Given the triangle with vertices at (1,4), (4,3), and (2,-1), sketch the image after the given transformation is applied. Based on your graph, identify the transformation as a translation, reflection, rotation, or other transformations, and state whether the transformation is an isometry.

1. (x,y) -> (x,-y)

2. (x,y) -> (y,-x)

3. (x,y) -> (2x,2y)

4. (x,y) -> (x+4,-y)

5. (x,y) -> (5-x,y)

6. (x,y) -> (x+4,y-3)

what is the  historic development of counting techniques in math with examples.

An Agriculture Department study of more than 94,000 samples from more than 20 crops showed that 73% of conventionally grown foods had residues from at least one pesticide. Moreover, conventionally grown foods were six times as likely to contain multiple pesticides as organic foods. Of the organic foods tested, 28%had pesticide residues, which includes 7% with multiple pesticide residues.

Compute two estimated probability distributions:

one for conventional produce and one for organic produce, showing the relative frequencies that a randomly selected product has no pesticide residues, has residues from a single pesticide, and has residues from multiple pesticides.

Assume a 2D physical system where the vectors |ψ1i and |ψ2i form an orthonormal basis of the space. Let’s define a new basis with |φ1i = √ 1 2 (|ψ1i + |ψ2i) and |φ2i = √ 1 2 (|ψ1i − |ψ2i). Given an operator Mˆ represented in the |ψii-basis by the matrix 1 1 , find the representation of Mˆ in the basis |φii-basis.

Consider the function ?(?) = ?^?2and x = 0, 0.25, 0.5, 1. Then use the suitable Newton interpolating polynomial to approximate f(0.75). Also, compute an error bound for your approximation.

The following data set provides information on the lottery sales, proceeds, and prizes by year in Iowa.

FY

Sales

Proceeds

Prizes

1992

$166,311,122

$45,678,558

$92,939,035

1993

$207,192,724

$56,092,638

$116,820,274

1994

$206,941,796

$56,654,308

$116,502,450

1995

$207,648,303

$58,159,175

$112,563,375

1996

$190,004,182

$51,337,907

$102,820,278

1997

$173,655,030

$43,282,909

$96,897,120

1998

$173,876,206

$42,947,928

$96,374,445

1999

$184,065,581

$45,782,809

$101,981,094

2000

$178,205,366

$44,769,519

$98,392,253

2001

$174,943,317

$44,250,798

$96,712,105

2002

$181,305,805

$48,165,186

$99,996,233

HelpCopy to ClipboardDownload CSV

Create a graph using the sales and year. What approximate range of sales would you expect for the year 2017?

Select the correct answer below:

Between 250 and 300 million dollars

Between 300 and 375 million dollars

Between 375 and 400 million dollars

Between 500 and 550 million dollars

(a) look at these the complex numbers z1 = − √ 3 + i and z2 = 3cis(π/4). write the following complex numbers in polar form, writing your answers in principal argument:

i. z1

ii. z1/|z1|. Additionally, convert only this answer into Cartesian form.

iii. z1z2

iv. z2/z1

v. (z1) ^-3

vi. All complex numbers w that satisfy w ³ = z1.

(b) On an Argand diagram, sketch the subset S of the complex plane defined by S = {z ∈ C : |z − i| ≤ 1, |z + 2 − 3i| ≤ |z − 2 + i|}.

Find the best quadratic approximation to f(x,y) = e^4ycos(-3x) about the origin (0,0) and estimate the value when this approximation is used to calculate f(0.1,0.1).Do not do the error approximation. Also, find the extreme values of the function f(x,y,z) = 8y²-4xz +16z - 35 on the surface 2x²+4y²+4z² = 64

The following data set provides information on the lottery sales, proceeds, and prizes by year in Iowa.

FY

Sales

Proceeds

Prizes

1992

$166,311,122

$45,678,558

$92,939,035

1993

$207,192,724

$56,092,638

$116,820,274

1994

$206,941,796

$56,654,308

$116,502,450

1995

$207,648,303

$58,159,175

$112,563,375

1996

$190,004,182

$51,337,907

$102,820,278

1997

$173,655,030

$43,282,909

$96,897,120

1998

$173,876,206

$42,947,928

$96,374,445

1999

$184,065,581

$45,782,809

$101,981,094

2000

$178,205,366

$44,769,519

$98,392,253

2001

$174,943,317

$44,250,798

$96,712,105

2002

$181,305,805

$48,165,186

$99,996,233

HelpCopy to ClipboardDownload CSV

Create a graph using the sales and year. What approximate range of sales would you expect for the year 2017?

Select the correct answer below:

Between 250 and 300 million dollars

Between 300 and 375 million dollars

Between 375 and 400 million dollars

Between 500 and 550 million dollars

Given triangle(ABC) with A-D-C, then BD < BA or BD < BC.
Prove that the set consisting of a circle and its interior is a convex set.

1) What is the best estimate for the distance covered between t=2 s and t=10 s by using Romberg integration (based on Trapezoidal rule)? Use three different h values of 2, 4 and 8.

t (s)	2	4	6	8	10
v (m/s)	0.166	0.55115	1.8299	6.0755	20.172

Describe the boundary lines for two- variable inequalities. Why are the boundary lines for two- variable inequalities with greater than and less represented by dotted lines? Provide examples.
First, define a boundary line and tell where it comes from. Then, describe what the boundary line can tell us about solutions to an inequality. You can also talk about how to know what part of a graph to shade. Finally , talk about the cases where we use each type of boundary line. ( solid and dotted/ dashed).
Real - life Relationship: If you have 100 $ available to buy party favors ( 3$ per bunch of balloons and 4 $ per bag of candy) than you can solve an inequality to find the possibilities . If x = # of bunches of balloons and y= number of bags of candy then we want to solve: 3x+ 4y<=100.
Some possible solutions are: no bunches of balloons and 25 bags of candy,20 bunches of balloons and 10 bags of candy. There are other possibilities!
Challenge: Imagine we have two boundary lines: one solid and one dashed. If they are not parallel is the point where they meet included in the solution? Why or why not?
If you are not sure, try an example, such as y < x + 1 and y < = 2x-4. Graph both boundary lines and find the point of intersection. Then , see if the coordinates satisfy both inequalities.

On 5/17/2020, a random sample of 1007 U.S. households finds that Trump has a 49% approval rating.

a) Use the 2SD method to find a 95% confidence interval estimate of the proportion of all U.S. households that approve of Trump on 5/17/2020. Show all work/steps to get the 2SD estimate. Round the margin of error to three decimal places. Work and Answer:

b) Use your answer from part (a) to fill in the red spaces below in order to write the results of the poll in these two notations:

According to the poll, on 5/17/2020, Trump has an approval rating of 49% ± _________%

According to the poll, on 5/17/2020, Trump’s approval rating was between ______% and ______%

c) If we were to use this same sample information to find a 90% confidence interval estimate instead of a 95% confidence interval estimate, then would our new 90% confidence interval be wider, or would it be narrower than the 95% estimate? Work and Answer:

solve using laPlace dy/dt+4y=40sin3t; y(0)=6 Please show all steps and write neat, thanks!

1. A tank initially contains 200 liters of saltwater, with a concentration of 2g/L salt. Saltwater with a concentration of 5g/L flows into the tank at 2L/min and the well-mixed solution flows out of the tank at the rate of 4L/min.

(a) Set up, but do NOT solve, the initial value problem whose solution will be the VOLUME OF LIQUID in the tank as a function of time

(b) Solve the IVP from the previous part and find the volume of liquid in the tank as a function of time.

(c) Set up, but do NOT solve, the initial value problem whose solution will be the MASS OF SALT in the tank as a function of time.

(d) Solve the IVP in part (c) and determine the mass of salt in the tank as a function of time (Show your work)