Last year janet purchased a $1,000 face value corporate bond with an 8% annual coupon rate and a 15-year maturity. At the time of the purchase, it had an expected yield to maturity of 10. 45%. If janet sold the bond today for $820. 17, what rate of return would she have earned for the past year?.

The amount owed by the debtor is $10865

The given parameters about the compound interest are

Principal Amount, P = $5300

Interest Rate, R = 8%

Time, t = 6 years

To calculate the amount owed, we make use of the following formula

A = P + CI

Where

Compound interest, CI = P(1 + R)^t - P

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this question, the formula is given as

A = P(1 + r/n)^nt

Where

n = 12, i.e compounded monthly

Substitute the known values in the above equation

A = 5300 * (1 + 8%/12)^(6*12)

Express 8% as decimal

A = 5300 * (1 + 0.08/12)^(6*12)

Evaluate the sum

A = 5300 * (1.01)^(6*12)

Evaluate the exponent

A = 5300 * 2.05

Evaluate the product

A = 10865

Hence, the value of the amount after 6 years is $10865

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A) The second equation is 2x - 4y +20=0, this system has no solutions.

B) The second equation is  x-2y-11=0, this system has infinite number of solutions.

An equation is a mathematical formula that expresses the equality of two expressions by connecting them with the equals sign =. The term equation and its cognates in various languages may have subtle changes in meaning.

Solving an equation with variables includes determining which variables' values result in equality. The variables for which the equation must be solved are also known as unknowns, and the unknown values that satisfy the equality are known as equation solutions. There are two sorts of equations: identities and conditional equations. An identity holds true for all variable values.

Given equation is,

2x - 4y = 22

A) Let the second equation be

2x - 4y +20=0

∴a₁/a₂=1

b₁/b₂=1

c₁/c₂=-11/10

Therefore, a₁/a₂=b₁/b₂≠c₁/c₂

Hence, the system has no solution.

B) Let the second equation be,

x-2y-11-0

Therefore,  a₁/a₂=b₁/b₂=c₁/c₂=2/1

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The values of x, y and z are 74°, 37° and 17° respectively

What is Angles?

An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.

Given,

x°, (4z + 6)°, 2y° and 106°

Lets solve,

x° and 106°

From the co-interior  angle

x + y = 180°

x° + 106° = 180°

x = 180 - 106

x = 74°

by alternate exterior angle

x = 2y

Since we know about the value of x

we can write it as

74 = 2y

y = 74/2

y = 37°

Now by alternate interior angles

(4z + 6) = x

(4z + 6) = 74

4z = 74 - 6

4z = 68

z = 68/4

z = 17°

Hence, Value of x, y and z is 74°, 37° and 17° respectively

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Certain figures are explained in both cases in perimeter as well as area,

to illustrate the examples of geometrical figures.

Geometrical shapes are  shapes that illustrates the shapes of different items. some figures have two dimensions, while others have three. Only the x and y axis are used for two-dimensional structure, whereas the x, y, and z axes are used for three-dimensional structures. The height of the object is displayed in the z-axis.

In Mathematics area and perimeter of certain figures are known,

Rectangle

Perimeter of a Rectangle = 2(a+b)

Area of Rectangle = a × b

Square

Perimeter of a Square = 4a

Area of a Square = a²

Triangle

Perimeter of a triangle = a + b +c , where a, b and c are the three different sides of the triangle.

Area of a triangle = 1/2 b × h; where b is the base and h is the height of the triangle.

Circle

Circumference of Circle = 2πr

Area of Circle = πr²

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The area of the rectangle 81 square units and the perimeter of the rectangle is 36 units.

In this question, we have been given the rectangle with coordinates (3,7), (3,-2), (-6.-2) and (-6,7)

We need to find the perimeter and area of the rectangle.

Using distance formula we find the length and width of the rectangle.

d1 = √(-2 - 7)² + (3 - 3)²

d1 = √(-9)²

d1 = 9

And d2 = √(-2 + 2)² + (-6-3)²

d2 = √(-9)²

d2 = 9

d3 = √(7 + 2)² + (-6 + 6)²

d3 = 9

This means, the length and width of rectangle are equal i.e., 9 units.

So, perimeter would be,

P = 4 * 9

P = 36 units

And the area would be,

A = 9 * 9

A = 81 square units

Therefore, the area of the rectangle 81 square units and the perimeter of the rectangle is 36 units.

