Consider the system modeled by the following difference equation. y(n) = 3y(n-1) + x(n − 2)
Assume the underlying system is casual with zero initial conditions. What is the transfer function?

The scale factor of Figure A to Figure B is A- 5:9

From the question, we have the following parameters that can be used in our computation:

Figure A and Figure B

The scale factor of Figure A to Figure B is calculated as

Scale factor = Figure B : Figure A

Substitute the known values in the above equation, so, we have the following representation

Scale factor = 20 : 36

Evaluate

Scale factor = 5 : 9

Hence, teh scale factor is 5 : 9

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Answer: 5.5

Step-by-step explanation:

0.72÷[tex]0.6^{2*2}[/tex]
Simplify the 2*2 to 4
0.72÷[tex]0.6^{4}[/tex]
[tex]0.6^{4}[/tex]=0.1296
0.72÷0.1296=5.555555556
5.555555556 can be rounded to 5.5

0.72÷[tex]0.6^{2}[/tex] x 2 on the other hand is 4 -- sorry I can't really see if it's both 2's as exponents or not
0.6^2=0.36
0.72÷0.36×2=4

0.125 liter of water this jug contain it is between 150ml and 100ml.

The conversion of 1 jug (beer jug) into a volume and capacity measure equals 1.14 liters, according to its commonly used equivalent volume and capacity unit type measure.

Three dimensions need to be taken into account in order to determine the round water tank's liter capacity. The length, breadth, and height make up those three dimensions. Let B, W, and H stand for length, width, and height, respectively. As a result, 240 x 28.31 = 6794.4 liters will be the tank's total volume in liters.

That given jug contain some water

Quantity of water is 125ML

1000ml = 1Liter

125ml = 0.125Liters.

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The y coordinate of the center of the circle is k=-1 and The radius of the circle is 7 units, the value of b in the equation is 49.

A circle is a two-dimensional, symmetrical figure in mathematics. The circle's center is a place inside the circle from which all points on the circle's edge are equally far.

The radius of the circle, abbreviated "r," is the distance from the center of the circle to a point on its edge.

The diameter of the circle, which is the greatest chord of any circle, is equal to the circle's doubled radius.

2 Radius times diameter Half of the circle is represented by the semicircle, and one-fourth by the circle's quadrant.

(PART A) To determine the y-coordinate of the center of the circle, we need to complete the square for both x and y. The equation can be transformed to the standard form for a circle: (x-h)² + (y-k)² = r², where (h,k) is the center of the circle and r is the radius.

First, complete the square for x:

x² - 4x + 4 = 4 + (x² - 4x)

x² - 4x + 4 + 4 = 4 + (x² - 4x) + 4

(x-2)² = (x² - 4x + 4) + 4

Next, complete the square for y:

y² + 2y + 1 = 1 + (y² + 2y) + 1

(y+1)² = (y² + 2y) + 1

Now, substitute the completed squares back into the original equation:

(x-2)² + (y+1)² = b

So, the y-coordinate of the center is k = -1.

(PART B) The radius of the circle is 7 units, so r = 7. Substitute this value and the coordinates of the center into the standard form of the equation:

(x-2)² + (y+1)² = 49

Finally, simplify to find the value of b:

b = 49.

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If the vector a = x + iy, then the complex conjugate of vector a is x - iy where x is the real part and b is the imaginary part.

A number that may be expressed as (a + ib), where a denotes the real component, b denotes the imaginary part, and I denotes a fictitious number called iota, which is equivalent to the root of -1. In mathematics, a conjugate is created by flipping the sign of one of a binomial's terms.

A complex number's reflection about the horizontal axis (real axis) on Arcand's plane is represented by the conjugate of that complex number.

Another definition of a complex conjugate or conjugate of a complex number is a complex number having the same real component as the original number and the opposite sign of the imaginary part while maintaining the same magnitude, i.e., the original complex number's 'i' changes to the conjugate's '-i'.

Let a = x + iy

Complex conjugate of a is

a* = x - iy

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It is used the observational study. A survey of high school students was conducted to see if students who take advanced classes are offered more scholarship money than students who do not take advanced classes

Now, According to the question:

"Information available from the question"

A survey of high school students was conducted to see if students who take advanced classes are offered more scholarship money than students who do not take advanced classes

Statisticians often refer to the "levels of measurement" of a variable, a measure, or a scale to distinguish between measured variables that have different properties. There are four basic levels: nominal, ordinal, interval, and ratio.

