find the greatest common factor of the following:
c) 2xy⁵, 6x³y³
d) 6x²y², 9xy³, 3x⁴y⁴
f) 10ab, 20bc, 30ca​

Answer:

Step-by-step explanation:

4(3n- 5) =

12n - 20

Main Answer:

The given equation describes a plant with an input signal i(t) and an output signal y(t). The transfer function G(s) represents the dynamics of the plant in the Laplace domain.

Explanation:

The given equation can be interpreted as a mathematical representation of a dynamic system, commonly referred to as a plant, which is characterized by an input signal i(t) and an output signal y(t). The plant's behavior is governed by a transfer function G(s) that relates the Laplace transform of the input signal to the Laplace transform of the output signal.

In the first equation, i(t) › = [ 2 ] ² (0+ [ 1 ] (0) + [ 2 ] 4 (0) (t) u(t) d(t), the input signal is represented by i(t). The term [ 2 ] ² (0) indicates the initial condition of the input signal at t=0. The term [ 1 ] (0) represents the initial condition of the first derivative of the input signal at t=0. Similarly, [ 2 ] 4 (0) (t) represents the initial condition of the second derivative of the input signal at t=0. The u(t) term represents the unit step function, which is 0 for t<0 and 1 for t≥0. The d(t) term represents the Dirac delta function, which is 0 for t≠0 and infinity for t=0.

In the second equation, y(t) = [n² - 2π 2-π] x(t) + u(t) ㅠ, the output signal is represented by y(t). The term [n² - 2π 2-π] x(t) represents the multiplication of the Laplace transform of the input signal x(t) by the transfer function [n² - 2π 2-π]. The term u(t) represents the unit step function that accounts for any additional input or disturbances.

The transfer function G(s) = s² + (2π)s / (s² - π² - 2π) describes the dynamics of the plant. It is a ratio of polynomials in the Laplace variable s, which represents the complex frequency domain. The numerator polynomial s² + (2π)s represents the dynamics of the plant's zeros, while the denominator polynomial s² - π² - 2π represents the dynamics of the plant's poles.

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Answer:

im pretty sure its -1 because thats the answer i had before my answers didnt save n the same test you had. im not 100 percent sure though

Step-by-step explanation:

The slope intercept form of the equation is B)y=2x-6.

What is slope intercept form of the equation?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b).   It provides both a slope and an intercept, which is why the form is known as the slope-intercept form.

Here let us take any two points \((x_1,y_1)=(0,-6)\) and \((x_2,y_2) =(1,-4)\) .

Now using slope formula slope m = \(\frac{y_2-y_1}{x_2-x_1}\)

=> slope m = \(\frac{-4+6}{1-0}\) = 2

Now using equation formula \(y-y_1=m(x-x_1)\) then,

=> y-(-6)=2(x-0)

=> y+6=2x

=> y=2x-6

Hence the slope intercept form of the equation is B)y=2x-6.

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a) The number of permutations of all the letters of the word HOLLYWOOD is 9,331,200. b) The number of permutations of all the letters of the word HOOLYWOOD is different from the answer in (a) because there are repeated letters. The number of permutations for HOOLYWOOD is 23,328,000.

a) To calculate the number of permutations of all the letters of the word HOLLYWOOD, we consider that all the letters are distinct. The word HOLLYWOOD has 9 letters.

The number of permutations of n distinct objects is given by n!, which represents the factorial of n.

Therefore, for HOLLYWOOD:

Number of permutations = 9!

Calculating:

9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 9,331,200

Thus, the number of permutations of all the letters of the word HOLLYWOOD is 9,331,200.

b) In the word HOOLYWOOD, there are repeated letters. The letter "O" appears twice, while the letters "O" and "L" appear once in HOLLYWOOD. However, the repeated letters "O" and "L" in HOOLYWOOD result in different permutations.

To calculate the number of permutations for HOOLYWOOD, we use the formula for permutations of objects with repeated elements. The formula is:

Number of permutations = n! / (r1! * r2! * ... * rk!)

Where n is the total number of objects and r1, r2, ..., rk are the frequencies of each repeated element.

For HOOLYWOOD:

Number of permutations = 9! / (2! * 2! * 2!)

