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satela [25.4K]
4 years ago
13

Three financial institutions, A,B,C, are offering different rates on a loan. Is a offer 3.15 % annual compounded monthly, B offe

rs 2.25% compounded quarterly, C offers 2.05% compounded daily. Determine which of the institutions offers best deal. Explain and make a conclusion.
Mathematics
1 answer:
coldgirl [10]4 years ago
8 0

Answer:

Step-by-step explanation:

Given that interest rates are as follows:

Let P be 100 dollars for each.

A) 3.15% compounded monthly.

Hence amount = 100(1+\frac{3.15}{1200} )^{12}

Final amount = 103.20 dollars

B) 2.25% compounded quarterly

Final amt. = 100(1+\frac{2.25}{400} )^4

=102.27

C) 2.05% compounded daily

Amount = 100(1+\frac{2.05}{36500} )^{365}

=102.07

Obviously A is the best deal.

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Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation with constant coefficients.
Anika [276]

Answer:

\boxed{\sf \ \ \ ax^2+bx^{-10} \ \ \  }

Step-by-step explanation:

Hello,

let's follow the advise and proceed with the substitution

first estimate y'(x) and y''(x) in function of y'(t), y''(t) and t

x(t)=e^t\\\dfrac{dx}{dt}=e^t\\y'(t)=\dfrac{dy}{dt}=\dfrac{dy}{dx}\dfrac{dx}{dt}=e^ty'(x)y'(x)=e^{-t}y'(t)\\y''(x)=\dfrac{d^2y}{dx^2}=\dfrac{d}{dx}(e^{-t}\dfrac{dy}{dt})=-e^{-t}\dfrac{dt}{dx}\dfrac{dy}{dt}+e^{-t}\dfrac{d}{dx}(\dfrac{dy}{dt})\\=-e^{-t}e^{-t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}\dfrac{dt}{dx}=-e^{-2t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}e^{-t}\\=e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt})

Now we can substitute in the equation

x^2y''(x)+9xy'(x)-20y(x)=0\\ e^{2t}[ \ e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}) \ ] + 9e^t [ \ e^{-t}\dfrac{dy}{dt} \ ] -20y=0\\ \dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}+ 9\dfrac{dy}{dt}-20y=0\\ \dfrac{d^2y}{dt^2}+ 8\dfrac{dy}{dt}-20y=0\\

so the new equation is

y''(t)+ 8y'(t)-20y(t)=0

the auxiliary equation is

x^2+8x-20=0\\ x^2-2x+10x-20=0\\x(x-2)+10(x-2)=0\\(x+10)(x-2)=0\\ x=-10\text{ or }x=2

so the solutions of the new equation are

y(t)=ae^{2t}+be^{-10t}

with a and b real

as

x(t)=e^t\\ t(x)=ln(x)

y(x)=ae^{2ln(x)}+be^{-10ln(x)}=ax^2+bx^{-10}

hope this helps

do not hesitate if you have any questions

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3 years ago
a bar graph shows that sports books received 9 votes.If the scale is 0 to 20 by twos, where should the bar end for the sports bo
boyakko [2]
It between the numbers 8 and 10
7 0
3 years ago
1. Amello has $25 to spend on maceuo this week. She loves lipstick och lostics . tube costs $4. What is the monimum number of lo
finlep [7]

Answer:

1. 4x ≤ 25

⇒ x ≤ 6.25

2. x + 4 < 25

⇒ x < 21

3. x + 4 ≥ 25

⇒ x ≥ 21

4. 4 + x ≤ 25

⇒ x ≤ 21

Step-by-step explanation:

1. 4x ≤ 25

⇒ x ≤ 6.25

2. x + 4 < 25

⇒ x < 21

3. x + 4 ≥ 25

⇒ x ≥ 21

4. 4 + x ≤ 25

⇒ x ≤ 21

4 0
3 years ago
Consider a bettering game where you bet $10 and have a probability of 0.45 of getting $20 back ($10 more than you started with)
Marina CMI [18]

Answer:

(a)

f(x) = P(X=x) = \begin{Bmatrix} 0.45 \,\,\, \text{for}  \,\,\, x = 10 \\ 0.55 \,\,\, \text{for}  \,\,\, x = -10 \end{matrix}

(b)

-1

(c)

30

Step-by-step explanation:

(a)

Your random variable will have two possible values, 30 and 0, one of them with a probability of 0.45 and the other one with a probability of 0.55. Therefore it looks like this.

f(x) = P(X=x) = \begin{Bmatrix} 0.45 \,\,\, \text{for}  \,\,\, x = 10 \\ 0.55 \,\,\, \text{for}  \,\,\, x = -10 \end{matrix}

(b)

The expected value of this PMF would be

E[X] = -10*0.55+10*0.45= -1 therefore on average you will have a dollar less.

(c)

For this one, if you play 20 times and your initial amount is 50$ then you have to compute the following expectation.

E[50+20*X] = 50+20*E[X] = 50-20 = 30

7 0
3 years ago
1, 4, 8, 13, 19, 26<br><br> Find sequence formula using the quadratic way.
Lesechka [4]

Answer:

Step-by-step explanation:

1(8)^2-1

its the first variable then the the third one and u raise it by what the number is and u subtract by one

6 0
3 years ago
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