Problem 23. Answer using Cauchy's Theorem. Given that C is a simple closed path, evaluate each of the following integrals. It is necessary to consider several cases. THOUGH APPLICABLE, DO NOT APPLY THE RESIDUE THEOREM IN THIS EXERCISE. i) ∫C dz/z^2 +4 ii) ∫C dz/z(z^2–1) iii) ∫C c^2/z^2 +9 . dz

Answer:

the answer will be 60  

Step-by-step explanation to find x and y's value:

x = 180-2(60)

now, we will do the same method to find y's value

y = 180-120 which will be 60

i hope this helps :)

In linear equation,  { 2x + 3y = 7.20 ,   { 4x + 2y = 8.80 the price per pound for oranges.

 What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Product B performed worse in the study because 32% failed to get relief with this product, whereas only 28% failed to get relief with Product A.

Working through this, the percentage who failed to find relief from product A is (25 - 18) / 25 = 28%. Doing the same type of calculation for product B, we can determine the percentage who failed to find relief as (50 - 34) / 50 = 32%. The description statement asks for which offered less relief, which we can find using the less than operator:

28% < 32%

Product A offered relief to all but 28% of the people, while product B offered relief to all but 32% of the people. Given that fewer people failed to find relief on product 28%, we can argue that more people did find relief on product A.

Given that the tests are both on multiples of 25 people, we can also see the percentages by multiplying the numerators and denominators to bring both to a scale of 100:

7/25 * 4/4 = 28% of product A users failed to find relief.

16/50 * 2/2 = 32% of product B users failed to find relief.

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16) Yes because each probability is between 0 and 1 and sum of all probability equals 1 so option A . 17) (D)= 0.44  18)(C)=1.7            
    
A) yes because each probability is between 0 and 1 and sum of all probability equals 1.            

:   ( σ <p(x)<1 and  Σ p(x)=1)

17)  probability that random selected passenger car an highway contain 2 or more people is 0.44

(P(x≥ 2)=p(x=2)+p(x=3)+p(x=4)+p(x=5)
P(x≥ 2=0.44
OR P(x≥ 2)=1-p(x≥ 2)=1-p(x=1)=1-0.56
p(x≥ 2)=0.44

18) Mean number of people in passenger cars are

E(X)=Σxp(x)=(1*0.56)+(2*0.28)+(3*0.08)+(4*0.06)+(5*0.02)
E(X)=1.7                        


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Answer:

61°

Step-by-step explanation:

B = 180°-58°-61°

= 61°

Answer:

\(\displaystyle \frac{dy}{dx}\Big|_{(1, 1)}=0\)

Step-by-step explanation:

We are given the equation:

\((x^2+y^2)^2=4x^2y\)

And we want to find the slope of the tangent line at the point (1,1).

Recall that the slope of the tangent line to a point of a function is given by the function's derivative.  

Thus, find the derivative of the equation. Take the derivative of both sides with respect to x:

\(\displaystyle \frac{d}{dx}\left[(x^2+y^2)^2\right]=\frac{d}{dx}\left[4x^2y\right]\)

Let's do each side individually.

Left:

We can use the chain rule:

\((u(v(x))'=u'(v(x))\cdot v'(x)\)

Let v(x) be x² + y² and u(x) is x². Thus, u'(x) is 2x. Therefore:

\(\displaystyle \frac{d}{dx}\left[(x^2+y^2)^2\right]=2\left(x^2+y^2\right)\left(\frac{d}{dx}\left[x^2+y^2\right]\right)\)

Differentiate:

\(\displaystyle \frac{d}{dx}[(x^2+y^2)^2]=2(x^2+y^2)\left(2x+2y\frac{dy}{dx}\right)\)

Factor. Therefore, our left side is:

\(\displaystyle 4(x^2+y^2)\left(x+y\frac{dy}{dx}\right)\)

Right:

We have:

\(\displaystyle \frac{d}{dx}\left[4x^2y\right]\)

We can move the constant multiple outside:

\(\displaystyle =4\frac{d}{dx}\left[x^2y\right]\)

We will use the Product Rule:

\(\displaystyle =4\left(\frac{d}{dx}\left[x^2\right]y+x^2\frac{d}{dx}\left[y\right]\right)\)

Differentiate:

\(\displaystyle =4\left(2xy+x^2\frac{dy}{dx}\right)\)

Therefore, our entire equation is:

\(\displaystyle 4(x^2+y^2)\left(x+y\frac{dy}{dx}\right)=4\left(2xy+x^2\frac{dy}{dx}\right)\)

To find the derivative at (1,1), substitute and evaluate dy/dx when x = 1 and y = 1. Hence:

\(\displaystyle 4((1)^2+(1)^2)\left((1)+(1)\frac{dy}{dx}\right)=4\left(2(1)(1)+(1)^2\frac{dy}{dx}\right)\)

Evaluate:

\(\displaystyle 4((1)+(1))\left(1+\frac{dy}{dx}\right)=4\left(2+\frac{dy}{dx}\right)\)

Further simplify:

\(\displaystyle 8\left(1+\frac{dy}{dx}\right)=8+4\frac{dy}{dx}\)

Distribute:

\(\displaystyle 8+8\frac{dy}{dx}=8+4\frac{dy}{dx}\)

Solve for dy/dx:

\(\displaystyle 4\frac{dy}{dx}=0\Rightarrow \frac{dy}{dx}=0\)

Therefore, the slope of the tangent line at the point (1, 1) is 0.

The length and the widths are 420.031 yards and 0.031 yards if a rectangular parking lot has a length that is 420 yards greater than the width.

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

Let L be the length and W be the width of the rectangle.

From the question:

L = 420 + W (based on the data given in the question)

LW  = 13

(420 + W)W = 13

W² + 420W - 13 = 0

After solving the above quadratic equation:

W = 0.031, W = -420.03 (width cannot be negative)

W = 0.031 yards (which is not practical but from a mathematical point of view it can be considered)

L = 420 + 0.031 = 420.031 yards

Thus, the length and the widths are 420.031 yards and 0.031 yards if a rectangular parking lot has a length that is 420 yards greater than the width.

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A quadrilateral whose diagonals are parallel is referred to as a parallelogram. A parallelogram has equal angles on each side. A parallelogram has equal lengths on its opposing sides.

A parallelogram's diagonals cut through one another. Show: If a quadrilateral's one set of opposing sides is congruent and parallel, the quadrilateral is a parallelogram.

ABCD is a parallelogram if — BC — AD and — BC — AD. A quadrilateral becomes a parallelogram if its diagonals are bisected by one another. Having four sides in two dimensions, a quadrilateral. Square, rectangle, rhombus, trapezium, parallelogram, and kite are all examples of 2D shapes that are quadrilaterals.

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Statistics is a branch of mathematics that involves collecting, analyzing, and interpreting data. According to Arthur Getis and Judith Getis, statistics is "the science of collecting, analyzing, and interpreting numerical data from samples to make inferences about populations" (Getis & Getis, 2019, p. 3).

Quantitative data refers to numerical data that can be measured and analyzed statistically. Examples of quantitative data include age, income, weight, and sales figures. Qualitative data, on the other hand, refers to non-numerical data that cannot be easily measured or analyzed statistically. Examples of qualitative data include opinions, attitudes, and beliefs.

One peer-reviewed study by Howard et al. (2017) compared the effectiveness of quantitative and qualitative research methods for evaluating the impact of educational programs on student learning outcomes. The study found that both quantitative and qualitative methods were useful in evaluating the impact of educational programs, but that each method had its strengths and weaknesses. Quantitative methods were more effective at measuring objective outcomes, such as test scores, while qualitative methods were better at capturing subjective experiences, such as student perceptions of the program.

Another study by Langer and Beckman (2005) examined the use of qualitative data in market research. The study found that qualitative data can provide valuable insights into consumer behavior and preferences that may not be captured by quantitative data alone.

Tables and charts are commonly used to represent quantitative and qualitative data. For quantitative data, tables and charts can be used to display frequency distributions, histograms, scatter plots, and other types of data. For qualitative data, tables and charts can be used to display themes, patterns, and other qualitative information.

The levels of data measurement refer to the different types of data that can be collected and analyzed. The four levels of data measurement are nominal, ordinal, interval, and ratio. Nominal data refers to data that is classified into categories, such as gender or race. Ordinal data refers to data that is ordered, such as the ranking of college football teams. Interval data refers to data that is measured on a scale with equal intervals, such as temperature in Celsius or Fahrenheit. Ratio data refers to data that has a true zero point, such as weight or height.

Statistics plays a critical role in business decision-making. Business managers use statistics to analyze sales data, identify trends, and forecast future demand for products and services. Statistics can also be used to evaluate the effectiveness of marketing campaigns, assess the risk of investment opportunities, and optimize supply chain management.

One business research question where statistics can be used is: "What is the relationship between employee satisfaction and customer satisfaction?" In a study by Meyer and Allen (1997), statistics were used to analyze survey data from employees and customers of a hotel chain. The study found that there was a positive correlation between employee satisfaction and customer satisfaction, suggesting that improving employee satisfaction could lead to higher customer satisfaction.

Another business research question where statistics can be used is: "What is the impact of social media on consumer purchasing behavior?" In a study by Chen and Xie (2011), statistics were used to analyze survey data from consumers about their social media use and purchasing behavior. The study found that social media use had a significant impact on consumer purchasing behavior, particularly for products that were socially visible, such as clothing and accessories.

In conclusion, statistics is a powerful tool that can be used to collect, analyze, and interpret data in a wide range of business settings. Business managers can use statistics to gain valuable insights into customer behavior, market trends, and other important factors that can affect business performance. By understanding the levels of data measurement, evaluating tables and charts, and using appropriate statistical methods, business managers can make informed decisions that lead to greater success.

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Hello!!

(4c+3)(3c−3)

=(4c+3)(3c+−3)

=(4c)(3c)+(4c)(−3)+(3)(3c)+(3)(−3)

=12c2−12c+9c−9

=12c2−3c−9

Answer^

Hope this helps ((brainliest!!!))

Answer:

C

Step-by-step explanation:

multiply the 1st equation by -3

The solution set of the given homogeneous system in parametric vector form is (x1,x2,x3)=(s,-2,-5)

Parametric vector form:

If there are m-free variables in the homogeneous equation, the solution set can be expressed as the span of m vectors:

x = s1v1 + s2v2 + ··· + sm vm. This is called a parametric equation or a parametric vector form of the solution.

A common parametric vector form uses the free variables as the parameters s1 through sm

Given is a system of equations

We are to solve them in parametric form.

x1 + 3x2 + x3 = 0 --------(1)

-4x1 + 9x2 + 2x3 = 0 ---------(2)

-3x2 - 6x3 = 0--------(3)

From equation(3)

-3x2=6x3

x2=-2x3

substitute in equation(1) and equation(2)

x1+3(-2x3)+x3=0

x1-6x3+x3=0

x1-5x3=0

x1=5x3

So the solution in parametric form is (x1,x2,x3) = (s,-2,5) for all real values.

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The point A(0,-2) is on the line y-3x=-2. So, the answer is A(0,-2).

Given the line equation

y-3x=-2,

we are to find the point among A(0,-2), B(-3,1) and C(1,1) which lies on this line.

To check if a point lies on a line, we substitute the values of x and y into the equation of the line. If the equation holds true, then the point lies on the line. If it doesn't, the point does not lie on the line.

Let us check for point A(0,-2)

Whether A(0,-2) lies on

y - 3x = -2

is determined by whether or not the following equation holds true:

-2 - 3(0) = -2LHS = -2RHS = -2

Therefore, point A(0,-2) is on the line

y-3x=-2.

So, the answer is A(0,-2).

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Answer:

Below

Step-by-step explanation:

The question states "round to nearest hundredth"   ....you rounded  to nearest 10th.....   I believe you can now find the correct answer...

in fraction form it is 13  11/13

Answer:

x=31

Step-by-step explanation:

-3x-3(19)=3-5x+2

2x-57=5

2x=62

x=31

Answer:

12.255

Step-by-step explanation:

Answer:

\(3p,3q,3r\)

Step-by-step explanation:

Dilation is not a rigid transformation, for it is not an isometry, hence a dilation produces similar and not congruent figures.

If we have to dilate a \(\bigtriangleup ABC\) with  scale factor of 3, with this centered at its origin,with its sides p, q and r. We'll have \(\bigtriangleup A'B'C'\) having 3p,3q, 3r.

The slope in a Dilation is considered carefully when it is not dilated at its center. Well it is. And we're not dilating line segments, then it'll look like this (check below)

\(D_3(x,y) A'=3A, B'=3B, C'=3C\\\)

So its line segments will be thrice the value of its original triangle as well.

Answer:

1.2 and 3q

Step-by-step explanation:

Answer:

B,C

Step-by-step explanation:

The sum of B is 1

The sum of C is -1/2

Let's try each option.

Option A:

-3 + 5 + (-1) = 2 + (-1) = 1

FALSE

Option B:

5 + (-8) + 4 = -3 + 4 = 1

TRUE

Option C:

-19/2 + 9 = -9.5 + 9 = -0.5

TRUE

Option D:

-17 + 36/2 = -17 + 18 = -1

FALSE

So, the correct answers are B and C

Best of Luck!

The triangle PSQ is an isosceles triangle, and the area of the triangle PSQ is 1360.62 square units

The given parameters are:

PS = SQ

Perimeter,  P = 50

SQ - PQ = 1

The perimeter is calculated using:

PS + SQ + PQ = 50

This gives

2SQ + PQ = 50

Make SQ the subject in SQ - PQ = 1

SQ = 1 + PQ

So, the equation 2SQ + PQ = 50 becomes

2(1 + PQ) + PQ = 50

Expand

2 + 2PQ + PQ = 50

Evaluate like terms

3PQ = 48

Divide by 3

PQ = 16

Substitute PQ = 16 in SQ - PQ = 1

SQ - 16 = 1

So:

SQ = 17

The area is then calculated using:

A = √[P * (P - PS) * (P - SQ) * (P - PQ)]

This gives

A = √[50 * (50 - 17) * (50 - 17) * (50 - 16)]

Evaluate

A = 1360.62

Hence, the area of the triangle PSQ is 1360.62 square units

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Answer:

a=28

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

a−6=22

Step 2: Add 6 to both sides.

a−6+6=22+6

a=28

The smallest positive integer n so that,

$$\renewcommand{\arraystretch}{1.5} \begin{pmatrix} -\frac{\sqrt{2}}{2} \frac{1}{n} \\ \frac{\sqrt{2}}{2} \frac{1}{n} \end{pmatrix}$$is a column matrix that contains integers,

we can write it as follows. $$\begin{pmatrix} -\frac{\sqrt{2}}{2} \frac{1}{n} \\ \frac{\sqrt{2}}{2} \frac{1}{n} \end{pmatrix} = \begin{pmatrix} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{pmatrix} \frac{1}{n}.$$Since n has to be an integer, we have to find the smallest positive integer n for which the right-hand side is a column matrix containing integers. Since the left-hand side has a factor of 1/n, we can see that the smallest value of n must be a divisor of the denominator of the left-hand side. The denominator of the left-hand side is $\sqrt{2}/2$. If we multiply this by 100, we get 70.710678.

Therefore, the smallest positive integer n that satisfies the equation is the smallest divisor of 70.710678. This is 2, and it gives us the column matrix $$\begin{pmatrix} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{pmatrix}.$$Therefore, the smallest positive integer n is 2.

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The equation can be written as 6 + (-6y) = -6y - 1 + (7).

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

The given is an equation with missing parts.

The left hand side of the equation does not contain a term with variable, but the right hand side contains it.

Adding that term in the left hand side, we get, 6 + (-6y) in the left hand side.

So the right hand side must be equal.

So the expression in the right hand side is -6y - 1 + (7).

Hence the expressions are 6 + (-6y) on the left hand side and  -6y - 1 + (7) on the right hand side.

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Answer:

4x-7=5

Step-by-step explanation: If you take 4(3) you get 12 -7 =5

Answer:

it's a fraction.

Answer:

A=2

Step-by-step explanation:

Answer:

A=2(wl+hl+hw)

This is the formula but what is the prism you want the area for.

\(y=mx+b\)

where m is slope

and b is y-intercept

9514 1404 393

Answer:

  168

Step-by-step explanation:

Below are shown the 7 different kinds of arrangements that can be made. Each of these can be permuted into 24 different arrangements by assigning colors in a different order than the one used here:

  {1, 2, 3, 4} ⇒ {green, blue, red, yellow}

Then the total number of possible correct colorings is 7·24 = 168.

__

These colorings were found using a computer program that identified all 168 viable colorings, then eliminated permutations. It started by identifying ways to color 2 rows, then adding rows based on that.

_____

You'll notice that the last on the attached list most closely matches the one in the problem statement.