Are the two ratios equivalent? 6:21 and 8:28 Explain.​

Therefore, the interest portion of the seventh payment is:7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7 - 7,000.

We have the following payments and their corresponding times of payment:At the end of year 1: $1,000At the end of year 2: $2,000At the end of year 3: $3,000At the end of year 4: $4,000At the end of year 5: $5,000At the end of year 6: $6,000At the end of year 7: $7,000

At the end of year 8: $8,000At the end of year 9: $9,000At the end of year 10: $10,000The present value of these payments is:PMT x [(1 - (1 + r)-n) / r]where PMT is the payment, r is the interest rate per year, and n is the number of years till payment.

For the first payment (end of year 1), the present value is:1,000 x [(1 - (1 + r)-1) / r]which equals

1,000 x (1 - 1 / (1 + r)) / r = 1,000 x ((1 + r - 1) / r) = 1,000

For the second payment (end of year 2), the present value is:2,000 x [(1 - (1 + r)-2) / r]which equals 2,000 x (1 - 1 / (1 + r)2) / r = 2,000 x ((1 + r - 1 / (1 + r)2) / r) = 2,000 x (1 + r) / r2

For the seventh payment (end of year 7), the present value is:

7,000 x [(1 - (1 + r)-7) / r]

which equals

7,000 x (1 - 1 / (1 + r)7) / r = 7,000 x ((1 + r - 1 / (1 + r)7) / r) = 7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7

For such more question on corresponding

https://brainly.com/question/11853802

#SPJ8

The equation that represents the distance, in kilometers, Seb travels (d) based on how many hours he bikes (t) at this rate is d = 20t

The given parameter is

constant rate of 20 kilometers per hour.

This means that

Rate = 20km per hour

When Seb bikes for t hours, the distance is

d = rate * t

This gives

d = 20t

Hence, the equation that represents the distance, in kilometers, Seb travels (d) based on how many hours he bikes (t) at this rate is d = 20t

This means that

t = 5

So, we have:

d = 20 * 5

Evaluate

d = 100

Hence, Seb will travel 100 kilometers if he bikes at this rate for 5 hours

Read more about rate and speed at:

https://brainly.com/question/4931057

#SPJ1

Answer:

1. d=20t

2. 50

Answer:

Option D.

Step-by-step explanation:

In a store cost of CD is $12.

If the cost of CD purchased was graphed on y-axis (output values) and the number of CDs produced on x - axis (input values),

A straight line with positive slope will be graphed because number of the CDs produced will be directly proportional to the cost of CDs.

Line will start from the origin and points lying on it will start from left to right.

Set of points will represent a function.

Therefore, Option D will be the answer.

the answer is d, a, e, c Answer:

Step-by-step explanation:

A locus, or point, line, or moving surface, is a curve or other shape created in mathematics by all the points that meet a specific equation describing the relationship between the coordinates.

To learn more about locus refer to:

https://brainly.com/question/19578071

#SPJ1

Answer:

JKM is 123 degrees and the measure of arc KL is 56

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

A formula for connecting two statements using the equal sign (=) to denote equivalence is known as a mathematical equation. A mathematical equation in algebra is a statement that proves the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 places an equal sign between the variables 3x + 5 and 14. The mathematical relationship between the two sentences on either side of a letter is established. Most of the time, the symbol serves as both the one and only variable. for instance, 2x – 4 = 2.

Here,

the two numbers' primary factors are as follows:

-25\(b^{2}\) + 15b

Common prime factors can be multiplied to determine the GCF:

=> -25\(b^{2}\)  = -(5)(5) * \(b^{2}\)

=> 15b = (5)(3)b

The expression can be factored in the following fashion because the GCF is 5b:

=> -(5)(5) * \(b^{2}\) +  (5)(3)b

=> (5b)(-5b+3)

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Answer:

48

Step-by-step explanation:

5x12x80% = 48

Answer:

48

Step-by-step explanation:

5 x 12 x 80% = 48

Answer:

6 units²

Step-by-step explanation:

The formula for the area of triangle is 0.5bh where b is the length of the base and h is the (perpendicular) height.

A=0.5bh

A=0.5(4)(3)

A=6

Answer: 80

Step-by-step explanation:

⇒  −(8 − 12) + 60 + (−4)²

⇒ -(-4) + 60 + 16

⇒ 4 + 60 + 16

⇒ 80

Answer:

Step-by-step explanation:

6x + 18 = 12x

=> 18 = 12x - 6x

=> 18 = 6x

\( = > x = \frac{18}{6} \)

=> x = 3 (Ans)

Step-by-step explanation:

6x+18=12x

18=12x-6x

collect liked terms

18=6x

divide both sides by 6

=3

\( \sf{\blue{«} \: \pink{ \large{ \underline{A\orange{N} \red{S} \green{W} \purple{E} \pink{{R}}}}}}\)

Expression: \(\displaystyle\sf (6-2x) +(15-3x)\)

Substituting \(\displaystyle\sf x=0.2\):

\(\displaystyle\sf (6-2(0.2)) +(15-3(0.2))\)

Simplifying the expression inside the parentheses:

\(\displaystyle\sf (6-0.4) +(15-0.6)\)

\(\displaystyle\sf 5.6 +14.4\)

Calculating the sum:

\(\displaystyle\sf 20\)

Therefore, \(\displaystyle\sf (6-2x) +(15-3x)\) evaluated at \(\displaystyle\sf x=0.2\) is equal to \(\displaystyle\sf 20\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

The missing reason is the Division Property of Equality.

Step-by-step explanation:

Answer:

C. 101 3/4; $1017.50

Step-by-step explanation:

Correct on E2020!

The value of H (Hypotenuse) will be 54.93

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The values are,

⇒ cos θ = 0.8192

⇒ A (Base) = 45

Now,

Since, The values are,

⇒ cos θ = 0.8192

⇒ A = 45

We know that;

⇒ cos θ = Base (A) / Hypotenuse (H)

Substitute all the values, we get;

⇒ 0.8192 = 45 / H

⇒ H = 45 / 0.8192

⇒ H = 54.93

Thus, The value of H (Hypotenuse) = 54.93

Learn more about the triangle visit:

https://brainly.com/question/13984402

#SPJ1

The integral of the greatest integer function ∫ [x]dx is equivalent to 0.

Given is to integrate the greatest integer function. We can write it as -

∫ [x]dx

We can expand the the integral as -

∫ [x]dx = \(\int\limits^0_b {x} \, dx +\int\limits^c_0 {x} \, dx\), where b = - ∞ and c = ∞

∫ [x]dx = \(\int\limits^0_b {x} \, dx +\int\limits^c_0 {x} \, dx\) =

- ∞ + ...... + (-5) + (-4) + (-3) + (-2) + (-1) + 0 + 1 + 2 + 3 + 4 + 5 + ..... + ∞

{ 1 + 2 + 3 + 4 + 5 + ..... + ∞ } + {- ∞ + ...... + (-5) + (-4) + (-3) + (-2) + (-1)}

{ 1 + 2 + 3 + 4 + 5 + ..... + ∞ } - {∞ + ...... + (5) + (4) + (3) + (2) + (1)}

{ 1 + 2 + 3 + 4 + 5 + ..... + ∞ } - {∞ + ...... + (5) + (4) + (3) + (2) + (1)}

{- 1/12 - (- 1/12)}                     {Ramanujan's infinite sum series}

-1/12 + 1/12

0

To solve more questions on integrals, visit the link-

https://brainly.com/question/18125359

#SPJ1

Answer:

(13, 11)

Step-by-step explanation:

The number inside the absolute value is x, but with the opposite sign

The other number is y

Answer: x=-14

Step-by-step explanation:

If the line is perpendicular to the x-axis, that means it is parallel to the y-axis. All lines that are parallel to the y-axis have the form x=. Since we know the line passes through the x value of -14, that means the equation of the line is x=-14.

9514 1404 393

Answer:

  4) 95.7 m

Step-by-step explanation:

The angle at the cliff base between Alan and Keith is ...

  B = 180° -29° -48° = 103°

The law of sines will tell you the distance KB from Keith to the cliff base is

  KB/sin(A) = KA/sin(B)

  KB = KA×sin(A)/sin(B) = (70 m)sin(29°)/sin(103°) ≈ 34.82935 m

The height of the cliff is found from the tangent relation ...

  Tan = Opposite/Adjacent

  tan(70°) = height/(34.83 m)

  height = (34.83 m)tan(70°) = 95.693 m

The height of the cliff is about 95.7 m.

_____

Additional comment

These problems can usually be resolved into two 2-D problems. Here, we can work out the distance we need from Keith to the cliff by considering only the ground plan of the site. Then we can work out the height of the cliff only considering the vertical plane containing Keith and the base of the cliff.

The attachment shows the ground plan triangle KAB.

The cubic regression equation that fits the points (1,-9), (2,-15), (3,-29),(-1,3) is given as follows:

f(x) = -x³ + 2x² - 5x - 5.

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, we have that:

Using the calculator, the equation is given by:

f(x) = -x³ + 2x² - 5x - 5.

More can be learned about regression equations at https://brainly.com/question/16793283

#SPJ1

Answer:

2 ( -2 ) -8 = -12

3 ( -3 ) -18 = -27

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

We know that BD = 2x - 1 and BC + CD = BD.  Thus, we can set the sum of (x- 3) and 7 equal to 2x - 1 to find x:

BC + CD = BD

x - 3 + 7 = 2x - 1

x + 4 = 2x - 1

x + 5 = 2x

5 = x

Thus, x = 5

Checking the validity of our answer:

We can check that our answer is correct by plugging in 5 for x in x - 3 and 2x - 1 and checking that we get the same answer on both sides of the equation:

5 - 3 + 7 = 2(5) - 1

2 + 7 = 10 - 1

9 = 9

Thus, our answer is correct.

Answer:

90 in^2

Step-by-step explanation:

The pattern that this system detects is a four-digit number that is divisible by 3.

1. The system starts by taking an input of a four-digit number.

2. It then checks if the last digit of the input number is divisible by 3.

3. If it is, the system continues to check if the sum of the remaining three digits is divisible by 3.

4. If this turns out to be true, the system will output a signal indicating that the input number is divisible by 3.

Learn more about divisible by 3 here

https://brainly.com/question/2273245

#SPJ4

Los capitales depositados en las cuentas de 2 %, 3 % y 4 % son 630.000, 420.000 y 315.000, respectivamente.

En este problema tenemos el caso de una suma de dinero distribuida y depositada en tres cuentas con tres tasas de interes simple distintas. Existe una tasa de interés simple cuando el interés generado sobre el capital no es acumulativo en el tiempo. El modelo de interés simple es descrito por la siguiente fórmula:

C' = C · (1 + r / 100)

Donde:

A continuación, describimos la ganancia registrada en cada cuenta tal que produce la misma ganancia:

Cuenta al 2 %:

z = x · (2 / 100)

z = 0.02 · x

0.02 · x - z = 0

Cuenta al 3 %:

z = y · (3 / 100)

z = 0.03 · y

0.03 · y - z = 0

Cuenta al 4 %:

z = (1.365.000 - x - y) · (4 / 100)

z = 54600 - 0.04 · x - 0.04 · y

0.04 · x + 0.04 · y + z = 54600

La solución de este sistema de ecuaciones lineales se obtiene mediante métodos numéricos:

(x, y, z) = (630.000, 420.000, 12.600)

Finalmente, el capital depositado en la cuenta al 4 % es:

c = 1.365.000 - 630.000 - 420.000

c = 315.000

Se deposita capitales de 630.000, 420.000 y 315.000 en las cuentas de 2 %, 3 % y 4 %, respectivamente.

Para aprender más sobre intereses simples: https://brainly.com/question/19664034

#SPJ1

Answer:

x>_-1

Step-by-step explanation:

x is such that x is greater or equal to -1

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

Learn more about axioms here:

https://brainly.com/question/2857184

#SPJ8

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

Read more about Partial Differential Equations at: https://brainly.com/question/28099315

#SPJ1