y[n] = x[2n] determine if the system is: linear, ti, causal, stable

Answers

Answer 1

Based on the given system equation y[n] = x[2n], the system is linear, time-invariant, causal, and stable.

Based on the given system equation y[n] = x[2n], we can determine the following properties:

1. Linearity: The system is linear because the output is a linear function of the input signal.

2. Time-Invariance (TI): The system is time-invariant, as the output does not depend on the specific time "n". A time shift in the input signal results in the same time shift in the output signal.

3. Causality: The system is causal because the output at time "n" only depends on the input at time "2n" and not on any future inputs.

4. Stability: The system is stable, as the output is bounded for any bounded input signal. A change in the input signal will not cause the output to become unbounded.

So, the system is linear, time-invariant, causal, and stable.

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Related Questions

what is 2/3/10 and 4/5/10? im so confused!

Answers

Answer:

the ten is the year and the middle number is the day and the 1st number is the   month

Step-by-step explanation:I'm in the 9th grade so we have to do this many times TwT

The graph of an equation has a minimum y value of 12. This minimum occurs at an x value of 3. What is true of the graph of the equation?

Answers

Answer:

i don't know

Step-by-step explanation:

Answer:

that it's a parabola with the equation

\( {(x - 3)}^{2} + 12\)

The graph of an equation has a minimum y value of 12. This minimum occurs at an x value of 3. What is

The graph of f(x) is shown.what is the value of x when f(x)=4

The graph of f(x) is shown.what is the value of x when f(x)=4

Answers

Answer:

X=3

Step-by-step explanation:

Use the numbers on the side once in each sentence. Use the rules for the order of operations to make each sentence true.(__+__) x ___ = 24with only -5 8 and 2

Answers

8 is the missing number that we need to make the statement true. Hence, the answer is (-5 + 8) x 8 = 24.

The given numbers are -5, 8 and 2 and the expression is (__+__)x___=24. The first step is to determine what operation must go inside the parentheses.

As (__+__) is multiplied by a number, it follows that the addition goes inside the parentheses.

Using the numbers -5, 8, and 2, the statement is true if we say that (-5+8)x(-5)=24.

Here's the detailed solution:

The given expression is (__+__) x ___ = 24.

We are given the numbers -5, 8, and 2 and we need to find the missing numbers to make the statement true.

Let's put -5, 8, and 2 in the expression:

First, we'll place the addition within parentheses: (-5 + 8)

Then, the expression becomes: (-5 + 8) x ___ = 24

This can be simplified to:

3 x ___ = 24

We need to find the value of the blank space in the expression above. Since 3 is multiplied by the unknown number, we can calculate the value of the blank as follows: 3 x 8 = 24

Therefore, 8 is the missing number that we need to make the statement true. Hence, the answer is (-5 + 8) x 8 = 24.

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which transformation proves congruence between shap a and shape b

Answers

Answer:

A congruence transformation is a transformation that doesn't change the size or shape of an object. There are three main types of congruence transformations, and those are reflections (flips), rotations (turns), and translations (slides).

Step-by-step explanation:

i hope that helps

Use the exchange rate £1 = €1.11 to convert €222 into £.

Answers

the answer is £200, if you divide 222 by 1.11 it gives you 200

I need help right now :(​

I need help right now :(

Answers

Answer:

The answer is 4 cm

Step-by-step explanation:

As we can see, the original triangle has a side length of 5 cm and 10 cm. Therefore, we can assume this ratio of 1:2 stays the same with the smaller triangle, making the answer 4 cm.

can some one give me a hand here???????​

can some one give me a hand here???????

Answers

-3/2 I think that’s the answer!

Suppose a company wants to introduce a new machine that will produce a marginal annual savings in dollars given by S '(x)= 175 - x^2, where x is the number of years of operation of the machine, while producing marginal annual costs in dollars of C'(x) = x^2 +11x. a. To maximize its net savings, for how many years should the company use this new machine? b. What are the net savings during the first year of use of the machine? c. What are the net savings over the period determined in part a?

Answers

a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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The diameters (cm) of plastic balls produced by two machines are independently and normally distributed by n(8; 0.17). let y denote the difference between the ball diameters produced by those two machines. what are the mean and the standard deviation of y ?

