making the assumption of no compounding interest, suppose you purchase a perpetuity bond from sense/net corporation for $3,000 with an annual coupon rate of 3% . specify all answers to the nearest dollar, and assume a discount rate equal to that of the current interest rate.

Answer:

7

Step-by-step explanation:

Answer:

To find ab you need to subtract 140 degrees from 180 degrees

That should equal 40 degrees

Step-by-step explanation:

Answer:

the answer to the question is 40

Answer:

44 bro

Step-by-step explanation:

The percentage of representatives staying at least two nights rented a car is 44%.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

So the percentage actually means a part per 100.

Percentage is usually denoted by the symbol '%'.

Given is a two way table.

From the table, the number of representatives staying at least 2 nights rented a car is 11.

Total number of representatives staying at least two nights = 14 + 11 = 25

Percentage = (11 / 25) × 100

                    = 0.44 × 100

                    = 44%

Hence the percentage for the required number is 44%.

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Answer: B

Step-by-step explanation:

I did this before and got a 100%.

Answer:

manly Scorpio track usually residual Flo 0 taken

Answer:

True

Step-by-step explanation:

Doing the math, the average person with the average stride living until 80 will walk a distance of around 110,000 miles. Which is the equivalent of walking about 5 times around the Earth, right on the equator.

Answer:

True

Step-by-step explanation:

Answer:

9.5; 72˚

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

two negative numbers multiplied equals a positive number

The area of the shaded triangle BDE is 4 cm²

The area is the amount of space within the perimeter of a 2D shape.

area of ΔADE= / *b *h

=1/2 * 8 *5

= 20 cm²

area of ΔBCD

= 26-20

= 6 cm²

area of CDE

= 1/2* 5 * 4

= 10 cm²

Area of shaded triangle,

=10-6

=4 cm²

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Answer:

4m = 56

Step-by-step explanation:

4 * m = 56

4m = 56

4/4m = 56/4

m = 14

Answer:

0-4 up to 3 5-9 up to 1 10-14 up to 4 15-19 up to 1 20-24 up to 3

Step-by-step explanation:

The median would be 22:

Step-by-step explanation: The median is the number that is in the middle

Simply defined, the median is the number right in the middle of a set.

But before I get down to finding the median, I will order the numbers from least to greatest:

15, 17, 19, 20, 21, 22, 23

Now, the middle number is 20. So that's the median.

As for the range, it's the difference between the largest number and the smallest one:

Range = Greatest number - Smallest number

           = 23 - 15

           = 6

In summary, the median, the number in the middle, is 20, and the range, the difference between the largest number and the smallest one, is 6.

a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

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The global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint is correct. Statement C.

The critical value is the value of x for which the double derivative of the function f(x) becomes zero.

When double derivative becomes zero, the graph of the function is neither increasing nor decreasing and hence, the the function attains either

a maxima or a minima.

Hence, he global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint.

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Based on the trend of the increase in children born out of wedlock, if this trend keeps increasing, the year with 67% of babies born out of wedlock will be 2055 .

In 1990, the 28% of children were born out of wedlock and this trend was increasing by 0.6% per year.

If the trend continues, the number of years till 67% of children born out of wedlock will be:

= (67%  - 28%) / 0.6%

= 65 years

The year will be:

= 1990 + 65

= 2055

The first part of the question is:

According to the National Center for Health Statistics, in 1990, 28% of babies in the United States were born to parents who were not married. Throughout the 1990s, this percentage increased by approximately 0.6 per year.

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Answer:

A' (2,-3)

B' (5,-5)

C' (5,-2)

D' (7,-3)

Step-by-step explanation:

I used desmos graphing calculator to help me solve

Answer: The answers would be A= 2,-3  B= 5,-5   C=-5-2  and D= 7,-3

#10. In order to find a ratio, all we need to do is set up a simple equation and then cross-multiply!

I'll show you !

In this case, we'll take the already established ration (14 : 8 ) and find the equivalent ratio where 7 is in place of 14 (7: x)

x will be the other table value we are looking for!

Now let's set up the equation and cross-multiply!

\(\frac{14}{8} = \frac{7}{x}\)

cross multiply 14 and x, then 8 and 7

We get:  14x = 56

solve to find x!

x = 56/14

x = 4 blankets

Now let's use the ratio 7: 4 to find what goes with 16 in the table!

\(\frac{7}{4} = \frac{x}{16}\)

4x = 112

x = 112/4

x = 28 towels

_________________________________________________-

#11. : Using the same method, I'll fill in the values of the table on #11

16 forks, 10 spoons

8 forks, 5 spoons,

48 forks, 30 spoons

_____________________________________________

#12. If the neighbor pays you $17 for every 2 hours of work, we need to find how many times 2 hours goes in 8 hours of work

We do this by dividing

8/2 = 4 times

2 hours of work goes into 8, 4 times!

Now we multiply 4 by $17 to find how much your neighbor owes you!

$17 × 4 = $68

Your neighbor owes you $68 !!!

B

Step-by-step explanation:

you have to divide the numbers to see if they equivalent.