In an observational study, we measure or survey members of a sample without trying to affect them. In a controlled experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive the treatment.

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The coordinates of A= are also (-3,4). The answer to the query is determined by the coordinates of the second endpoint B. (x, y). The midpoint's coordinates can be calculated using the formula below:

The following are b's coordinates: B= (-7,-8) (-7,-8)

We are given the midpoint's coordinates as M= (-5,-2).

Furthermore, A='s coordinates are (-3,4). The solution to the question depends on the coordinates of the second endpoint B.

the coordinates of B (x, y). The following formula can be used to determine the midpoint's coordinates:

[tex]$& x_m=\frac{x_a+x_b}{2} \\[/tex]

[tex]$& y_m=\frac{y_a+y_b}{2}[/tex]

We know xa = -3 and xm = -5. Solve the first equation for x b :

[tex]$2 x_m=x_a+x_b \Rightarrow x_b=2 x_m-x_a[/tex]

Substituting:

[tex]$& x_b=2 \cdot(-5)-(-3)=-10+3 \\[/tex]

[tex]$& x_b=-7[/tex]

We can solve the second equation for xb and get:

[tex]$y_b=2 y_m-y_a[/tex]

Since ya = 4 and ym = -2, then:

[tex]$& y_b=2 \cdot(-2)-(4)=-4-4 \\[/tex]

[tex]$& y_b=-8[/tex]

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Answer: 66.2°F

Step-by-step explanation: (19°C × 9/5) + 32 = 66.2°F

Answer is 66.2°F.

How to calculate 19 °C in °F?

The base formula for this c to f converter is

Fahrenheit = (19 °C x 9/5) + 32

                 = 66.2°F

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The correct way to order these amounts from greatest to the least is 0.6 gal, 1.9 L, and 3.8 pints.

To determine this, the best is to use the same units for all the amounts, in this case, I will convert everything to liters.

Pints to liters:

1 pt = 0.47 l

3.8 pt =  x

x= 3.8 x 0.47 = 1.78 liters

Gallons to liters:

1 gal = 3.78

0.6 gal = x

3.78 x 0.6 = 2.27 liters

Based on this, the correct way to order the amount is 0.6 gallons, 1.9 liters, and 3.8 pints.

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The total number of permutations of the three tasks: 336 x 3! (3 factorial) = 40320

This question uses the combination and permutation theory. Combinations are used to calculate the total number of ways to assign the three tasks to the 8 people, and permutations are used to multiply the total number of ways to assign the three tasks by the total number of permutations of the three tasks.

given below :

1. Calculate the total number of ways to assign the three tasks to the 8 people: 8 x 7 x 6 = 336

2. Multiply the total number of ways to assign the three tasks by the total number of permutations of the three tasks: 336 x 3! (3 factorial) = 40320

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The simplification of the expression gives 3 + √3

Simplification of an expression is defined as a way of writing an expression in the most efficient and compact form without affecting the value of the original expression

Surds are represented by square roots of non-perfect squares and are expressed using the radical symbol (√). For example, √2 is a surd, as it cannot be expressed as a finite decimal or a fraction.

√3(√3 - 1) =  (√3)*√3 + (√3)*1

                 = 3 + √3

Therefore, the expression can be simplified as 3 + √3

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Answer:

The new ratio of the history to the maths to the science books would be 22:43:55. With the addition of 20 history, 40 maths, and 10 science books, the total number of books in the library is now 570. The new ratio of the history to the maths to the science books is therefore 22:43:55.

Step-by-step explanation:

The required formula for given transformation is  2√(x - 4) - 3.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

The formula for the function g(x) can be found by applying the transformations to f(x):

Shift down 3 units: g(x) = f(x) - 3

Shift left 4 units: g(x - 4) = f(x) - 3

So, the formula for g(x) is:

g(x) = f(x - 4) - 3

= 2√(x - 4) - 3.

Thus, required formula is 2√(x - 4) - 3.

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Mean and median measures of central tendency would be affected if the outlier 11 was added to the data set.

As per the given data, the data set is 27, 20, 34, 37, 21, 42, and 39.

Mean of the data is the sum of all observations divided by the total number of observations.

Mean = [tex]$\frac{27+20+ 34+ 37+ 21+ 42+ 39}{7}[/tex]

Mean = [tex]$\frac{220}{7}[/tex]

Mean = 31.42

The median of the data for an odd number of observations is the middlemost term.