Answers

The standard deviation of the difference \( y \) is approximately 0.583.

The mean and standard deviation of the difference, denoted as \( y \), between the ball diameters produced by the two machines can be determined based on the given information that the diameters are independently and normally distributed by \( N(8, 0.17) \).

The mean of the difference can be calculated as the difference between the means of the individual distributions:

\(\[\text{Mean of } y = \text{Mean of machine 1} - \text{Mean of machine 2}\]\)

Since both machines have the same mean of 8 (given by \( N(8, 0.17) \)), the mean of \( y \) is:

\(\[\text{Mean of } y = 8 - 8 = 0\]\)

Therefore, the mean of the difference \( y \) is 0.

To calculate the standard deviation of the difference, we can use the property that the variance of the sum or difference of independent random variables is equal to the sum of their variances.

The variance of the difference can be calculated as:

\(\[\text{Variance of } y = \text{Variance of machine 1} + \text{Variance of machine 2}\]\)

Since the variance is equal to the square of the standard deviation, we can find the standard deviation of \( y \) by taking the square root of the variance.

Given that the variance of each machine is 0.17 (given by \( N(8, 0.17) \)), the variance of \( y \) is:

\(\[\text{Variance of } y = 0.17 + 0.17 = 0.34\]\)

Taking the square root of the variance, we obtain:

\(\[\text{Standard deviation of } y = \sqrt{0.34} \approx 0.583\]\)

Therefore, the standard deviation of the difference \( y \) is approximately 0.583.

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What two numbers satisfy the following two conditions?
-Multiplies to -50
-Adds to 23

Answers

Answer:

-25 and 2

Step-by-step explanation:

Answer:

-2 and 25

Step-by-step explanation:

-2*25=-50

25+(-2)=23

stteps for solving 6(4x-3) are shown

which of these is not a part of the solution prosess

Answers

Answer:2 4  −  1 8

Step-by-step explanation:

The sum of a number and two times a smaller number is 62. Three times the bigger number exceeds the smaller number by 116.

Answers

Answer:

10 and 42

Step-by-step explanation:

The difficulty with word problems is translating them into math.

Let's do that

---------------------

The sum of a number and two times a smaller number is 62.

let's call the bigger number b, and the smaller number s

b + 2s = 62

Three times the bigger number exceeds the smaller number by 116

3b = s + 116

-----------------------

Now manipulate one of the equations to isolate the variable

3b = s + 116

Subtract 116 from both sides

3b - 116 = s

substitute for s = 3b - 116 in

b + 2s = 62

b + 2(3b - 116) = 62

Distribute

b + 6b - 232 = 62

combine like terms

7b = 294

Divide both sides by 7

b = 42

to find s plug in b = 42 into

b + 2s = 62

42 + 2s = 62

subtract 42 from both side

2s = 20

divide both sides by 2

s = 10

Somebody pls!! “Write the equation of the line in fully simplified slope-
intercept form.”

Somebody pls!! Write the equation of the line in fully simplified slope-intercept form.

Answers

Answer:

y = 3/5x + 5

Step-by-step explanation:

Slope-intercept form is y = mx + b where m is the slope (rise / run of the line) and b is y-intercept (y value of where the line intersects with the y-axis.

The line is rising up 3 and run to the right 5 and so it's slope is 3/5. The line intersects with the y-axis at a y value of 5 and so it's y-intercept is 5.

Therefore, your answer in slope-intercept form is y = 3/5x + 5.

Distance between (1,4) and (5,4)

Answers

\(distance = \sqrt{(5 - 1) {}^{2} + (4 - 4) {}^{2} } \\ = \sqrt{4 {}^{2} } \\ = 4 \: units\)

4 units over. 0 units down/up

Can someone help me? ​

Can someone help me?

Answers

The answer is A because: -4-4(-1) > -1 this becomes -4+4 > -1 (when you multiply two negatives it makes a positive) then it becomes 0>-1 which is true

What is the term that relates to the way data tend to cluster around some middle or central value.

Answers

Central tendency, is the term that relates to the way data tend to cluster around some middle or central value.

Measures of central tendency are summary statistics that represent the center point or typical value of a dataset. Examples of these measures include the mean, median, and mode. These statistics indicate where most values in a distribution. Mode in statistics is the number of times a number is repeated. The number which is repeated maximum times in a series of data is known as the modular number. The mode is used to compare data that has extreme figures. Central tendency simply means most scores in a normally distributed set of data tend to cluster near the center of a distribution.

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if olive construction company gets the job, what is the probability that base construction company did not bid?

Answers

If Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.

What is probability?

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.

The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

So, the probability that the base construction company did not bid:

\(\begin{aligned}& P(A \mid B)=\frac{P(B \mid A) P(A)}{P(B \mid A) P(A)+P\left(B \mid A^{\prime}\right) P\left(A^{\prime}\right)} \\& P\left(B^{\prime} \mid O\right)=\frac{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)}{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)+P(O \mid B) P(B)} \\& P\left(B^{\prime} \mid O\right)=\frac{(0.5)(0.3)}{(0.5)(0.3)+(0.25)(0.7)} \\& P\left(B^{\prime} \mid O\right)=\frac{0.15}{0.15+0.175} \\& P\left(B^{\prime} \mid O\right)=0.4615\end{aligned}\)

Therefore, if Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.

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What is the answer to the question at the top?​

What is the answer to the question at the top?

Answers

Answer:

To make him feel a little better

Step-by-step explanation:

:)

To forget about what he was suffering from , or to do what the thing he loves.. I don’t know if am I right I’m just guessing

The geometry of the clf3 molecule is best described as
a. distorted tetrahedral.
b. tetrahedral.
c. trigonal pyramidal.
d. trigonal planar.
e. t-shaped.

Answers

Answer:

The right option is option e.T-shaped.

Step-by-step explanation:

The molecular geometry or shape of clf3 is T-shaped. It acquires such shape because of presence of two lone pairs which take equatorial position and there are greater repulsions. The hybridisation is sp3d and it has 2 lone pairs

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The geometry of the clf3 molecule is best described as a. distorted tetrahedral. b. tetrahedral. c. trigonal

Option e) T-shaped

Hybridization in chemistry is defined as the concept of mixing two atomic orbitals to create a new type of hybridized orbital.

This mixing often leads to the formation of hybrid orbitals of different energies, shapes, etc. completely different.

During  hybridization, atomic orbitals of equivalent energies are mixed  and mainly involves the fusion of two "s" or two "p" orbitals, or the mixing of "s" orbitals with the "p"" orbitals as well as "s` orbitals with  `d` orbitals.

The newly formed orbitals are called hybrid orbitals.

The shape or molecular geometry  of ClF₃ is T-shaped. It acquires such a shape due to the presence of two lone pairs in the equatorial position and has greater repulsion. The hybrid is sp³d and it has 2 lone pairs.

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Please answer it now in two minutes

Please answer it now in two minutes

Answers

Answer:

c = 6√2

Step-by-step explanation:

The following data were obtained from the question:

Angle θ = 30°

Opposite = 3√2

Hypothenus = c

The value of 'c' can be obtained by using the sine ratio as shown below:

Sine θ = Opposite /Hypothenus

Sine 30° = 3√2/c

Cross multiply

c × sine 30° = 3√2

Divide both side by sine 30°

c = 3√2 / sine 30°

But: sine 30° = 1/2

c = 3√2 / sine 30°

c = 3√2 ÷ 1/2

c = 3√2 × 2

c = 6√2 yard

Therefore, the value of 'c' is 6√2 yard.

a term used to describe the case when the independent variables in a multiple regression model are correlated is . a. correlation b. multicollinearity c. linearity d. regression

Answers

Multicollinearity refers to a situation in multiple regression where the independent variables, or predictors, in a statistical model are correlated with each other. Option B multicollinearity is correct.

Multicollinearity can result in several problems, including:

Difficulty in interpreting regression coefficients: When predictor variables are highly correlated, it becomes challenging to interpret the individual effect of each predictor on the dependent variable, as the effects may be confounded or mixed up.Unstable estimates of regression coefficients: Multicollinearity can lead to unstable or unreliable estimates of regression coefficients, as small changes in the data or the model can result in large changes in the estimated coefficients.Reduced statistical power: Multicollinearity can reduce the statistical power of a multiple regression model, making it harder to detect significant relationships between the predictors and the dependent variable.Increased standard errors: Multicollinearity can lead to increased standard errors of the regression coefficients, which can result in wider confidence intervals and decreased precision in estimating the true coefficients.

It is important to identify and address multicollinearity in a multiple regression model to ensure accurate and reliable interpretation of the results. This can be done through techniques such as variance inflation factor (VIF) analysis, principal component analysis (PCA), or using a subset of predictors with low intercorrelation.

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The term used to describe the case when the independent variables in a multiple regression model are correlated is

b. multicollinearity  is correct.

Multiple regression is a typical method in statistical modelling for determining the association between a dependent variable and two or more independent variables.

The fundamental tenet of multiple regression is that there is no correlation between the independent variables. Multicollinearity is the outcome when this assumption is broken, which can happen in real life.

When two or more independent variables in a multiple regression model have a high correlation with one another, multicollinearity arises.

Due to these issues, the model's coefficients may not be correctly interpreted, producing estimates that are inaccurate and unstable.

It is challenging to separate the distinct impacts of each independent variable on the dependent variable when multicollinearity is present because these effects are entangled and difficult to separate.

b. multicollinearity is correct option.

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Tom has 2 pieces of wood. One is 45 inches and the other is 65 inches long. He wants to cut both of wood into smaller pieces so that all the pieces are the same length. If he wants the pieces to be as long as possible, how long should each piece be? How many total pieces will he have?

Answers

Answer:

Each piece will be 5 inches long and the total number of pieces will be 22

Step-by-step explanation:

For all the pieces to be of the same length, it means the chosen length must be a number which is a factor of both 45 and 65

The number which is the same factor as both asides 1 will be 5

So he intends having the length of each of the pieces to be 5 inches each

In the 45 inches, the number of pieces he will get will be 45/5 = 9 pieces

In the 65 inches, the number of pieces he will get will be 65/5 = 13 pieces

The number of total pieces will be 13 + 9 = 22 pieces

at memorial hospital, jamie operates a new state-of-the-art mri scanner that serves approximately 10 patients during an 8-hour shift. patients are scheduled for various lengths of time, depending on the complexity of their scan. the image quality is significantly superior to what it was on previous scanners, but the number of patients served per day remains the same. this situation attests to the fact that

Answers

The image quality is significantly superior to what it was on previous scanners, but the number of patients served per day remains the same. this situation attests to the fact that the service sector has seen improvement in quality of service, but productivity remains about the same.

Improvement in quality of service:

Putting the customer first, balancing efficiency and customer satisfaction (experience), and focusing on employee engagement are three key strategies for improving contact center service quality.

Productivity:

Productivity is the efficiency with which goods and services are produced and is represented by a scale. A measure of productivity is often expressed as a ratio of total output to a single input or total input in a production process. Typically the output per unit of input over a period of time. The most common example is a measure of (aggregate) labor productivity, an example of which is GDP per worker. There are various definitions of productivity (including those not defined by the ratio of outputs to inputs), and the choice depends on the purpose of measuring productivity and the availability of data gain. The main reason for differences in different measures of productivity usually has to do with how outputs and inputs are aggregated (directly or indirectly) to obtain such relative measures of productivity doing conduct.

Importance of Productivity:

Productivity gains are defined as the process of getting more out of every hour of work. Improving productivity can take many forms, including: Capital, Investments in equipment, software, infrastructure, machinery, etc. equate to labor. Productivity is important for individuals (workers and consumers), business leaders, and analysts(such as policy makers and government statisticians).

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Josiah plants vegetable seeds in rows. Each row has the same number of seeds in it. He plants more than one row of seeds. What could be the total number of seeds he plants?

Answers

The total number of seeds that Josiah would plant would be = nR×S

How to determine the total number of seeds that Josiah will plant?

To determine the total number of seeds that Josiah will plant will be to add the seeds in the total number of rooms he planted.

Let each row be represented as = nR

Where n represents the number of rows planted by him.

Let the seed be represented as = S

The total number of seeds he planted = nR×S

Therefore, the total number of seeds that was planted Josiah would be = nR×S.

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9
A system of___
is when
you have two or more linear
inequalities

Answers

Answer: the answer is linear inequalities

Step-by-step explanation:

plz mark brainliest

Joseph needs 345 cement blocks to build a wall 40 cm thick. He needs 205 cement blocks to build a wall 25 cm thick. Each block costs $0.75. How much more will the thicker wall cost?

Answers

9514 1404 393

Answer:

  $105

Step-by-step explanation:

The thicker wall takes 345 -205 = 140 more blocks. Each of those costs $0.75, so the added blocks will cost ...

  140 × $0.75 = $105

The thicker wall will cost $105 more.

What is order of magnitude?

Answers

The magnitude of the number of the minutes in the school is 2.

What magnitude is 0 in?

Although the order of magnitude of zero is not specified, it is occasionally stated to have a magnitude of. Zero is less than any other positive number, and so is its order of magnitude, according to this infinitely negative order of magnitude.

Can a magnitude order be negative?

There can be no negative magnitude. The component of the vector that lacks direction is its length (positive or negative).

The order of magnitude is the approximate representation of the logarithmic of the order's value and is typically considered to be 10 taken as the base.

On a scale of 10 logarithmic, the difference in the order of magnitude can be quantified.

The value storage is where you may find the number into the various magnetic.

As a result, the number of minutes spent in school is 2.

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Complete question -

What is the Order of Magnitude of the number of minutes in a school day?

identify the surface with the given vector equation. r(s, t) = s sin(7t), s2, s cos(7t)

Answers

The surface represented by the vector equation r(s, t) = s sin(7t), \(s^2\), s cos(7t) is a twisted surface that extends uniformly in the s-direction while exhibiting sinusoidal variations in the s-direction with a phase shift of π/2.

The given vector equation is r(s, t) = s sin(7t), \(s^2\), s cos(7t).

By analyzing the components of the vector equation, we can identify the surface represented by it.

The first component, s sin(7t), indicates that the surface varies in the s and t directions as s sin(7t).

This component suggests a sinusoidal variation in the s-direction with respect to the parameter t.

The second component, \(s^2\), is independent of t and remains constant.

This suggests that the surface extends uniformly in the s-direction and does not vary with t.

The third component, s cos(7t), indicates that the surface varies in the s and t directions as s cos(7t). This component suggests a sinusoidal variation in the s-direction with respect to the parameter t, but with a phase shift of π/2 compared to the first component.

Putting these components together, we can conclude that the surface represented by the vector equation r(s, t) = s sin(7t), \(s^2\), s cos(7t) is a twisted surface that extends uniformly in the s-direction while exhibiting sinusoidal variations in the s-direction with a phase shift of π/2 between the first and third components.

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Xoca-COLOR1. Determine if the value of the given variable is a solu(6 points each)a) *x+5 -3(x + 2) -^(3) +5=143) +.241215for 2-3nources7729 +0-42ho4-4-4x+5=3(x+2)=-4

Answers

Solving:

4x+5=3(x+2)-4

4x + 5 = 3x + 6 - 4

4x + 5 = 3x + 2

collect like terms, we have:

4x - 3x = 2 - 5

x = -3

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Question 12 Calculate the price of a 4.8 percent coupon bond with 5 years left to maturity and a market interest rate (YTM) of 3.0 percent. (Assume interest payments are semiannual and par value is $1,000.) a.$ 1,083.00 b.$1,125.00 c.$1,075.30 d.$ 1,098.50 What is the author's purpose in writing the passage?A. to convince people that the Grand Canyon is worthy of preservationB. to provide a list of the features that make the Grand Canyon uniqueC. to celebrate the many beautiful sights and sounds of the Grand CanyonD. to explain how the Grand Canyon was formed by wind, rain, and riversColoradoby John Wesley Powell The wonders of the Grand Canyon cannot be adequately represented in symbols of speech, nor by speech itself. The resources of the visual arts are taxed beyond their powers in attempting to portray its phenomenal beauty. Language and illustration combined must fail. The elements that unite to make the Grand Canyon the most sublime spectacle in nature are many and exceedingly diverse. The giant forms, which result from the sculpture of tempests through ages too long for man to compute, are wrought into endless details. To describe these forms would be a task equal in magnitude to that of describing the stars in the sky or the abundant beauties of the forest with its traceries of foliage presented by oak and pine and poplar, by beech and linden and hawthorn, by tulip and lily and rose, by fern and moss and lichen. Besides the elements of form, there are elements of color. The rainbow is not more replete with hues. But form and color do not exhaust all the divine qualities of the Grand Canyon. It is the land of music. The river thunders in perpetual roar, swelling in floods of music when the storm rains play upon the rocks, and fading away in soft and low murmurs when the infinite blue of the sky is unveiled. With the melody of the great tide rising and falling, swelling and vanishing forever, other melodies are heard in the gorges of the lateral canyons, while the waters plunge in the rapids among the rocks or leap in great cataracts. Thus, the Grand Canyon is a land of song. Mountains of music swell in the rivers, hills of music billow in the creeks, and meadows of music murmur in the rills that ripple over the rocks. Altogether it is a symphony of diverse melodies. All this is the music of waters. The adamant foundations of the earth have been wrought into a sublime harp, upon which the clouds of the skies play with mighty tempests or with gentle showers. An object has a mass of 400 g and a volume of 25 cm3.Find the density of the object in g/cm3. . how is finding the sum of an infinite geometric series different from finding the nth partial sum? Ava bought some pens for $ 2 each and some pencils for $ 1 each. She bought 3 more pens than pencils and spent a total of $ 12. 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Responses perform ultrasound, massage and apply heat or cold perform ultrasound, massage and apply heat or cold assess muscle tone and range of motion assess muscle tone and range of motion develop a treatment plan that might include exercise develop a treatment plan that might include exercise perform a computed tomography (CT) scan perform a computed tomography (CT) scan Please answer as soon as possible correctly Most of the excessive carbon dioxide that is expected to cause global warming is generated by All of these are correct. green plants. burning of fossil fuels and production of cement and clearing of forests only. production of cement and clearing of forests. burning of fossil fuels. The relation that the law of demand defines is-a. income and price of a commodityb. price and quantity of a commodityc. income and quantity demandedd. quantity demanded and quantity supplied batang LOR Asta 342 27 89 51 63 167 899 312 573 5740 563 206 277 5435 Cash and cash equivalente Accounts receivable Inventory Total current ansets property, plant, and equipment Las accumulated depreciation et property, plant, and equipment Total aseta abilities and stockholders' equity Current liabilities Accounts payable Accrued liabilities Income taxes payable Total current liabilities Bonde payable Total liabilities Stockholders' equity. Common stock Retained earnings Total stockholders' equity Total liabilities and stockholders' equity 544 33 56 133 140 273 63 26 48 137 14 285 manual 98 369 467 $ 740 57 150 5435 of the year was 385. Cash dividends were $73. The company did not sell of retire any property, anno equipment during the year. The net cash provided by used in operating activities for the year was Multiple Choice $31 $553 $354 Using MATLAB, generate a 2.5 cycle hanning window signal (using 'hann' function) and an FFT plot using the following:f=25000; %frequencyT=1/f; %periodo=2*pi*f;tvec=linspace(0,1.5*T,250); %time stepy=sin(o*tvec); %signal Which of the following are true of fibrous joints? Select all that apply.A) tightly bound by ligamentsB) flexibleC) stationary D) only found in the knee If we wanted to make the statement that a particular point on a production possibility frontier was both allocaltvely and technically efficient, which of the following additional pieces of information would we need? Selected answer will be automatically saved. For keyboard navigation, press up/down anrow keys to select an answer: a The relative prices of the goods. b Consumer preferences between the goods. c The costs of production of the goods: d We don't need any additional information -if a point is technically efficient, it is also allocatively efficient. Find anequation for the ellipse described:Vertices at (2, 5) & (2, -1); c = 2