consumers who click on mobile ads is between 0.363 and 0.537.

Using the following calculation, we can determine the 98% confidence interval for the actual percentage of consumers who click on mobile ads:

point estimate ± margin of error

where the sample proportion (0.45) serves as the point estimate and the following formula is used to get the margin of error:

z * standard error of the proportion

where the standard error of the proportion is determined by the formula below, and z is the z-score for a 98% confidence level.

the standard deviation of the proportion = square root of (sample proportion * (1 - sample proportion) / sample size)

With the values entered, we obtain:

standard deviation of the proportion= square root of (0.45 * (1 - 0.45) / 150) = 0.037

The z-score at a 98% confidence level, according to a z-table, is 2.33.

Therefore, the error margin is:

2.33 * 0.037 = 0.087

The 98% confidence interval for the actual percentage of consumers who click on mobile ads is as follows:

0.45 ± 0.087 = (0.363, 0.537)

Thus, We have a 98% confidence level that the actual percentage of consumers that click on mobile ads is between 0.363 and 0.537.

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Selecting all students with last names beginning with the letter M would not produce a random sample of a school population of 1000 students. Hence the answer is no.

A random sample is obtained by selecting individuals from a population in a way that ensures every member of the population has an equal chance of being included in the sample.

By choosing only students with last names beginning with the letter M, you are introducing a bias and not providing an equal chance for all students to be selected.

To obtain a random sample of 1000 students from a school population, you would need to use a random selection method that ensures each student has an equal probability of being chosen.

This could be achieved through techniques such as random number generators, random sampling software, or random sampling techniques like stratified or cluster sampling.

Selecting all students with last names beginning with the letter M would not meet the requirements of a random sample, as it would not provide an equal chance for all students in the population to be included.

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