A sinking fund is established to discharge a debt of $20,000 in 15 years. If deposits are made at the end of each 6-month period and interest is paid at the rate of 5%, compounded semiannually, what is the amount of each deposit? (Round your answer to the nearest cent.)

Answer:

[tex]NK \approx 7.001[/tex], [tex]MK = 2[/tex], [tex]MF \approx 7.001[/tex], [tex]A_{AMNFD} = 49.007[/tex]

Step-by-step explanation:

According to the statement, we find the following inputs:

[tex]\angle MDK = \angle DMF = 45^{\circ}[/tex] (Due to the condition of isosceles trapezoid)

[tex]MD = 9[/tex]

[tex]NF = 5[/tex]

Given than longer base and shorter base are parallel to each other, we conclude that:

[tex]\angle KND = 180^{\circ} -\angle NKD - \angle KDN[/tex]

[tex]\angle KND = 180^{\circ}-90^{\circ}-45^{\circ}[/tex]

[tex]\angle KND = 45^{\circ}[/tex]

[tex]\angle FND = 90^{\circ}-\angle KND[/tex]

[tex]\angle FND = 45^{\circ}[/tex] (By definition of complementary angles)

[tex]\angle FND = \angle NFM = 45^{\circ}[/tex] (Due to the condition of isosceles trapezoid)

[tex]\angle MDK = \angle DMF = \angle FND = \angle NFM = 45^{\circ}[/tex]

[tex]\angle NOF = \angle MOD = \angle MOF = \angle FOD = 90^{\circ}[/tex] (By definitions of complementary and vertical angles and the theorem that states that sum of internal angles within a triangle equals 180º)

[tex]MO = DO = \frac{\sqrt{2}}{2}\cdot MD[/tex] (By theorem for 45-45-90 Right Triangle)

[tex]NO = OF = \frac{\sqrt{2}}{2}\cdot NF[/tex] (By theorem for 45-45-90 Right Triangle)

If we know that [tex]MD = 9[/tex] and [tex]NF = 5[/tex], then we find that:

[tex]DO = MO \approx 6.364[/tex]

[tex]NO = OF \approx 3.536[/tex]

The value of MK is obtained from the following relationship:

[tex]MK = \frac{MD-NF}{2}[/tex]

[tex]MK = \frac{9-5}{2}[/tex]

[tex]MK = 2[/tex]

And the value of KD is calculated from this expression:

[tex]KD = MD-MK[/tex]

[tex]KD = 9-2[/tex]

[tex]KD = 7[/tex]

Now by the Pythagorean Theorem we find that:

[tex]NK = \sqrt{(NO+DO)^{2}-KD^{2}}[/tex]

[tex]NK = \sqrt{9.9^{2}-7^{2}}[/tex]

[tex]NK \approx 7.001[/tex]

And considering the symmetry characteristics of an isosceles trapezoid, we determine MF:

[tex]MF = NO + DO \approx 7.001[/tex]

Lastly, the area of the isosceles trapezoid is determined by the following formula:

[tex]A_{AMNFD} = NF\cdot NK + MK\cdot NK[/tex]

[tex]A_{AMNFD} = NK\cdot (NF+MK)[/tex]

If we know that [tex]NK \approx 7.001[/tex], [tex]NF = 5[/tex] and [tex]MK = 2[/tex], then the area of the figure is:

[tex]A_{AMNFD} = (7.001)\cdot (5+2)[/tex]

[tex]A_{AMNFD} = 49.007[/tex]

Answer:

L=8, W=4

Step-by-step explanation:

2L+2W=p

2(4)+2(8)=p

8+16=24

Answer:

length = 8 in.; width = 4 in

Step-by-step explanation:

Answer:

14x+7y=-214x+7y=−2

Step-by-step explanation:

I think that can help :) wanna chat add me as  friend

Answer:

√13

Step-by-step explanation:

length √(2^2+3^2)=√13.

Answer:

Step-by-step explanation:

19-4x+15x  combine like terms

19+11x

Answer:

B. FE=40

Step-by-step explanation:

A. correct because FE = 58  6(8)+10=58

C. correct because 6(8)+10=40

D. correct because DF= 40  8(8)-24=40

Answer:

The angle of CAD is 100°.

Step-by-step explanation:

Given that total angles in a triangle is 180° so you will have to find the angle of CAB :

∠CAB + ∠ACB + ∠ABC = 180°

∠CAB + 80° + 20° = 180°

∠CAB + 100° = 180°

∠CAB = 180° - 100°

∠CAB = 80°

Next, you have to subtract it from 180° because straight line have a degree of 180°

∠CAD = 180° - 80°

∠CAD = 100°

Answer:

0.78 x 10^ 0

Step-by-step explanation:

Answer:

Today: Friday, 06 November 2020

Hour: 10.15 WIB (Indonesia)

_______________________________

so,

6c = 6 × 5 = 30

4b = 4 × (-3) = -12

Example:

4b - 6c

= 4(-3) - 6(5)

= -12 - 30

= - 42

4b + 6c

= 4(-3) + 6(5)

= -12 + 30

= 18

Answer:

93

Step-by-step explanation:

the total of all those are 150 so if you multiply it by three you get 450

so multiply pizza by three too

to get 93

Answer:

93 students

Step-by-step explanation:

You first need to add up all the numbers on the chart, 36 + 29 + 54 + 31. You would then get 150. Divide 450 / 150 = 3. You multiply the amount of students chose pizza by 3 and you get 93. 31 * 3 = 93.