First, arrange the data in ascending order.

20, 21, 27, 34, 37, 39, 42

Middlemost term = 34.

The mode of the data is the most repeated data.

As no number is repeated there will be no mode.

As given 11 is added to the data set.

Mean = [tex]$\frac{27+20+ 34+ 37+ 21+ 42+ 39+11}{8}[/tex]

Mean = [tex]$\frac{231}{8}[/tex]

Mean = 28.8

The median of the data for an even number of observations is the average of the middle two terms.

First, arrange the data in ascending order.

11, 20, 21, 27, 34, 37, 39, 42

Median = [tex]$\frac{27+34}{2}[/tex]

Median = [tex]$\frac{61}{2}[/tex]

Median = 30.5

For the new data set also there will be no mode as there are no repeated numbers.

Comparing old and new values there is a change in the values of mean and median.

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Step-by-step explanation:

when multiplying factors of the same base, we can simply add the exponents.

when dividing, we subtract.

so,

z⁹xz⁶/z⁷ = xz^(9+6-7) = xz⁸

The timeline which correctly organizes the founding of important world religions are;

Judaism, Buddhism, Christianity, and Islam

The correct answer choice is option B.

Chronological order is the order of events from the first to the last.

Christianity was founded about 2,000 years ago.

Islam was founded about 1,400 years ago.

Hinduism was founded about 3,500 years ago.

Buddhism was founded about 2,500 years ago.

Judaism was founded about 4,000 years ago

Arrangements from the first to the last;

Therefore, the important world religions are in the order; Judaism, Hinduism, Buddhism, Christianity and Islam.

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The graphed quadratic equation, in vertex form, is:

y = 3*(x - 2)^2 - 5

So the correct option is C.

Remember that for a quadratic equation with a leading coefficient a and a vertex (h, k), the vertex form is:

y = a*(x - h)^2 + k

Here we can see that the vertex is at the point (2, -5), replacing that we will get:

y = a*(x - 2)^2 - 5

We also can see that the parabola passes through (0, 7), then we can replace that to get:

7 = a*(0 - 2)^2 - 5

7 = 4a - 5

7 + 5 = 4a

12/4 = a

3 = a

The quadratic equation is:

y = 3*(x - 2)^2 - 5

The correct option is C.

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The mass in grams of 0. 450 moles of magnesium sulfate, MgSO4 in grams is 54.2.

The mole, which is 6.0221023 molecular entities, is the basic unit of a substance. One mole of a substance is equivalent to that substance's molecular weight.

The link between moles and molar mass means that the quantity of moles in a material is equal to the product of its mass and molecular mass.

The molar mass of magnesium sulphate is:

Magnesium = 24

Oxygen = 16 x 4 = 64

Sulphate = 32

Thus, the mass of magnesium sulphate is = 24 + 64 + 32 = 120 grams.

Now, moles is equal to:

Moles = given mass/molecular mass

Putting the values:

moles = given mass / 120

0.450 x 120 = given mass

Given mass = 54g.

Thus, the given mass of the magnesium sulphate is 54 g.

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Bias results from random variation and will always be present, while bias results from samples that do not represent the population. Bias can usually be reduced when the sample size is larger.

Bias is an error that occurs in statistical studies when the results are not representative of the true population. Bias can occur when the sample size is too small, or when the sample does not accurately reflect the population. This means that even if the study is perfectly designed, bias will still exist. Additionally, bias can result from samples that do not represent the population. For example, if a study is conducted on a population that is predominantly male, then the results may be biased towards male behavior. Finally, bias is usually reduced when the sample size is larger. This is because a larger sample size provides for more accurate results, as there is less of a chance that random variation will affect the data. Therefore, increasing the sample size is a helpful way to reduce bias in a study.

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Answer:

When the increase in demand is greater than the decrease in supply, the equilibrium price rises and the equilibrium quantity increases.

What is economic equilibrium?

Economic equilibrium, as used in economics, is a state in which forces such as supply and demand are in balance and where, in the absence of external influences, the values of economic variables will remain constant.

The equilibrium quantity rises if the rise in demand outweighs the fall in supply. The equilibrium quantity falls if the rise in demand is smaller than the fall in supply. Equilibrium price rises in each scenario.

The supply and demand curves move in opposition to one another. However, the supply curve shifted to the left while the demand curve shifted to the right (signalling a rise in demand) (indicating a decrease in supply).