Calculating:

9! / (2! * 2! * 2!) = 362,880 / (2 * 2 * 2) = 23,328,000

Therefore, the number of permutations for HOOLYWOOD is 23,328,000.

The number of permutations of all the letters of the word HOLLYWOOD is 9,331,200, while the number of permutations for HOOLYWOOD is 23,328,000. The difference arises because the word HOOLYWOOD has repeated letters, which increases the number of possible permutations.

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Answer: skew lines

Step-by-step explanation:

skew lines are two lines that do not intersect and are not coplanar

When selecting the appropriate number of treatment conditions, it is essential to consider factors such as resources, research complexity, and confounding variables.

Having conditions that are proportional to each other means that the level or intensity of each condition varies in direct proportion to the others, such that if one condition is increased or decreased, the others are also adjusted in a corresponding manner.

When choosing the appropriate number of treatment conditions for an experiment, there are several issues to consider. One of these is the ability to distinguish differences between treatment conditions.

Having conditions that are proportional to each other means that the differences between treatment conditions are consistent across all levels of the independent variable. In other words, if the independent variable increases by a certain amount, the difference between the treatment conditions remains constant. This can be important for ensuring that the treatment effects are interpretable and generalizable to other populations.

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Answer:

D. 1 liter

Step-by-step explanation:

1000 milliliters = 1 liter

Player 1: 1000 ml or 1 liter

Player 2: 500 ml or .5 liter

Player 3: 500 ml or .5 liter

Player 4: 2000 ml or 2 liter

Add: 1 + .5 +.5 +2 = 4

Subtract: 5 - 4 = 1

Answer: You have 1 liter left  

The smaller and larger number are 45 and 62 respectively

Linear equations are equations that has a leading degrees of 1

Let the first number be x

Let the second number be y

If one number is 17 greater than a second number, then;

x = 17 + y

y is the lesser number

When the lesser is subtracted from twice the greater differance is 79, this means

2x - y = 79

Substitute equation 1 into 2

2(17 + y) - y = 79

2(17) + 2y - y = 79

34 + y = 79

y = 79 - 34

y = 45

Determine the larger number

x = 17 + y

x = 17 + 45

x = 62

Therefore the smaller and larger number are 45 and 62 respectively

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Answer:

1. 2.85 minutes   2. 3.12 minutes

Step-by-step explanation:

I jest finished the test

Answer:

2.85 minutes   and   3.12 minutes is your answer ok now go workout and get ripped

Step-by-step explanation:

the probability that a student, answering each question at random, will answer at least 14 questions correctly is approximately 0.0000039 rounded to seven decimal places.

To calculate the probability that a student, answering each question at random, will answer at least 14 questions correctly, we can use the binomial probability formula.

The probability of answering a question correctly by random chance is 1 out of 5, which can be expressed as 1/5 or 0.2.

Let's denote:

n = number of trials (number of questions) = 20

p = probability of success (probability of answering a question correctly) = 0.2

x = number of successful outcomes (number of questions answered correctly)

We want to calculate the probability of answering at least 14 questions correctly, which means we need to find the probability of getting 14, 15, 16, 17, 18, 19, or 20 questions correct.

Using the binomial probability formula, we can calculate the probability for each case and sum them up:

P(X ≥ 14) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)

P(X = k) = (n choose k) * \(p^k * (1 - p)^{(n - k)\)

Using this formula for each value of k and adding them up, we find:

P(X ≥ 14) ≈ 0.0000039

Therefore, the probability that a student, answering each question at random, will answer at least 14 questions correctly is approximately 0.0000039 rounded to seven decimal places.

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Complete question is below

A student takes a multiple choice test with 20 questions. Each question has 5 possible answers, only one of which is correct. { a) If a student answers each question at random, what is the probability that they will answer at least 14 questions correctly? Round your answer to seven decimal places.

Using the normal distribution, it is found that there is a 62.4% probability that a data value is between 37 and 41.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem, the mean and the standard deviation are given, respectively, by:

\(\mu = 38, \sigma = 2\)

As a proportion, the probability that a data value is between 37 and 41 is the p-value of Z when X = 41 subtracted by the p-value of Z when X = 37, hence:

X = 41:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{41 - 38}{2}\)

Z = 1.5

Z = 1.5 has a p-value of 0.933.

