A kindergarten teacher asked the students' parents to send their child to school with two fruits (apples and/or oranges). Below are the combinations of fruits brought to class the next day.
Fruit
2 Apples : 9 students
1 Apple and 1 Orange : 4 students
2 Oranges : 8 students

What is the frequency of oranges in the classroom? Round your answer to 4 decimal places.

Answers

Answer 1

The frequency of oranges in the classroom can be calculated as follows:Frequency of oranges in the classroom = Total number of oranges / Total number of fruits= 16/42 = 0.3809 (rounded to 4 decimal places)Thus, the frequency of oranges in the classroom is approximately 0.3809.

To determine the frequency of oranges in the classroom, we need to calculate the proportion of students who brought oranges out of the total number of students.

First, let's calculate the total number of students:

Total students = Number of students with 2 apples + Number of students with 1 apple and 1 orange + Number of students with 2 oranges

Total students = 9 + 4 + 8 = 21

Next, let's calculate the number of students who brought oranges:

Number of students with oranges = Number of students with 1 apple and 1 orange + Number of students with 2 oranges

Number of students with oranges = 4 + 8 = 12

Finally, we can calculate the frequency of oranges:

Frequency of oranges = Number of students with oranges / Total students

Frequency of oranges = 12 / 21 ≈ 0.5714 (rounded to 4 decimal places)

Therefore, the frequency of oranges in the classroom is approximately 0.5714.

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Answer 2

To determine the frequency of oranges in the classroom, it is important to add up the total number of fruits brought to the classroom. The given information is as follows:

2 Apples: 9 students

1 Apple and 1 Orange: 4 students

2 Oranges: 8 students

Thus, the frequency of oranges in the classroom is approximately 0.2105.

Total number of fruits = 2(9) + 1(4) + 2(8)

= 18 + 4 + 16

= 38 fruit in total

So, total number fruits are 38.

Frequency of oranges = Number of oranges / Total number of fruits

There are 8 oranges brought to class, so the frequency of oranges is:

8 / 38 ≈ 0.2105 (rounded to 4 decimal places)

Hence, the frequency of oranges in the classroom is approximately 0.2105.

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Related Questions

Solve for x and the length of segment GH.

Answers

Answer:

If two secant segments intersect outside a circle, then the product of the secant segment with its external portion equals the product of the other secant segment with its external portion.

45(45) = (2x + 75)(27)

2,025 = (2x + 75)(27)

2x + 75 = 75, so x = 0 and GH = 48

Find the area of this kite.
3 m
5 m
6 m
5 m

Answers

Answer:

450m

Step-by-step explanation:

Min is about to roll a six-sided number cube.What is the probability that she will roll an even number? A) 1/4.. B) 1/3 C) 1/2 D) 5/6

Answers

Answer:

C) 1/2

Step-by-step explanation:

3 of the 6 numbers on a cube are even. 3/6 = 1/2

solve the following question

Answers

Given:

The expressions are:

[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}[/tex]

[tex]\dfrac{x^2-y^2}{4x+4y}\cdot \dfrac{x+y}{x-y}[/tex]

To find:

The simplified form of the given expressions.

Solution:

We have,

[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}[/tex]

It can be written as:

[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}=\dfrac{12a^{2+1}bc^3}{40b^4c^2}[/tex]

[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}=\dfrac{3a^{3}c^{3-2}}{10b^{4-1}}[/tex]

[tex]\dfrac{2a^2b}{2c^2}\cdot \dfrac{6ac^3}{20b^4}=\dfrac{3a^{3}c^{1}}{10b^3}[/tex]

Therefore, the value of the given expression is [tex]\dfrac{3a^{3}c}{10b^3}[/tex].

We have,

[tex]\dfrac{x^2-y^2}{4x+4y}\cdot \dfrac{x+y}{x-y}[/tex]

It can be written as:

[tex]\dfrac{x^2-y^2}{4x+4y}\cdot \dfrac{x+y}{x-y}=\dfrac{(x+y)(x-y)}{4(x+y)}\cdot \dfrac{x+y}{x-y}[/tex]

[tex]\dfrac{x^2-y^2}{4x+4y}\cdot \dfrac{x+y}{x-y}=\dfrac{x+y}{4}[/tex]

Therefore, the value of the given expression is [tex]\dfrac{x+y}{4}[/tex].