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A scale drawing of an NFL goal post uses a scale of 2 inches equal 5 feet if the actual width of the goal posts is 18 1/2 feet what is the width of the goal post on the drawing.

If 3 inches on the scale drawing represents 5 feet in actuality, determine the actual area of a kitchen if the area of the scale drawing is 45 inches 3 inches to 5 feet is 1:20

From the question asked you cannot determine the area. (No width given) You state the measurement is 45 inches (not square inches) 45 inches at 20:1 = 900 inches or 75 feet (linear)

Hence the answer is 75 ft.

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Answer:

75 ft

Step-by-step explanation:

The mean of the following data is 0.1800

acc to our question-

hence,The mean of the following data is 0.1800

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15

5 t = 30$

1t = 30/5

= 6$ per ticket

then, 90$/6 = 15 tickets

Answer:

9cm r=2x3x9= 54. Find the volume of the cube. Include units. 5cm ... Not to scale. Work out the volume of the prism. Area of front. 3x5=15. 3cm 4x8=32. 10cm.

Step-by-step explanation:

Answer:

  470 cm³

Step-by-step explanation:

You want the volume of a prism with an L-shaped base.

The volume of a prism is given by ...

  V = Bh

where B is the area of the base, and h is the distance between bases.

The base is has an L-shape. Its area can be found by extending the horizontal line to divide the figure into two rectangles.

The top rectangle is 4cm × 5cm, so has an area of ...

  A = LW = (4 cm)(5 cm) = 20 cm²

The bottom rectangle is 9 cm × 3 cm, so has an area of ...

  A = LW = (9 cm)(3 cm) = 27 cm²

Then the total base area is ...

  B = (top rectangle area) + (bottom rectangle area)

  B = (20 cm²) +(27 cm²) = 47 cm²

Then the volume is ...

  V = Bh = (47 cm²)(10 cm) = 470 cm³

The volume of the prism is 470 cm³.

Answer:

68.21 and 39.79

Step-by-step explanation:

When it says that they are going to "share" it means that the number  (108) is going to be divided amongst the two of them. So you are going to do an addition problem which is 12+7=19. So you are going to do 12/19*108=68.21.  Then to find the second number it's 7/19*108=39.79.

i) The first term, a is 3 and the common difference, d, is 2

ii) The first term, a is 18 and the common difference, d, is -5

iii) The first term, a is 8 and the common difference, d, is 11

iv) The first term, a is -15 and the common difference, d, is -4

v) The first term, a is 4.5 and the common difference, d, is 0.8

From the question, we are to determine the first terms and the common differences of the arithmetic sequences.

The first term, a, is the first number in the sequence and the common difference, d, is the value of the difference between the second term and the first term.

That is,

Common difference = Second term - First term

i) 3, 5, 7, 9, ...

a = 3

d = 5 - 3

d = 2

ii) 18, 13, 8, 3, ...

a = 18

d = 13 - 18

d = -5

iii) 8, 19, 30, 41, ...

a = 8

d = 19 - 8

d = 11

iv) -15, -19, -23, -27, ...

a = -15

d = -19 - (-15) = -19 + 15

d = -4

v) 4.5, 5.3, 6.1, 6.9, ...

a = 4.5

d = 5.3 - 4.5

d = 0.8

Hence, the first term is 4.5 and the common difference is 0.8

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1260 tickets were sold on the first game

For the second game, the ratio of the number of sold tickets to number of unsold tickets is 13:2

Total ratio = 13+2 = 15

There were 240 unsold tickets for the second game. Let total number of tickets for the second game be x

This means that

240 = 2/15 × x

2x/15 = 240

2x = 15 × 240= 3600

x = 3600/2 = 1800

1800 tickets were sold for the second game. Assuming total number of tickets for the first game is equal to total number of tickets for the second game. Therefore,

Total number of tickets sold for the first game is 1800

The ratio of sold tickets to unsold tickets for the first game was 7:3.

Total ratio = 7+3 = 10

Number of sold tickets for the first game would be

7/10 × 1800 = 12600/10

= 1260 tickets

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Answer:

21.475 minutes  

(Rounded) 21 minutes

Step-by-step explanation:

T(t)  =  TA  + (T0 - TA)e^(-kt)

We know that after 12 minutes...

