b) The circumference of a circular field is 220 m.
(i) Find its diameter and radius.
(ii) Find the cost of paving stones all over it at Rs 25 per sq. m.​

The present worth (PW) of each project is calculated based on the given cash flows and the firm's minimum attractive rate of return (MARR) of 10% per year.

To calculate the PW of each project, we discount the cash flows at the MARR of 10% per year. The PW for each project is determined as follows:

Project 1: EOY 0: -\(10,000 + (5,125 / (1 + 0.10)^1) + (5,125 / (1 + 0.10)^2) + (5,125 / (1 + 0.10)^3) = $10,682.13\)

Project 2: EOY 0: -\(8,500 + (4,450 / (1 + 0.10)^1) + (4,450 / (1 + 0.10)^2) + (4,450 / (1 + 0.10)^3) = $9,202.79\)

Project 3: EOY 0: \(11,000 + (5,400 / (1 + 0.10)^1) + (5,400 / (1 + 0.10)^2) + (5,400 / (1 + 0.10)^3) = $9,834.71\)

The project with the highest PW is recommended. In this case, Project 1 has the highest PW of $10,682.13, so it would be the recommended project.

The IRR for each project can be determined by finding the discount rate that makes the PW equal to zero. Using the cash flows provided, the IRR for each project can be calculated using a trial-and-error approach or financial software. Let's assume the IRRs are as follows:

Project 1: IRR ≈ 17.5%

Project 2: IRR ≈ 15.3%

Project 3: IRR ≈ 13.8%

The project with the highest PW may differ from the project with the largest IRR due to the timing and magnitude of cash flows. The PW takes into account the timing of cash flows and discounts them to the present value. It represents the total value created by the project over its lifetime. On the other hand, the IRR considers the rate of return that equates the present value of cash inflows to the initial investment. It represents the project's internal rate of return.

Therefore, a project with a higher PW indicates higher overall value, while a project with a larger IRR implies a higher rate of return. These measures can lead to different rankings depending on the cash flow patterns and the MARR.

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A 2x3x2 factorial design has three independent variables. What is a factorial design? A factorial design is an experimental design that studies the impact of two or more independent variables on a dependent variable.

The notation of a factorial design specifies how many independent variables are used and how many levels each independent variable has. In a 2x3x2 factorial design, there are three independent variables, with the first variable having two levels, the second variable having three levels, and the third variable having two levels.

The number of treatments or conditions required to create all feasible combinations of the independent variables is equal to the total number of cells in the design matrix, which can be computed as the product of the levels for each factor.

In this case, the number of cells would be 2x3x2=12.Therefore, a 2x3x2 factorial design has three independent variables and 12 treatment groups..

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Answer:

125.7 mm

Step-by-step explanation:

Circumference=πd=π·40≈125.66371 mm

Question: find the slope of the line that passes through these two points. (1,3) (4,6)

Solution:

By definition, the slope of a line is given by the following equation:

where (X1,Y1) and (X2,Y2) are points on the line. In our case, we can take the points:

(X1,Y1) = (1,3)

(X2,Y2) = (4,6)

and replace them into the slope equation:

then, we can conclude that the correct answer is:

After Putting the given values in the above formula, P(ECUFCUGC) = 1 – [0.5 + 0.37 + 0.43]P(ECUFCUGC) = 1 – 1.3P(ECUFCUGC) = -0.3x = P(ECUFCUGC) = 1 – [P(E) + P(F) + P(G)]x = 1 – [0.5 + 0.37 + 0.43]x = 1 – 1.3x = -0.3

Therefore, P(ECUFCUGC) = -0.3.

Given,

P(E) = 0.5P(F) = 0.37P(G) = 0.43P(ENF) = 0.24P(ENG) = 0.2P(FNG) = 0.22P(ENFNG) = 0.14Calculation:Using the formula, P(ENF) = P(E) + P(F) – P(ENF)0.24 = 0.5 + 0.37 – P(ENF)P(ENF) = 0.63 – 0.24P(ENF) = 0.39Similarly,P(ENG) = P(E) + P(G) – P(ENG)0.2 = 0.5 + 0.43 – P(ENG)P(ENG) = 0.93 – 0.2P(ENG) = 0.73

Also, P(FNG) = P(F) + P(G) – P(FNG)0.22 = 0.37 + 0.43 – P(FNG)P(FNG) = 0.58 – 0.22P(FNG) = 0.36Therefore,P(ENFN'G) = P(E) + P(F) + P(G) – P(ENF) – P(ENG) – P(FNG) + P(ENFNG)0.14 = 0.5 + 0.37 + 0.43 – 0.63 + 0.2 + 0.36 + P(ENFN'G)P(ENFN'G) = 0.57P(ECUFCUGC) = P(E') + P(F') + P(G')0.5 + 0.63 + 0.57 = 1.7P(ECUFCUGC) = 1 – 1.7P(ECUFCUGC) = -0.7x = P(ECUFCUGC) = -0.7As probability cannot be negative,

Therefore, P(ECUFCUGC) = 1 – [P(E) + P(F) + P(G)]

Putting the given values in the above formula, P(ECUFCUGC) = 1 – [0.5 + 0.37 + 0.43]P(ECUFCUGC) = 1 – 1.3P(ECUFCUGC) = -0.3x = P(ECUFCUGC) = 1 – [P(E) + P(F) + P(G)]x = 1 – [0.5 + 0.37 + 0.43]x = 1 – 1.3x = -0.3Therefore, P(ECUFCUGC) = -0.3.

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To determine if vector b is in the column space of matrix A, we need to check if there exists a solution to the equation Ax = b.

(a) Is b in col(A)?

We have matrix A and vector b as:

A = [1 -3; 20 6]

b = [2; 0]

To check if b is in col(A), we need to see if there exists a vector x such that Ax = b. We can solve this system of equations:

1x - 3y = 2

20x + 6y = 0

By solving this system, we find that there is no solution. Therefore, b is not in the column space of A.

(b) Set up and solve the normal equations to find the least-squares approximation to Ax = b.

To find the least-squares approximation, we can solve the normal equations:

A^T * A * x = A^T * b

where A^T is the transpose of A.

A^T = [1 20; -3 6]

A^T * A = [1 20; -3 6] * [1 -3; 20 6] = [401 -57; -57 405]

A^T * b = [1 20; -3 6] * [2; 0] = [2; -6]

Now, we can solve the normal equations:

[401 -57; -57 405] * x = [2; -6]

By solving this system of equations, we can find the least-squares solution x.

(c) Calculate the error associated with your approximation in part (b).

To calculate the error, we can subtract the approximated value Ax from the actual value b. The error vector e is given by:

e = b - Ax

Substituting the values:

e = [2; 0] - [1 -3; 20 6] * x

By evaluating this expression, we can find the error associated with the least-squares approximation.

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Answer:

In Mathematics, surds are the values in square root that cannot be further simplified into whole numbers or integers. Surds are irrational numbers. The examples of surds are √2, √3, √5, etc., as these values cannot be further simplified.

Step-by-step explanation:

The smallest distance of the line to the point is of:

5.36 units.

Suppose the line is defined as follows:

ax + by + c = 0.

The coordinates of the points are as follows:

(x0,y0).

Then the shortest distance of the point to the line is:

D = |a(x0) + b(y0) + c|/sqrt(a²+b²).

In this problem, the line goes through these two points:

(2/7, 3) and (-2,11).

The slope is given by the change in y divided by the change in x, hence:

m = (11 - 3)/(-2 -2/7) = -3.5.

Then:

y = -3.5x + b.

When x = -2, y = 11, hence the intercept is calculated as follows:

11 = -3.5(-2) + b

11 = 7 + b

b = 4.

Then the line is:

y = -3.5x + 4.

3.5x + y - 4 = 0. (standard format, a = 3.5, b = 1).

The coordinates of the point are as follows:

(x0,y0) = (-3,-5).

Then the shortest distance is:

D = |3.5(-3) + 1(-5) - 4|/sqrt(3.5²+1²).

D = 19.5/sqrt(3.5²+1²).

D = 5.36 units.

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Answer:

8

Step-by-step explanation:

\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)

Answer:

\(8b+56\)

Step-by-step explanation:

Given the following question:

\(8(b+7)\)

To rewrite any expression using the distributive property we have to multiply the number outside of the paratheses to the numbers/variables within the paratheses.

\(8(b+7)\)
\(8\times b=8b\)
\(7\times8=56\)
\(8b+56\)

Your answer is "8b + 56."

Hope this helps.

Answer:

\(\sqrt{59}\)

Step-by-step explanation:

7^2 is 49 and 8^2 is 64, which means the square root of any number between 49 and 64 (exclusive) will be in between 7 and 8, and it's also going to be irrational, because it's not a perfect square.

One number between 49 and 64 is 59, so \(\sqrt{59}\) is an irrational number between 7 and 8

The first polynomial has 2 incongruent roots modulo 13, and the second polynomial has 0 incongruent roots modulo 13.

To find the number of incongruent roots modulo 13 for the given polynomials, we will examine them separately.

For the polynomial \(x^2 + 3x + 2\), we can test each possible value of x (0 to 12) to check for roots modulo 13. After testing, we find that x=4 and x=9 are roots, as they satisfy the equation\((4^2 + 3*4 + 2)\) ≡ 0 (mod 13) and \((9^2 + 3*9 + 2)\) ≡ 0 (mod 13).

Therefore, there are 2 incongruent roots modulo 13 for this polynomial.

For the polynomial \(x^4 + x^2 + x + 1\), we again test each possible value of x (0 to 12) modulo 13. In this case, we find no values of x satisfying the equation\(x^4 + x^2 + x + 1\) ≡ 0 (mod 13). Thus, there are 0 incongruent roots modulo 13 for this polynomial.

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No, The relation is not a function A. Because two points with the same x value have different y values.

What does a math function mean?

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).

We know a relation is a function if it is one-to-one or many-to-one.

But a relation one to many implies one input corresponds to two different outputs is not a function.

From the graph the function two different outputs 4 and 6 correspond to the same input 7.

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The complete question is -

Is this relation a function? Justify your answer.

 A) No, because  two points with the same x- value have different y - values.

B) No,  because  two points with the same y- value have different x - values.

C) Yes, because every x and y - value is alone .

D) Yes, beacuse the number of x - values is the same as the number of y- values .

Jasper's early withdrawal reduced his future annuity payments by $16,906.31.

To help Jasper compute his future annuity payment,

First, we have to calculate the future value (FV) of his investment at age 60 if he had not made any early withdrawals using the formula:

FV = \(PV (1 + r/n)^{(n*t)}\)

where:

PV = present value (amount invested)

r = annual interest rate,

n = number of compounding periods per year

t = number of years.

Given:

PV = $34,000

r = 5.4% per year

n = 12 (monthly compounding)

t = 14 years (from age 46 to age 60)

Logging the values, we get:

FV = \($34,000 (1 + 0.054/12)^{(12*14)}\)

= \($34,000 (12.0045/12)^{168}\)

= \($34,000 (1.000375)^{168}\)

FV = $68,786.56

This is the amount he would have received at age 60 if he had not withdrawn early.

Next, we shall now estimate the surrender charge and IRS fee that Jasper has to pay for his early withdrawal of $9,200.

Surrender charge = 2.2% x $9,200 = $202.40

IRS fee = 10% x $9,200 = $920

So, the total amount that Jasper receives from his early withdrawal is:

Amount received = $9,200 - $202.40 - $920 = $8,077.60

To calculate the new FV Jasper's investment by adjusting the present value (PV).

Subtract the withdrawn amount and add back the surrender charge:

New PV = $34,000 - $8,077.60 + $202.40 = $26,125.80

So, the new future value can then be calculated using the same formula:

New FV = $\($26,125.80 (1 + 0.054/12)^{(12*12)}\)

New FV = $\($26,125.80 (1.0045)^{144}\)

New FV = $26,125.80 x 2.2424

New FV = $58,651.29

Thus, Jasper's early withdrawal reduced his future annuity payments by $68,786.56 - $51,880.25 which is $16,906.31.

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The true statements about g(x) = x2 - 4x + 3 and f(x) = x2 - 4x are

The functions are given as:

\(g(x) = x^2 - 4x + 3\)

\(f(x) =x^2 - 4x\)

Start by differentiating the function g(x)

g'(x) = 2x - 4

Set to 0

2x - 4 = 0

Add 4 to both sides

2x = 4

Divide by 2

x = 2 ----- this represents the axis of symmetry of function g(x)

Substitute x = 2 in \(g(x) = x^2 - 4x + 3\)

\(g(2) = 2^2 -4*2 + 3\)

g(2) = -1

This means that the vertex of the function g(x) is (2,-1)

Next, differentiate the function f(x)

f'(x) = 2x - 4

Set to 0

2x - 4 = 0

Add 4 to both sides

2x = 4

Divide by 2

x = 2 ----- this represents the axis of symmetry of function f(x) (same as g(x))

Substitute x = 2 in \(f(x) =x^2 - 4x\)

\(f(2) = 2^2 -4 * 2\)

f(2) = -4

This means that the vertex of the function f(x) is (2,-4)

By comparing the vertices (2,-4) and (2,-1).

We can see that (2,-4) is below (2,-1).

Hence, the true statements are (a) and (b)

Which statements about functions g(x) = x2 - 4x + 3 and f(x) = x2 - 4x are true? Select all that apply.

A. The vertex of the graph of function g is above the vertex of the graph of function f.

B. The graphs have the same axis of symmetry.

c. Function f has a maximum value and function g has a minimum value.​

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Answer:

Step-by-step explanation:

15/22 divided by 10/11 equals 3/4 calculated by inverting the second fraction and multiply this fraction with first fraction.

To divide fractions 15/22 divided by 10/11.

Invert the second fraction 10/11.

To invert a fraction, simply swap the numerator and the denominator.

10/11 becomes 11/10.

Multiply the first fraction by the inverted second fraction:

(15/22) × (11/10)

= (15 × 11) / (22 × 10)

= 165 / 220.

The greatest common divisor (GCD) of 165 and 220 is 55, so we can simplify the fraction by dividing both the numerator and the denominator by 55:

165 / 220

= (165 ÷ 55) / (220 ÷ 55)

= 3/4.

So, 15/22 divided by 10/11 is equal to 3/4.

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The corresponding equation is 4q + 3p = 22.

What is the slope of a line ?

The ratio of the change in the y coordinate to the change in the x coordinate is known as a line's b in mathematics.

Y and X, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate. Locate two locations along the chosen line and find their coordinates.

Find the y-coordinate difference between these two places (rise). Find the difference between the x-coordinates of these two points (run). Subtract the difference in y-coordinates from the difference in x-coordinates (rise/run or slope).

The slope is defined as the relationship between the rise, or vertical change, between two points and the change, or horizontal change, between the same two points and can be represented as an equation.

Given that, coordinates are (p, 1/2) and (-8, q), slope is 3/4.

m = (y2 - y1)/(x2 - x1)

34 = (q - 1/2)/-8 - p

-24 - 3p = 4q - 2

4q + 3p = 22

The corresponding equation is 4q + 3p = 22.

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Let's define the next variable:

x: the original second prize (in tickets)

The first time, she won 50 tickets. The second time, she won 4 times the number of tickets of the original second prize, that is, 4x. Altogether she won 200 tickets. That is,

50 + 4x = 200

50 is adding on the left, then it will subtract on the right

4x = 200 - 50

4x = 150

4 is multiplying on the left, then it will divide on the right

x = 150/4

x = 37.5

The original second prize was 37.5 tickets

There are 12 months.

3725/12 = 310.

310 per month was lost.

Heart/brainliest would help me reach Genius!

Answer:

Step-by-step explanation:

we know that there are 12 months in a year

Jared lost 3725 in 12 months

we want to find out how much he lost in 1 month

divide by 12

we get

310.416666667

this is $ 310.42 rounded up

Answer:

2,000 D)

Step-by-step explanation:

The functions P models the population of Greenleaf t years after 2000 is P(t) = -1.6t + 4034, the correct option is D.

We are given that;

Year 2000 2010  population 862 846

Now,

To find the linear function from two points, you can use the slope-intercept form of the equation, which is y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, you can use the formula

\($m = \frac{y_2 - y_1}{x_2 - x_1}$\)

where \($(x_1, y_1) and (x_2, y_2)$\) are the given points.

To find the y-intercept, you can plug in one of the points and the slope into the equation and solve for b.

(2000, 862) and (2010, 846).

Using the formula for slope, we get:

\($m = \frac{846 - 862}{2010 - 2000} = \frac{-16}{10} = -1.6$\)

Using the point (2000, 862) and the slope -1.6, we get:

862 = -1.6(2000) + b

Solving for b, we get:

b = 862 + 1.6(2000) = 4034

Therefore, by the linear function answer will be P(t) = -1.6t + 4034.

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Answer:

65 degrees

Step-by-step explanation:

Answer:

1. obtuse angle 105 degrees

2. acute angle  60 degrees

Step-by-step explanation:

Answer: 20inch

Step-by-step explanation:

Using the Pythagoras theorem:-

25^2 = 15^2 + x^2    where x = the width of the screen.

625 = 225 + x^2

x = √(625 - 225) = √400

= =  20 ins

Answer:

D

Step-by-step explanation:

It compares two values.

Hope this helps!

Answer:

D because it have asked the question

The value of the function is f(5)=32.

What is function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here the given function is,

a(x)=5\(\vert x-10\vert\) +7

Now take a(x) as f(x) then,

=> f(x)=5\(\vert x-10\vert\) +7

Put x=5  into f(x) then,

=>  f(5) =5\(\vert5-10\vert+7\)

=> f(5) =\(5\vert-5\vert+7\)

=> f(5) = 5.5+7

=> f(5)=25+7 =32.

Hence the value of the function is f(5)=32.

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The degrees of freedom in a regression model is 2 if the model that has 10 observations and 7 independent variables.

The amount of rows of training data used to fit the model equals the degrees of freedom.

Total observation = 10

Number of independent variables = 7

Degree of freedom for regression = 10 – 7 - 1

= 2

Thus, the degrees of freedom in a regression model is 2 if the model that has 10 observations and 7 independent variables.

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Answer:

Purplemath

Recall that negative exponents indicates that we need to move the base to the other side of the fraction line.

(The "1's" in the simplifications above are for clarity's sake, in case it's been a while since you last worked with negative powers. One doesn't usually include them in one's work.)

In the context of simplifying with exponents, negative exponents can create extra steps in the simplification process.

Step-by-step explanation:

Answer:

b = 16

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the angles and equate to 180

b + 15 + 8b - 18 + 39 = 180

9b + 36 = 180 ( subtract 36 from both sides )

9b = 144 ( divide both sides by 9 )

b = 16