In the case increase in demand > decrease in supply

In this instance, the supply curve's leftward movement is proportionally less than the rightward change of the demand curve. So, the price and the equilibrium quantity both increase.

Therefore, the equilibrium price and quantity increases.

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Answer:  Decreasing, if it "Halves (cuts in half)". If it was increasing, it would probably say double.

Step-by-step explanation:

So, if it was being cut in half every two days, we would only be counting days 2, 4, and 6.

So days 2, it would be cut in half, and go from 500 to 250. Day 4, it would go from 250 to 125. The day 6, it would go from 125 to 62.5.

In 6 days, the investment will be worth $62.50

The answer to 5.6 to the power of 6 is 95,788.67.

According to the question

The result of multiplying 5.6 by itself 6 times is expressed as 5.6 to the power of 6. In this situation, the number 5.6 is being exponentiated, which is a mathematical process that elevates a number to a specified power, which is the power of six. This formula yields an actual number, which is the result of multiplying 5.6 by 6 times. Both a calculator and manual multiplication may be used to figure this out. The outcome of this computation is represented numerically as 95,788.67, which represents the value that is achieved when the number 5.6 is multiplied by itself six times.

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The answer to 5.6 to the power of 6 is 95,788.67.

According to the question

The result of multiplying 5.6 by itself 6 times is expressed as 5.6 to the power of 6. In this situation, the number 5.6 is being exponentiated, which is a mathematical process that elevates a number to a specified power, which is the power of six. This formula yields an actual number, which is the result of multiplying 5.6 by 6 times. Both a calculator and manual multiplication may be used to figure this out. The outcome of this computation is represented numerically as 95,788.67, which represents the value that is achieved when the number 5.6 is multiplied by itself six times.

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Answer:

Step-by-step explanation: First you need to know the powers, the power of a number says how many times to use the number in a multiplication. Therefore, you should be able to multiply that by ur number.

Assuming the point (x, y) is in the indicated quadrant, the given ratio are as follows;

Quadrant II, x/y is a negative ratio.

Quadrant III, y/x is a positive ratio.

In Mathematics, a quadrant can be defined as the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate.

This ultimately implies that, there are four (4) major quadrants in any graph and these include the following:

Now, we can determine the whether the given ratios are positive or negative:

Quadrant II, x/y = -x/y (negative ratio).

Quadrant III, y/x = -y/-x (positive ratio).

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Step-by-step explanation:

1. true

5 is a constant (term).

2. false

7y is not a coefficient. 7 is the coefficient for that y-term.

3. true

7y + 2x + 5 is the sum of 3 terms.

4. false

7y is not a factor. it would have to be multiplied to something else to be a factor for that something else.

5. false

they would be like terms, if both were constants, or both contained y.

6. false

The length of the patio in the drawing, according to the scale of the drawing of 12 cm : 7 m, is 36 cm.

A scale is defined to be the ratio between the size of a given original object and a new object, which is its representation but is either smaller or bigger. It refers to the relative size of an object. Sometimes it is called a scale factor.

We are given a scale of the drawing of 12 cm : 7 m. Also, the actual length of the front patio is 21 m. To find the length of the patio in the drawing, we'll use algebra.

First, we write an equation that contains the scale of the drawing and the ratio of the actual length of the front patio to the length of the patio in the drawing, which is unknown still so we use a variabel x:

12 cm / 7 m = x / 21 m

Note that we're asked to find the length of the patio in the drawing in centimeters, so we'll then need to convert from meters to centimeters. Remember that 1 meter is defined to be equal to 100 centimeters.

12 cm / (7 · 100) = x / (21 · 100)

12 cm / 700 cm = x / 2,100 cm

Finally, let's solve for x.

12 / 700 = x / 2,100

3 / 175 = x / 2,100

6,300 = 175x

175x = 6,300

x = 36

Since x = 36 and it represents the length of the patio in the drawing, it then is equal to 36 centimeters.

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Volume = a3, where an is the length of the cube's sides or edges, is how you can calculate the volume of a cube.

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This triangle is not a right triangle because the sum of the squares of the two smaller sides is not equal to the square of the largest side.

To determine if a triangle is a right triangle, you can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two smaller sides is equal to the square of the largest side.

In this case, we can compare the squares of the sides with lengths of 33 km and 72 km, and the square of the side with length 78 km:

33^2 + 72^2 = 5184 + 5184 = 10368

78^2 = 6084

Since 10368 is not equal to 6084, we can conclude that this triangle is not a right triangle.

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