Answer:

Step-by-step explanation:

\(A=P(1+r)^t\\ d=12000((1.0475)^5-(1.05)^4\\ \\ d=\$ 547.84\)

Answer:

Step-by-step explanation:

P(-2,-1) and Q(4,3)

average of x-coordinates = (-2+4)/2 = 1

average of y-coordinates = (-1+3)/2 = 1

midpoint of PQ: (1,1)

distance between midpoint and Q = √((4-1)²+(3-1)²) = √13

(x-1)² + (y-1)² = 13

The equation of the circle is \((x - 1)^{2} + (y - 1)^{2} = \frac{52}{4}\)

A circle is a shape consisting of all points in a plane that are at a given distance from a given point (the Centre) Equivalently .

Equation of circle

The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle.

The equation of circle represents all the points that lie on the circumference of the circle .

The standard equation of a circle with center at \((h , k )\) and radius r is

  \((x - h)^{2} + (y - k)^{2} = r^{2}\)

The distance formula in coordinate geometry is used to calculate the distance between two given points.

The formula says the distance between two points (\(x_{1} ,y_{1}\)), and (\(x_{2} , y_{2}\))

\(Distance(D) = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} }\)

The Midpoint Formula:

The midpoint of two ends coordinates points,  (\(x_{1} ,y_{1}\)), and (\(x_{2} , y_{2}\)) is the point M can be found by using:

\(M = \frac{x_{1} + x_{2}}{2}, \ \ \frac{y_{1} + y_{2}}{2}\)

According to the question

P = (-2,-1) and Q = (4,3) are the

endpoints of the diameter of a circle

Therefore, distance between point P and Q which is diameter of circle is

 \(Distance(D) = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} }\)

P(-2,-1) =  (\(x_{1} ,y_{1}\))

Q (4,3) =  (\(x_{2} , y_{2}\))

Now,

Diameter of circle = \(\sqrt{(4 - (-2) )^{2} + (3 - (-1) )^{2} }\)

                             = \(\sqrt{(6 )^{2} + (4 )^{2} }\)

                             = \(\sqrt{(36 + 16) }\)

                             = \(\sqrt{52}\)

As , radius  =  \(\frac{diameter }{2}\)

       radius (r) =  \(\frac{\sqrt{52}}{2}\)          

As we know The center of the circle separates the diameter into two equal segments called radii and radii are equal in a circle .

i.e mid point of coordinates of diameter are coordinates of circle .

\(M = \frac{x_{1} + x_{2}}{2}, \ \ \frac{y_{1} + y_{2}}{2}\)

\(Centre of circle (h,k) = \frac{x_{1} + x_{2}}{2}, \ \ \frac{y_{1} + y_{2}}{2}\)

\(h = \frac{x_{1} + x_{2}}{2}, \ \ k = \frac{y_{1} + y_{2}}{2}\)

\(h = \frac{ -2 + 4}{2}, \ \ k = \frac{-1 + 3}{2}\)

\(h = 1, \ \ k = 1\)

Now , substitute the value in the equation of circle

\((x - h)^{2} + (y - k)^{2} = r^{2}\)

\((x - 1)^{2} + (y - 1)^{2} = \frac{52}{4}\)

Hence, the equation of the circle is \((x - 1)^{2} + (y - 1)^{2} = \frac{52}{4}\)

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The slope and the y-intercept of the line y = 4x + 5 are given as follows:

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

The function for this problem is given as follows:

y = 4x + 5.

Hence the slope and the intercept are given as follows:

The problem asks for the slope and the intercept of y = 4x + 5.

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There are 0.5 centimeters in 5 milimeters

Here, we want to calculate the number of centimeters in 5 milimeters

For convenience sake, we write centimeters as cm and millimeters as mm

10 mm = 1 cm

5 mm = x cm

Mathematically;

x * 10 = 5 * 1

10x = 5

x = 5/10

x = 0.5 cm

For a curve to be a density curve, it must meet certain conditions such as it should be non-negative, and the area under the curve should equal 1. Furthermore, the curve should be continuous and smooth, and there should be no values outside the range of the data.

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The time needed to pay the compound interest of Rs 6,305 is given as follows:

3 years.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

The parameters for this problem are given as follows:

P = 40000, A(t) = 40000 + 6305 = 46305, n = 1, r = 0.05.

Hence the time is obtained as follows:

\(40000(1.05)^t = 46305\)

\((1.05)^t = \frac{46305}{40000}\)

\(t = \log{\left(\frac{46305}{40000}\right)}{\log{1.05}}\)

t = 3 years.

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The inequality tha calculates the possible values of x is x < 2

From the question, we have the following parameters that can be used in our computation:

The figure

Where, we have

3x + 2 < 10

And, we have

2x + 6 < 10

Evaluate the expressions

So, we have

3x < 8 and 2x < 4

Evaluate

x < 8/3 and x < 2

Hence, the inequality tha calculates x is x < 2

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The least common multiple (LCM) of numbers a and b is the smallest positive integer that is divisible by both a and b.

To find the LCM of 20 and 88, proceed as follows:

* List all prime factors of each number:

20 = 2 x 2 x 5

88 = 2 x 2 x 2 x 11

* Multiply all prime numbers found as many times as they occur most often.

LCM = 2 x 2 x 2 x 5 x 11

LCM = 440