You roll 2 six sided dice. What are the odds of rolling 2 sixes?

A. 1/6
B. 1/36
C. 1/18
D. 1/12

Answers

you will have 1/6 odds
You will have 1/12 odds

what goes up a hill with three legs and goes down a hill with four legs?

Answers

Answer:

i don't know what goes up with three leg and goes down with 4

Answer:

u

Step-by-step explanation:

Multiple Choice
What is the volume of the pyramid?
A pyramid with height 8 ft and width 7ft.



A. 56 ft³
B.
130 two-thirdsft³

C. 196 ft³
D. 392 ft³

Answers

b because l*w*h and then you do multiplication and you get the answer

To test the hypothesis that the population mean mu 6.0. a sample siren-29 yields a samole mean 6.42S and sample standard deviation 7.440 Calculate the value and choose the correct conclusion.

Answers

Since our test statistic is smaller than this critical value, we can conclude that the sample mean of 6.42 is not statistically significant and therefore cannot be used to reject the null hypothesis that the population mean is 6.0.

The first step here is to calculate the test statistic, which is also called a t-statistic or a z-score. This is done by subtracting the population mean from the sample mean, and dividing this difference by the standard deviation of the sample (dividing by the standard error if the population standard deviation is known). In this case, we have:

Test Statistic = (Sample Mean - Population Mean) / (Sample Standard Deviation / √n)

Test Statistic = (6.42 - 6.0) / (7.44 / √29)

Test Statistic = 0.42 / (7.44 / 5.385)

Test Statistic = 0.42 / 1.377

Test Statistic = 0.305

Now that we have the test statistic, we can compare it to the t-table or z-table (depending on if the population standard deviation is known) to determine whether or not the calculated value is statistically significant. For example, if we assume a 95% confidence level, the critical value of z (the p-value) is 1.96.

Since our test statistic is smaller than this critical value, we can conclude that the sample mean of 6.42 is not statistically significant and therefore cannot be used to reject the null hypothesis that the population mean is 6.0.

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Helpppp please and ty

Answers

Answer:

-2, -1, 0, 1

Step-by-step explanation:

you hover over the stars

find the missing angle measurement

Answers

3x+7+10x+17=180
13x+24=180
Subtract 24 from both sides
156/13
x= 12

Someone please help me I’ll give out brainliest please dont answer if you don’t know

Answers

First use the distributive property by multiplying the 3 with each term inside the parentheses:

-8 + 3c + 3 + c

Now combine like terms:

-8 + 3 = -5

3c + c = 4c

Combine for final answer:

-5 + 4c which can also be written as 4c-5

Answer:

first let's multiply 3 by the bracket

-8+3*c+3*1+c=-8+3c+3+c

then add the numbers that have the same variables -8+3+3c+c

=-8+3+4c then add the numbers

=-5+4c is the answer

you can also write it like this

4c-5

Consider the following IVP: y' = ty +t^2, 0<= t<= 2, y(0) = 1 The exact solution of this IVP is y(t) = y = -t^2 – 2(t + 1) + 3et Use Euler's method with step size h = 0.1 to approximate y(1).

Answers

The approximate value of y(1) using Euler's method with a step size of h = 0.1 is 1.

Using Euler's method and a step size of h = 0.1, we can use the given initial value problem (IVP) and iterate through the interval [0, 1] in steps of size h to approximate the value of y(1). Let's begin by determining the number of steps required: n = (1-0) / 0.1 = 10.

Utilizing the accompanying recipe, we can repeat through the span beginning with the underlying condition y(0) = 1.

y(i+1) is equivalent to y(i) + h * (t(i) * y(i) + t(i)2), where I is among 0 and n-1, t(i) is equivalent to I * h, and y(i) is the surmised worth of y at t(i).

At each step, we can inexact the upsides of y utilizing the recipe gave:

The approximate value of y(1) is 1, assuming Euler's method and a step size of h = 0.1. y(0) = 1 y(1)  y(0) + 0.1 * (0 * y(0) + 02) = 1 + 0.1 * (0 + 0) = 1.

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Write 3.41 x 106 in standard form
(24 points)

Answers

Answer:

3,410,000

Step-by-step explanation:

3.41 * 10^6 = 3.41 * 1,000,000 = 3,410,000

Answer:

3,410,000

plz mark me as brainliest

put the cells in the right spot please :(

Answers

The First one is a eukaryote.
The Second one is a prokaryote.
The Third one is a prokaryote.
The Fourth one is a eukaryote.
The Fifth one is a prokaryote.
The Sixth one is a eukaryote.
The last one is a prokaryote.


Hope it helps.☺️

Write the exact value of the side length, in units, of a square whose area in square units is: 100/9

Answers

Answer: 10/3 units

Step-by-step explanation: sqrt 100/9= 10/3

kohl's rectangular gold garden has an area of 54 square feet wood what would be their dimensions of the garden

Answers

Kohl's rectangular gold garden has an area of 54 square feet. To determine the dimensions of the garden, we need to find two numbers whose product is 54.

To find the dimensions of the garden, we can factorize the area of 54 square feet. The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. Since the garden is rectangular, we are looking for two numbers whose product is 54.

By examining the factors, we can see that the dimensions of the garden could be 6 feet by 9 feet, as their product is indeed 54. Alternatively, the garden could have dimensions of 3 feet by 18 feet, as their product is also 54. Both sets of dimensions result in an area of 54 square feet.

Therefore, the possible dimensions of Kohl's rectangular gold garden could be either 6 feet by 9 feet or 3 feet by 18 feet.

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A number pattern starts with 10 and follows the rule multiply by 3." What is true
about all of the numbers in this pattern?
1:They have a 3 in the tens place.
2:They have a 0 in the ones place.
3:They are odd numbers.
4: They can be odd or even numbers.

Answers

Answer:

1. and 2. I belive are true sorry if wrong

Step-by-step explanation:

A pizza parlor uses 42 tomatoes for each batch of tomato sauce. About how many batches of sauce can the pizza parlor make from its last shipment of 1,236 tomatoes?

Answers

Divide the total tomatoes in use by the average amount of tomatoes used in a single batch.

1,236/42 = 29.428 (about 29 batches can be made)

CORRECT ANSWER GETS BRAINLIEST
The difference between two numbers is 15. Find the two numbers if twice the small number plus three times the large number total 75. (Be sure to use let statments and an equation when solving)

Answers

Answer:

21 and 6

Step-by-step explanation:

a will be the larger, b the smaller:

a - b = 15

2b + 3a = 75

First, we'll solve the first equation for a in terms of b:

a = b + 15

Then substitute that in for a in the second equation to get a numerical value for b:

2b + 3(b + 15) = 75

2b + 3b + 45 = 75

5b = 30

b = 6

Next, we'll get a numerical value for a:

a - b = 15

a - 6 = 15

a = 21

Check the math:

2(6) + 3(21) = 12 + 63 = 75

Please lmk if you have questions.

Over the past month, a garment manufacturer produced 800 dresses. The distribution of the amount of fabric required to make the dresses is

not normal.

The average amount of fabric needed to make a dress is 4 yards, with a standard deviation of 2 of a yard. Suppose a series of samples, each

containing 180 dresses, are selected from the dresses produced in the past month.

Would it be appropriate to model the distribution of a sample mean with a normal model?

Answers

Answer:

Yes it will be appropriate to model the distribution of a sample mean with a normal model

Step-by-step explanation:

Given that the population is not normal, and the sample is sufficiently large, according to the Central Limit theorem, the distribution of the mean pf the sampling distribution will be approximately normal not withstanding the population from which the sample is obtained. Therefore, the mean, [tex]\overline x[/tex], and the standard deviation, [tex]\dfrac{\sigma}{\sqrt{n} }[/tex], of the sample will be equal to the mean, μ, and standard deviation, σ, of the of the population

Therefore, it will be appropriate to model the distribution of a sample mean with a normal model

Answer:

yes

Step-by-step explanation:

i got it right on plato

Hypothesis Testing:
Step 1: State the hypotheses H = μ = 30 (claim) and H₁ = μ ≠ 30
Step 2: The level of significance and critical region.
α= 5% and two - tailed test
critical value = ± 1.96
Step 3: Compute for the value of one-sample t-test.
t = (x-μ)/(s/ √n)
t= (30.1 - 30)/ (1.3 √15)
t = - 0.3
Step 4: Decision rule. Do not reject the null hypothesis since the test value falls in the non-critical region.
Step 5: Conclusion. There is not enough evidence to support the claim that mean weight of their product is 30 grams.

Answers

In this hypothesis testing scenario, the null hypothesis (H) states that the mean (μ) weight of a product is equal to 30 grams.

The one-sample t-test is computed using the formula t = (x - μ) / (s / √n), where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size. In this case, the calculated t-value is -0.3.

Based on the decision rule, since the calculated t-value of -0.3 falls within the non-critical region (-1.96 to 1.96), we do not reject the null hypothesis.

Therefore, the conclusion is that there is not enough evidence to support the claim that the mean weight of the product is 30 grams. The data does not provide sufficient statistical evidence to conclude that the mean weight significantly differs from 30 grams.

It's important to note that in hypothesis testing, the result does not prove that the null hypothesis is true; rather, it suggests that there is not enough evidence to reject it based on the given data and significance level.

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Can some plz help me

Answers

This is a guess but I think 24 hope I helped :))

Which point A,B,C or D is in the solution
set of the inequality graphed below?

Answers

Answer:

I would need to see the graph to answer this question.

Can someone help me with this. Will Mark brainliest.

Answers

Answer:

b(-1,-8)

Step-by-step explanation:

assuming x2 and y2 are the coordinates of b.

and x1 and y1 are the coordinates of A

midpoint are (xm, ym)

formula xm= (x1+x2)/2

ym=(y1+y2)/2

Note: In the following problem, it is important to show all the steps used to get your answers.
Suppose an imaginary closed economy is characterized by the following:
C = c0 + c1 (Y − T)
T = 300 I = 400 G = 400
C is consumption, Y and YD are, respectively, income and disposable income, T is the level
of taxes, I and G, are, respectively, private investment, and government spending.
c0 and c1 are, respectively, autonomous consumption and the marginal propensity to con-
sume; their values are unknown. However, the expression for private saving, S, is as specified
below.
S = 0.5Y − 500
1. Find the equilibrium values of GDP, consumption, disposable income, and private saving.
(5 points)
2. Find the expression of the investment multiplier in terms of c0 and/or c1. (3 points)
3. Find the values of c0 and c1 and the value of the investment multiplier (Hint: you’ll prob-
ably find c0 is equal to an even number, which is multiple of 2). (5 points)
4. From this question on, you must use when needed the values of c0 and c1 found in the pre-
vious question. Suppose now that the government tax revenue, T, has both autonomous
and endogenous components, in the sense that the tax level depends on the level of in-
come.
T = t0 + t1Y

t0 is the autonomous tax level, and t1 is the marginal tax rate.
Given the values of private investment and government spending mentioned above, find
the expression for the equilibrium GDP in terms of c0, c1, t0 and t1. (4 points)

5. Assuming that t0 = 200 find the value of the marginal tax rate that will yield the same
level of equilibrium GDP as the one obtained (1). (4 points)
6. Find the expression for the investment multiplier in terms of c1and t1 and possibly c0, and
t0. (4 points)
7. Assume now that private investment, I, increases by 50. Find the change in GDP, ∆Y,
induced by the change in investment, ∆I = 50. (4 points)
8. The government does not like the change in GDP induced by the increase in private in-
vestment. It wants to bring it back to the level found in Question (1). For that purpose, it
has the options to change its spending or to change taxes.
(a) If the government changes its spending alone, find the level of ∆G required to coun-
teract the effect on GDP of the fall in investment. (4 points)
(b) If the government changes instead the level of its autonomous taxes alone, find the
level of ∆t0 required to counteract the effect on GDP of the fall in investment. Explain
what happened. (4 points)
(c) How does ∆G compare to ∆t0? Explain the difference, if there is any. (4 points)
(d) In which direction should the government change its marginal tax rate, t1 (increase
or decrease), if it uses it as the sole policy instrument to counteract the effect of the
change in investment? Explain intuitively your answer. (4 points)

Only need to answer 5-8 questions!!!!

Answers

5. Assuming that t0 = 200 find the value of the marginal tax rate that will yield the same level of equilibrium GDP as the one obtained

(1). Solution: Given, T = t0 + t1Y and T = 300

Substituting the given values, we get300 = 200 + t1YGDP, Y = C + I + G + X - M

where, Y = GDP; C = consumption; I = private investment; G = government spending; X = exports; M = imports

We know, C = c0 + c1 (Y − T) Disposable income, YD = Y − T

So, C = c0 + c1 (Y − T) = c0 + c1YD

From the question, S = 0.5Y − 500

We know that, private saving, S = Y − C − T

So, Y − C − T = 0.5Y − 500 ⇒ 0.5Y = C + T + 500

Putting the values,

0.5Y = (c0 + c1YD) + T + 500 ⇒ 0.5Y = (c0 + c1(Y - T)) + T + 500 ⇒ 0.5Y = c0 + c1Y - c1T + T + 500

Solving the above expression, we get

0.5Y - c1Y = c0 - 0.5T + 500 ⇒ 0.5(1-c1)Y = c0 - 0.5T + 500

Hence, Y = (c0 - 0.5T + 500) / (0.5 - c1)

Again, from the question, Y = C + I + G + X - M

Substituting the values we get,

(c0 + c1(Y − T)) + 400 = I + 400 + Y - 500 + X - X0.5Y − 500 + 400 = I + 300 + X − G ⇒ 0.5Y + I = 1200 + G + X

Assuming equilibrium GDP Y = Y*, private investment I = I*, government spending G = G* and net exports X = X*, so0.5Y* + I* = 1200 + G* + X*

Now, from the given information of S, we have S = Y* − C* − T.

Substituting for C* from the equation above, we get S = Y* − (c0 + c1(Y* − T)) − T ⇒ S = Y* − c0 − c1Y* + c1T − T

Substituting for Y* from above, we have S = ((c0 - 0.5T + 500) / (0.5 - c1)) - c0 - c1[((c0 - 0.5T + 500) / (0.5 - c1))] + c1T - T

Now, we need to find the value of t1 when t0 = 200. For this, we need to substitute the value of t0 and Y* in T = t0 + t1YSo, 300 = 200 + t1Y* ⇒ t1 = (300 - 200) / Y* ⇒ t1 = 0.1

Therefore, the value of the marginal tax rate t1 is 0.1.

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PLS hurry!! I'LL MARK BRAINLIEST!

Answers

Answer:

A. 5+x-12=2x-7

-7+x+2x-7

x=2x

x-2x=0

-x=0-> x=0

B.

when X=-0.5

5+(-0.5)-12=2 (-0.5)-7

-7.5=-8 (answer does not work)

when X=0

5+0-12=2(0)-7

-7=-7 (answer works)

when x=1

5+1-12=2(1)-7

18=-5 (answer does not work)

Step-by-step explanation:

Answer:

[tex]x=0[/tex]

Step-by-step explanation:

A) From this case you would need to narrow down the whole equation...

Like this: [tex]5+x-12=2x-7[/tex]  →  [tex]x-7=2x-7[/tex]  →  [tex]x=0[/tex]

B) To prove that one of these numbers solve the equation, we would have to check it ourselves.

Like this: [tex]5+(-0.5)-12=2(-0.5)-7[/tex]  →  [tex]-7.5=-8[/tex] (SO THIS WON'T WORK)

[tex]5+0-12=2*0-7[/tex]  →  [tex]0=0[/tex] (THIS WORKS!)

[tex]5+1-12=2(1)-7[/tex]  →  [tex]-6=-5[/tex] (NOR DOES THIS WORK)

Therefore: [tex]x=0[/tex] will work to solve the equation correctly

A particle at and moves number line so that its position as tízku v in given by x * d(t) = (1 - 2) ^ 2 * (1 - 6)
(a) When is the particle moving to the right?
(b) When is the particle at rest?
(c) When does the particle change direction?
(d) What is the farthen left of the origin that the particle moves

Answers

The particle never moves to the right of the origin. Hence, the farthest left of the origin that the particle moves is at x=-∞.

Given that, the position of the particle is [tex]x*d(t)=(1-2)^2*(1-6).[/tex]

Initially, the position of the particle is[tex]x*d(t)=(-1)^2*(-5)=5.[/tex]

The displacement of the particle can be given as the difference between the final position and the initial position. Therefore, the displacement of the particle is [tex]Δx=0-5=-5.[/tex]

(a) Since the value of the displacement is negative, the particle is moving to the left.

(b) The particle will be at rest when the velocity of the particle is zero. Here,[tex]v=d/dt (x*d(t))=x*d'(t)[/tex]

When the velocity of the particle is zero, then x*d'(t)=0.So, either x=0 or d'(t)=0.

When x=0, the particle will be at rest at the origin.

To find out the value of t, substitute x=0 in the given equation,

we get[tex]0=(-1)^2*(-5).[/tex] This is not possible. Therefore, the particle will never be at rest.

(c) When the direction of the velocity changes, the particle changes direction. The velocity of the particle is given as v=d/dt (x*d(t))=x*d'(t).

From the above equation, we see that the velocity of the particle changes direction when x changes direction. The direction of x changes at x=0.

(d) The farthest left of the origin that the particle moves is at x=-∞ when t=0.

Thus, the particle never moves to the right of the origin. Hence, the farthest left of the origin that the particle moves is at x=-∞.

Note: Here, we have considered the absolute values of -1 and -5.

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Aim High To The Sky


James McDonald


Aim high to the sky,

In all that you do.

Because you just never know,


What it takes to be you.


Be strong and be brave,

But at the same time be kind.


And always be sure,

That you're using your mind.


Based on the poem the reader can conclude that the speaker -

A. feels effort and thoughtfulness to others are all important

B, thinks trying your best is the only important thing

C.feels that success is the most important thing in life

D. thinks that everyone will succeed if they work hard enough


( PLEASE HELP )

Answers

Answer:

A

Step-by-step explanation:

Because That's The Main Idea

Marianna is painting a ramp for the school play in the shape of a right triangular prism. The ramp has dimensions as shown below. She will not paint the back or bottom surfaces of the ramp. What is the surface area of the ramp?

Just include the front and sides of the ramp.

A
4 square inches

B
300 square inches

C
2,905 square inches

D
3,672 square inches

Answers

Answer: The correct answer will be 4

Step-by-step explanation:

plzzzz help with the square ( parallelograms)

Answers

Answer:

#1=8

#2=3

Step-by-step explanation:

Other Questions
Let D be the region bounded by a curve 2+y = 3xy in the first quadrant. Find the are: of D (Hint: parametrise the curve so that y/x = t). Unearned revenue is classified asa. an asset account.b. a revenue account.c. a contra-revenue account.d. a liability account. using the elements and principles of composition as a guide, analyze and compare the church of the holy family and the cathedral of notre dame at chartres. A self-compassionate personA never gets angry,B has a big group of friends.C lets herself feel sad sometimes,D only hangs out with nice people. Which statements about quantitative research are accurate? (Select all that apply.)Select one or more:a. The results of quantitative research should be generalized back to the population from which the sample was drawn.b. The methods of quantitative research are consistent with the philosophy of logical positivism.c. Quantitative research addresses quantities, relationships, and causes.d. Quantitative research predominates in the nursing research literature.e. Quantitative research is always experimental.f. Quantitative research tells the story of the research participants' daily lives, within their culture. For each of the following systems, determine whether or not the system is (1) linear, (2) time-invariant, and (3) causal: a. y[n]=x[n]cos(0.2n) b. y[n]=x[n]x[n1] c. y[n]=x[n] d. y[n]=Ax[n]+B, where A and B are nonzero constants. decide as a group on a well-known firm you will research. For each of the following pairs of vectors and y, find the vector projection p of c onto y, and verify that p and x p are orthogonal. (a) = (3, 4)T ard y = (1,0)T. (c) x = ( = (1,1,1)". (d) x = (2,-5,4)" and y = (1,2,-1)" (b) x = (3.5)", and y (1,1)". 2.4,3)1 and y perform a retrosynthetic analysis of the alcohol. the alcohol is secondary , so it is formed by reaction of the grignard reagent with a ketone. As discussed in class, Treasury Inflation-Protected Securities (TIPS) is a popular type of debt instrument:a) What is a TIPS? How is it different from regular treasury securities.b) Suppose you purchased a TIPS with a par value of $1 million. The coupon rate is 3.2%. Assume that the inflation in first six months is 3.6% (annual rate). Compute (i) inflation adjusted principal at the end of the first six months, (ii) the coupon payment at the end of the first six months.c) Assume that the inflation in the second half year is 4.0% (annual rate). Compute (i) inflation adjusted principal at the end of the second six months, (ii) the coupon payment at the end of the second six months. Suppose the repo rate for a T-bond is 4.15%, and the haircut for an overnight repo is 2%. You plan to buy 100 T-bonds with $1K price per bond today, and sell it in the following day.a) How much of the purchase price can you borrow by repoing out the bond? How much your own capital should be added to purchase the 100 T-bonds?b) How much Repo interest will you have to pay tomorrow?c) What bond prices tomorrow would have wiped out the margin (i.e., lose your own capital)? Let (e_t ) be a zero mean white noise procent. Suppose that the observed process is Yt =e_t + _et-1, is either 3 or 1/3.(a) Find the autocorrelation function for (Y_t) both when =3 and =1/3 (b) You should have discovered that the time series is stationary regardless of the value of '' and that the autocorrelation functions are the same for =3 and = 1/3. For simplicity, suppose that the process mean is known to be zero and the variance of Y_t is known to be 1. You observe the series (Y_t) for t - 1,2...n and suppose that you can produce good estimates of the wutocorrelations pk. Do you think that you could determine which value of is correct (3 or 1/3) based on the estimate of pk? Why or why not? There is a function f(t) which is given by: f(t) = sin(t/T) for 0 t 2T and f(t) = 0 for 2T tThis function repeats periodically outside the interval [0,T] with period T (assuming that 2T a) what are the restrictions that would be expected for the Fourier coefficient a_j. Which Fourier coefficient is expected to be the largest?b) Calculate the Fourier expansion , thus verifying the prediction . Why is working capital management important? Give concrete examples of how companies manage their cash, receivables, inventory and payables. Initial studies of the influenza A virus by Walter Fitch and colleagues showed that a.selection by the human immune system drives change in virus's hemagglutinin's antigenic sitesb.influenza A actually has DNA as its genetic materialprotein evolution in influenza A is consistent with the neutral theoryc.selection is causing influenza A to become more virulent over time Suppose Stan earned $115,000 in 1947. If the CPI was 82 in 1947, and was 246 in 1990, what is Stan Musials 1947 salary in 1990 dollars? If the real value of an item bought ten years ago is less than its nominal value at that time, what can one infer about the change in the overall price level during this ten year period? If the inflation rate decreased from 3.33% to 2.90% between October and November, while the nominal interest rate increased from 4.75% to 4.80%, what is the real interest rate in November? Suppose you paid 50 cents for a candy in 1970. The CPI in 1970 was 38.8, while the CPI in 2010 was 218.1. What is the value of the same candy in 2010 dollars? In 1980 the population of alligators in a particular region was estimated to be 1100. In 2005 the population had grown to an estimated 6500. Using the Malthusian law for population growth, estimate the alligator population in this region in the year 2020. (...) The alligator population in this region in the year 2020 is estimated to be (Round to the nearest whole number as needed.) Greenville purchased land and a building for $300,000. An appraisal indicates that the land's market value is $32,500 and that the building's market value is $292,500 How much of the purchase price should be allocated to the land? How much of the purchase price should be allocated to the building? a. Land: $32,500, Building: $292,500 b. Land: $270,000, Building: $30,000 c. Land: $30,000, Building $270,000 d. Land $292,500, Building: $32,500 A new highway is to be constructed. Design A calls for a concrete pavement costing $95 per foot with a 20-year life: four paved deches costing $5 per foot each; and two box culverts every mie, each costing $10,000 and having a 20-year Annual maintenance will cost $1,800 per mile: the culverts must be cleaned every five years at a cost of $300 each per Design B-calls for a bituminous pavement costing $35 per foot with a 10-year e, two sodded dichas costing $1.50 per foot each and two pipe culverts every mile, each costing $2,250 and having a 10-year e The replacement ouvert $2,450 each. Annual maintenance will cost $2,600 per mile; the culverts must be cleaned yearly at a cost of $225 each per mile, and the annual ditch maintenance will cost $1.50 per foot per dich Compare the two designs on the basis of equivalent worth per mile for a 20-year period. Find the most economical design on the basis of AW and PW if the MARR is 10% per year How much energy is required to heat 40. 7 g of water (H2O) from 10C to 70C? Your answer should have three significant figures. Where: cice=2. 06 J/gC cwater=4. 18 J/gC Hfus=334 J/g The four major market entry strategies are export, investment, countertrade and agents. True or false