Therefore, 93 students would say pizza is there favorite food.

Hope this helps :)

Answer:

3=k

Answer:

She can travel 7 miles in the taxi.

Step-by-step explanation:

2.75×7=19.25

Answer:

I hope this is good enough:

Step-by-step explanation:

I dis graph it just use demo's graphing system.

Answer:

Evaluation: √2

Simplified: |-2|+2

Hope this helps!

Answer:

11.18033989

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

4x - 2 and 3x + 6 are alternate angles and congruent, thus

4x - 2 = 3x + 6 ( subtract 3x from both sides )

x - 2 = 6 ( add 2 to both sides )

x = 8

Answer:

4y + x = 8

Step-by-step explanation:

firstly, we choose any 2 points on the line

point 1 = (0,2)

point 2 = (4,1)

x1 = 0, x2 = 4

y1 = 2, y2 = 1

from,

[tex] \dfrac{y2 - y1}{x2 - x1} = \dfrac{y- y1}{x- x1} [/tex]

[tex] \dfrac{1 - 2}{4 - 0} = \dfrac{y- 2}{x- 0} [/tex]

[tex] \dfrac{ - 1}{4} = \dfrac{y- 2}{x- 0} [/tex]

Cross multiplying,

-1(x) = 4(y - 2)

-x = 4y - 8

4y + x = 8

Answer:

Endpoint = (32,-23)

Step-by-step explanation:

end point = (16,-17)

midpoint = 24,-20)

other point = (x,y)

(x + 16)/2 = 24

x + 16 = 24 * 2

x + 16 = 48

x + 16-16 = 48-16

x = 32

======================

(y - 17/2 = - 20

y - 17 = - 20 * 2

y - 17 = - 40

y - 17+17 = - 40 + 17

y = - 23

Answer:   [tex]\frac{x^8}{256y^{20}}[/tex]

If the font is too small, it says x^8 all over top 256y^20 as one big fraction.

========================================================

Work Shown:

[tex]\left(\frac{5x^3}{20xy^5}\right)^4\\\\\\\left(\frac{x^2}{4y^5}\right)^4\\\\\\\frac{\left(x^2\right)^4}{(4^1)^4\left(y^5\right)^4}\\\\\\\frac{x^{2*4}}{4^{1*4}y^{5*4}}\\\\\\\frac{x^{8}}{4^{4}y^{20}}\\\\\\\frac{x^{8}}{256y^{20}}\\\\\\[/tex]

Answer:

The answer is B

Step-by-step explanation:

Answer:

Learn vocabulary, terms, and more with flashcards, games, and other study tools. ... The Fee that a driver pays to have automobile insurance is called a ... She receives 7% on her first $1,000 in sales and 15% on the balance of her sales. ... The Jackson's sublet their summer cottage during the winter and spring months.

Step-by-step explanation:

Answer:

Your answer is:  [tex]2j^{2}(j-4)[/tex]

Factor [tex]2j^{2}[/tex]out of [tex]2j^{3} -8j^{2}[/tex]

Step-by-step explanation:

Hope this helped : )

Answer:

It was sold at $32.40.

Step-by-step explanation:

hope this helpss :))

Answer:

devide them by each other and then when it is deamal form put it in %

:)

Step-by-step explanation:

Brainliest plz

Answer:

Cost of the Pizza is 20%

Cost of the Cheeseburger is 30%

Cost of the Fries is 125%

Step-by-step explanation:

Answer:

Yes because they both only have one zero so the discriminant for both is 0

Step-by-step explanation:

explanation above lol

The two functions have the same discriminant b² - 4a = 0.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

We know, Discriminant in a quadratic equation ax² + bx + c is, b² - 4ac.

Now, From the graph the discriminant and properties here,

D = 0 as the vertex of the parabola intersect only at one point.

b² - 4ac = 0.

The blue graph intersects at (2, 0) and the red graph intersects at (- 2, 0).

So, they have the same discriminant.

learn more about quadratic equations here :

https://brainly.com/question/30098550

#SPJ2

Answer:

it would be 0.64

Step-by-step explanation:

Answer:First three terms: 11,20,29 .

Step-by-step explanation:

Write a systems of equations. tn=a+(n−1)d. sn=n2 (2a+(n−1)d). So,. 110=11+(n−1)d 726=n2(22+(n−1)d).

I hope this is right

Answer:

188.88

Step-by-step explanation:

Answer:

10:7

Step-by-step explanation: