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3 years ago

Which interval notation represents the inequality 0 < x ≤ 5?

Mathematics

1 answer:

Bogdan [553]3 years ago

3 0

Answer:

B. (0,5). Hope this helps you

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11. Mr Lee bought a second hand car for

Marrrta [24]

Answer :

Depends on the rate compound interest is accrued. See answers.

Step-by-step explanation:

We need the compound interest formula which is:

$A = P (1+\frac{r}{n} )^{nt}$

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

It doesn't say how frequently the interest is compounded, so we will do monthly, quarterly, and yearly.

MONTHLY

So we know the car costs $25,480 and he made a down payment of $10,000. By subtracting the down payment from the purchase price we find the loan amount.

$25,480 - $10,000 = $15,480

P = 15,480

r = 4.75% = .0475

n = 12 (12 months in a year)

t = 2

Plug everything into the compound interest formula.

$A = P (1+\frac{r}{n} )^{nt}$

$A = 15480(1+\frac{.0475}{12})^{12*2}$

$A = 15480(1+\frac{.0475}{12})^{24}$

$A = 15480(1+.00396)^{24}$

$A = 15480(1.00396)^{24}$

$A = 15480*1.0992$

$A = $17016.14$

Mr. Lee paid $17,016.14 when the bill came due at 2 years with interest compounded monthly.

QUARTERLY

P = 15,480

r = 4.75% = .0475

n = 4 (4 quarters in a year)

t = 2

$A = P (1+\frac{r}{n} )^{nt}$

$A = 15480(1+\frac{.0475}{4})^{4*2}$

$A = 15480(1+\frac{.0475}{4})^{8}$

$A = 15480(1+.0119})^{8}$

$A = 15480(1.0119)^{8}$

$A = 15480*1.099$

$A = 15480(1.099)$

$A = 17013.20$

Mr. Lee paid $17,013.20 when the bill came due at 2 years with interest compounded quarterly.

YEARLY

P = 15,480

r = 4.75% = .0475

n = 1

t = 2

$A = P (1+\frac{r}{n} )^{nt}$

$A = 15480(1+\frac{.0475}{1})^{1*2}$

$A = 15480(1+\frac{.0475}{12})^{2}$

$A = 15480(1+.0475})^{2}$

$A = 15480(1.0475)^{2}$

$A = 15480*1.0973$

$A = 16985.53$

Mr. Lee paid $16,985.53 when the bill came due at 2 years with interest compounded yearly.

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3 years ago

Use Euler’s method to estimate the value of y(20). Use a step size of ∆x = 5. Please fill out the remainder of the chart complet

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Answer:

y(20)=14,322

Step-by-step explanation:

We need to solve the equation:

$dy/dx=0.4xy$

with initial point

$y(0) = 2$

with incerments

$\Delta x=h=5$

By Euler's method, we have:

$y(x+h)=y(x)+h*f'(x,y)$

We start with the initial point

$y(5)=y(0)+5*f'(0,2)=2+5*(0.4*0*2)=2$

And we continue until we reach the value for y(20)

$y(10)=y(5)+5*f'(5,2)=2+5*(0.4*5*2)=2+20=22\\\\\\y(15)=y(10)+5*f'(10,22)=22+5*(0.4*10*22)=22+440=462\\\\\\y(20)=y(15)+5*f'(15,462)=462+5*(0.4*15*462)=462+13,860\\\\y(20)=14,322$

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3 years ago