140  = 70  + ( 165 - 70)e^(-k* 12)    

1 ) Simplify and subtract 70 from both sides

70 = ( 95)e^(-12k)      

2 ) Divide both sides by  25

70/95  = e^(-12k)      

3 ) Take the Ln of both sides

Ln (70/95) =  Ln e^(-12k)    

and we can write  Ln (70/95)  = (-12k)  Ln e

[ Ln e  =1, so we can ignore this  ]

4 ) Divide both sides by -12

Ln (70/95) / -12  = k  ≈   .02545

So...

5 ) We want to find this  125  =  70  + ( 165 - 70)e^(-.02545t)

6 ) 55 = (95)e^(-.02545*t)

7 ) 55/95  =  e^(-.02545*t)      take the Ln of both sides

8 ) Ln (55/95)  = Ln e ^(-.02545 *t)

9 ) Ln (55/95)  =  (-.02545 * t)  * Ln e

10 ) Ln (55/95) = -.02545 * t    

11 ) Ln (55/95) / (-.02545)  = t  ≈ 21.475 minutes

12 ) If we are rounding then it would be 21 minutes

Hope this helps! :)

The probability  to unlock the tablet on his first try is [tex]P=\frac{1}{10^{9} }[/tex].

According to the statement

We have to find that the probability  to unlock the tablet on his first try.

For this purpose, we know that the

Probability is the the ratio of the number of outcomes to the total number of possible outcomes.

And

The desired outcomes is the 1 because only 1 password is the correct.

And the total outcomes is the

Nine-digit codes.so,

[tex]T=10^{9}[/tex]

Because For each digit, there are 10 possible outcomes.

And the probability is the

[tex]P=\frac{1}{10^{9} }[/tex].

So, The probability  to unlock the tablet on his first try is [tex]P=\frac{1}{10^{9} }[/tex].

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The probability that at least 1 of them is a universal donor 20.1%

A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Mathematics' study of random events is known as probability, and there are four primary forms of probability: axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you might argue that it is the likelihood that a specific event will occur.

According to the given equation:-

The probability that at least one of every three is O-negative is 20.1%

Note that the question is unfinished. The following question is similar:

Type O-negative individuals can donate blood to anyone. In other words, O-negative blood can be transfused to any patient. Only 7.2% of Americans have blood that is O-negative. What is the likelihood that at least one of the ten Americans we randomly choose donating blood is a universal donor?

Detailed explanation:

7.2%, or 0.072, of the population has O-negative blood.

Probability of not being O-negative is equal to 1 - P(O-negative), which is 1 - 0.072, or 0.928.

Using the multiplication rule, calculate the likelihood that 10 persons are O-negative.

Probability that 10 is not zero = (P (not O-negative) ¹⁰ = (0.928) (0.928) ¹⁰ =0.4737

Therefore, the probability that at least one is O-negative is given by the formula: 1 - P(not O-negative) = 1 - 0.4737 = 0.5263.

P(at least 1 in 10 being O-negative) = 52.63% in percentage

to 3 arbitrary donors

likelihood of 3 not - (P) negative (not O-negative) ³ = (0.928) (0.928) ³ = 0.7991

As a result, the likelihood that at least 1 is O-negative is equal to 1 - P(3 not O-negative) = 1 - 0.7991 = 0.2009.

P(at least 1 out of 3 being O-negative) = 20.1% in percentage

Examine all related responses

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Answer:

Step-by-step explanation: The number of yellow sweets is 28. Step-by-step explanation: Ratio of red to yellow sweets is 3:7. Total sweet is 40. total ratio is 3 + 7 = 10.

Answer:

Step-by-step explanation:

well 56^2 is 56*56, 56*56= 3136

1. 3136x-88x

2. 3048x+88x

Answer:

2 1/3's

Step-by-step explanation:

1/3 +  1/3 = 2/3

In the given problem, the number of  1/3 is in 7/9, 7/3

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.

Given that,

the number 7/9

fraction number 1/3

the number of fraction 7/9 has of 1/3 is,

⇒ 7/9÷1/3

⇒ 7/3

Hence, the result is 7/3

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Answer: first one

Step-by-step explanation:

After solving the value of x = 1/2.

From the figure:

AB = 4 ,BD = 3,DE = 4

AD = AB + BD

= 4+3

= 7

ADE is a right angle triangle.

AE^2 = AD^2+DE^2

= 7^2 + 4^2

= 49 + 16

= 65

AE = [tex]\sqrt{65}[/tex]

AC = AE/2

= [tex]\sqrt{65}[/tex]/2

ABC is a right angle triangle.

AC^2 = AB^2+BC^2

[tex](\sqrt{65}/2)^2[/tex]= 4^2+x^2

65/4 = 16 + x^2

65/4 - 16 = x^2

65 - 16*4 / 4 = x^2

1/4 = x^2

x = [tex]\sqrt{1/4}[/tex]

x = 1/2

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y = x - 3

slope: 1

y=intercept; (0,-3)

To travel 24 miles of distance it require 16 gallons of gas

Ratio :

                                   A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Proportion :

                  A proportion is an equation in which two ratios are set equal to each other,

From the graph,

       We are observing that,

                                                 The boat uses 4 gallons to travel 6 miles. Traveling 4 times as far is expected to require 4 times the gas.

            In 4 gallons of gas  travelling 6 miles,

that is,

In simple word,            

        4 gallons = 6 miles

          Multiply both side by 4 we get,

        4 x 4 gallons = 6x4 miles

        16 gallons = 24 miles

Thus we can say,

                           To travel 24 miles of distance it require 16 gallons of gas

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Step-by-step explanation:

Its a simple algebraic expression

Here, d-1 is the largest possible value of N.

Given info,

For an arbitrary Markov chain on a state space consisting of exactly d states, find (with proof) the largest possible positive integer n such that for some states i,j, we have p(n) ij > 0 but p(n) ij.

We will prove that N ≤ d - 1

In light of this, there are states I and j such that the path from I to j has at least N edges, which implies that the path from I to j has at least d edges.

However, since there are only d states, the distance between any two states can be no greater than d-1. N can't thus be bigger than d-1.

Now, d-1 is the largest possible N because if we take a look at a Markov chain, if I is between 1 and d, we can only move to state 2 and if I is already at state d, we can only move to state d-1. However, if I am already at state 1, we can only move to state 1 and if I am already at state 2, we can only move to state i+1.

This sample contains d-1 edges on the way from state 1 to d. N = d-1 hence holds in this situation.

Therefore, N can have a value as large as d-1.

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Answer: That is a fraction. As an improper fraction, it's 17/6.

Step-by-step explanation:

Answer:

Now, 2 5/6 is a mixed fraction. To convert a mixed fraction to an improper fraction, we have to calculate (2 + 5/6). 2 + 5/6 = (12 + 5) / 6 = 17/6. Hence, 2 5/6 as a fraction is equal to 17/6.

If a shuttle was launched every day, about 1 failures would one expect in 300 years.

Finding an estimate or approximation—a value that can be used for a purpose despite the possibility of incomplete, uncertain, or unstable input data—is the process of estimation. Despite this, the value is still useful because it was created using the most up-to-date data.

Here,

There are about 110,000 days in 300 years, so the expected number of failures is about 10/11 ≈ 1.

This assumes the launch conditions are identical for each of the launches, or that whatever variation there might be has no effect on the probability. These are bad assumptions.

If a shuttle was launched every day, one might anticipate one failure every 300 years.

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Option (a) is the correct option and the rate of change of the cost per person is 74/1.  

As, we are given the table that the cost per person to buy tickets for an upcoming concert.

Persons                             Cost

    2                                     148

    3                                     222

    4                                     296

    5                                     370

So, the rate of change is,

rate of change = change in cost / change in persons

Rate of change = (222 - 148)/(3 - 2)

= 74/1

= 74

So, 74/1 is the rate of change.

Hence, Option (a) is the correct option and the rate of change of the cost per person is 74/1.  

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The inequality for the statement:-2/7 is at most the product of a number and -4/5. is --4x/5 ≤ -2/7

Information from the question

the statement: -2/7 is at most the product of a number and -4/5

Inequality is a means of representing the relationship existing between the positive and negative parts of equations, using other terms aside exactly using equal to

at most means the highest value hence the answer is either the number or less.

let the number be x

x * -4/5 ≤ -2/7

--4x/5 ≤ -2/7

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