X = 37:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{37 - 38}{2}\)

Z = -0.5

Z = -0.5 has a p-value of 0.309.

0.933 - 0.309 = 0.624,

0.624 = 62.4% probability that a data value is between 37 and 41.

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Answer:

I'm but ask a assistant

Step-by-step explanation:

ok

From the information in the word problem we are able to set up the following inequality:  

3y + 2 - y = 12   |   where x is the larger number of two numbers in a set (x, y)  

We know this because the problem states that [x = 3y + 2] or 3 times the smaller number plus two.  

We also know that x - y = 12.

So, we substitute x in [x - y = 12] with 3y + 2 that we found out above, and we get the following:

3y + 2 - y = 12

Now, we solve the inequality

3y + 2 - y = 12

-> subtract 2 from both sides :: 3y - y = 10

-> subtract y from 3y              :: 2y = 10

-> divide both sides by 2        :: y = 5

So now we have y, the smaller number, which is equal to 5. Next, to find x we simply plug y=5 back in to either the value of x, [3y + 2], or the inequality of x - y = 12. I will show both:  

x - y = 12

-> substitute y for 5     :: x - 5 = 12

-> add 5 to both sides :: x = 17

OR

3y + 2 = x

-> substitute y with 5 :: 3(5) + 2 = x

-> multiply 3, 5          :: 15 + 2 = x

-> add 15, 2              :: 17 = x

So there you have it:  

x = 17 , y = 5

You can go back and use these values to check your answer and make sure they work with the word problem.  

Remember to look for the setup to an inequality in the word problem. Anything that says BLANK times this number, or 4 less than that number, is trying to set you up with an inequality problem.  

(just another form of the equation)

brainliest will be appreciated as well

If the variables are not quantitative we cannot do the arithmetic required in the formulas for r.

Quantitative order:

Therefore, if the variables are not quantitative we cannot do the arithmetic required in the formulas for r.

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- Mean: 119.43- Median: 118.50- Mode: 110 - Count: 28

To find the mean, we add up all the values and divide by the number of observations. In this case, the sum of the values is 3342, and since there are 28 observations, the mean is 3342/28 = 119.43.

The median is the middle value when the data is arranged in ascending order. In this case, there are 28 observations, so the median is the average of the 14th and 15th values. When the data is ordered, the 14th value is 118 and the 15th value is 124. Therefore, the median is (118 + 124)/2 = 118.50.

The mode is the value that appears most frequently in the dataset. In this case, the value 110 appears three times, which is more than any other value. Hence, the mode is 110.

The count simply refers to the number of observations in the dataset, which is 28 in this case.

(b) The data is skewed right.

When data is symmetric, it means that the values are evenly distributed around the mean, resulting in a bell-shaped curve. In this case, the data is not symmetric. Looking at the dataset, we can observe that there are several smaller values on the left side, while the right side has a few larger values. This indicates a right skew or positive skewness.

Skewness refers to the asymmetry of a distribution. In a right-skewed distribution, the tail of the distribution extends towards the right, indicating a longer right tail. Therefore, the correct answer is b. Skewed right, indicating that the data is positively skewed.

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Answer:

5x + 6

Step-by-step explanation:

first multiply 1/2 by 10x, that's 5x. then multiply 1/2 by 12, that's 6

Answer:

5x + 6

Step-by-step explanation:

\( \frac{1}{2} (10x + 12) \\ = (\frac{1}{2} \times 10x) + (\frac{1}{2} \times 12) \\ = \frac{10x}{2} + \frac{12}{2} \\ = 5x + 6\)

Answer:

the awsure is 8

Step-by-step explanation:

hope this helped

The 10th term of the geometric sequence is -1/6.

Let the following be a geometric sequence:

    a(1), a(2), a(3), a(4), a(5), ....

Then we have:

a(2) = a(1) . r

a(3) = a(2) . r

Continue the process, we have

a(n) = a(n-1) . r

Where:

a(n) = nth term

a(n-1) = (n-1)th term

r = ratio

In the given problem, a(9) = -1/3, r = 1/2

Plug these into the above formula:

a(10) = a(9) . r

        = (-1/3) . 1/2 = -1/6

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The linearized equation for the non-linear equation z = x² + 4xy + 6xy² in the region defined by 8 ≤ x ≤ 10, 2 ≤ y ≤ 4 is given by :

z ≈ 244 + 20(x - 8) + 128(y - 2).

When using the linearized equation to calculate the value of z at x = 8, y = 2, the error is 0.

1.1. To linearize the equation in the given region, we need to find the partial derivatives of z with respect to x and y:

∂z/∂x = 2x + 4y

∂z/∂y = 4x + 6xy

At the point (x₀, y₀) = (8, 2), we substitute these values:

∂z/∂x = 2(8) + 4(2) = 16 + 8 = 24

∂z/∂y = 4(8) + 6(8)(2) = 32 + 96 = 128

The linearized equation is given by:

z ≈ z₀ + ∂z/∂x * (x - x₀) + ∂z/∂y * (y - y₀)

Substituting the values, we get:

z ≈ z₀ + 24 * (x - 8) + 128 * (y - 2)

1.2. To find the error when using the linearized equation to calculate the value of z at x = 8, y = 2, we substitute these values:

z ≈ z₀ + 24 * (8 - 8) + 128 * (2 - 2)

= z₀

Therefore, the linearized equation gives the exact value of z at x = 8, y = 2, and the error is 0.

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Answer:

21.75

Step-by-step explanation:

65.25/3=21.75

Answer:

$21.75 per scarf

Step-by-step explanation:

Take the total cost and divide by the number of scarves

65.25 /3

21.75

Each scarf costs 21.75

$21.75 per scarf

Answer:

150

Step-by-step explanation:

When excluding stoppages, the speed of a bus is 54 km/h, and including stoppages, it is 36 km/h. the bus stop is 20 minutes per hour

We have to Calculate the distance traveled by bus in 1 hour excluding stoppages and calculate the distance traveled by bus in 1 hour including stoppages. Then we have to calculate the time taken to cover that difference between the distances and convert the calculated time into minutes.

Given data:

The speed of a bus while excluding stoppages = 54 km/h.

the speed of the bus while including stoppages = 36 km/hr.

From the given data we can say that:

The Distance traveled by bus in 1 hour, excluding stoppages is = 54 km.

The Distance traveled by bus in 1 hour, including stoppages, is = 36 km.

Distance traveled = Distance traveled by bus in 1 hour excluding stoppages – distance traveled by bus in 1 hour including stoppages

= 54km − 36km = 18km

The bus covers 18 km less due to stoppages.

the time taken to cover18 km, = distance traveled / speed of the bus

= 18km / 54km/hour

= 1 / 3 hour

Time taken in minutes = ( 1 / 3×60 )minutes

=20minutes

Therefore, the bus stops per hour for 20 minutes.

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Answer:

x = 15 , x = 2

Step-by-step explanation:

\(x^2 -17x + 30 =0\\\\x^2 -2x-15x +30=0\\\\x(x-2)-15x(x-2) =0\\\\(x-15)(x-2)=0\\\\\)

x = 15 , x = 2

Answer:

19 miles per gallon

Step-by-step explanation:

95975 - 95842 = 133

133 divided by 7 = 19

Answer:

−10−1(−2)^3−1(−2)(−11)

● −10−1(−8)−1(−2)(−11)

●−10+8−1(−2)(−11)

●−10+8−22

●−10+8−22

☆Answer:-24

○●○●○●○●○●○

Hope it helps

Have a great day!!

Answer:

5027.2ft^2

Step-by-step explanation:

Given data

Radius= 40ft

The expression for the area covered is given as

A= πr^2

Substitute

A= 3.142*40^2

A=3.142*1600

A=5027.2ft^2

Hence the area covered is 5027.2ft^2

The rotational symmetry of the pentagon is given as follows:

A. 108° rotational symmetry.

The sum of the interior angle measures of a polygon with n sides is given by the equation presented as follows:

S(n) = 180 x (n - 2).

A pentagon has 5 sides, hence the sum of the measures of the internal angles is given as follows:

S(5) = 180 x (5 - 2)

S(5) = 540º.

A regular pentagon has all angle measures the same, hence the measure for the rotational symmetry is given as follows:

540/5 = 108º.

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Answer:

4.5 or just say 4 if your gonna round it up. hope this helped :)

Step-by-step explanation: