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Mekhanik [1.2K]
1 year ago
13

5. You deposit $300 in an account Urat pays 1.48% annual interest. What is the balance after 1 year if the

Mathematics
1 answer:
kirill [66]1 year ago
8 0

Answer:

The correct option is (A) $304.47.

Step-by-step explanation:

The formula to compute the future value (<em>FV</em>) of an amount (A), compounded daily at an interest rate of <em>r</em>%, for a period of <em>n</em> years is:

FV=A\times [1+\frac{r\%}{365}]^{n\times 365}

The information provided is:

A = $300

r% = 1.48%

n = 1 year

Compute the future value as follows:

FV=A\times [1+\frac{r\%}{365}]^{n\times 365}

      =300\times [1+\frac{0.0148}{365}]^{365}\\\\=300\times (1.00004055)^{365}\\\\=300\times 1.014911\\\\=304.4733\\\\\approx \$304.47

Thus, the balance after 1 year is $304.47.

The correct option is (A).

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jake makes 9 loaves of olive bread. he uses 30 grams of olives in each loaf.he started with 1 kilogram of olives.how many grams
8090 [49]
Considering that 1 kilogram is equal to 1000 grams and he made 9 loaves of bread using 30 grams each time, that equates to 270 grams of olives. 1000 - 270 = 730. Your answer is 730 grams of olives remain. Hope this helped.
6 0
2 years ago
Solve the recurrence relation: hn = 5hn−1 − 6hn−2 − 4hn−3 + 8hn−4 with initial values h0 = 0, h1 = 1, h2 = 1, and h3 = 2 using (
musickatia [10]
(a) Suppose h_n=r^n is a solution for this recurrence, with r\neq0. Then

r^n=5r^{n-1}-6r^{n-2}-4r^{n-3}+8r^{n-4}
\implies1=\dfrac5r-\dfrac6{r^2}-\dfrac4{r^3}+\dfrac8{r^4}
\implies r^4-5r^3+6r^2+4r-8=0
\implies (r-2)^3(r+1)=0\implies r=2,r=-1

So we expect a general solution of the form

h_n=c_1(-1)^n+(c_2+c_3n+c_4n^2)2^n

With h_0=0,h_1=1,h_2=1,h_3=2, we get four equations in four unknowns:

\begin{cases}c_1+c_2=0\\-c_1+2c_2+2c_3+2c_4=1\\c_1+4c_2+8c_3+16c_4=1\\-c_1+8c_2+24c_3+72c_4=2\end{cases}\implies c_1=-\dfrac8{27},c_2=\dfrac8{27},c_3=\dfrac7{72},c_4=-\dfrac1{24}

So the particular solution to the recurrence is

h_n=-\dfrac8{27}(-1)^n+\left(\dfrac8{27}+\dfrac{7n}{72}-\dfrac{n^2}{24}\right)2^n

(b) Let G(x)=\displaystyle\sum_{n\ge0}h_nx^n be the generating function for h_n. Multiply both sides of the recurrence by x^n and sum over all n\ge4.

\displaystyle\sum_{n\ge4}h_nx^n=5\sum_{n\ge4}h_{n-1}x^n-6\sum_{n\ge4}h_{n-2}x^n-4\sum_{n\ge4}h_{n-3}x^n+8\sum_{n\ge4}h_{n-4}x^n
\displaystyle\sum_{n\ge4}h_nx^n=5x\sum_{n\ge3}h_nx^n-6x^2\sum_{n\ge2}h_nx^n-4x^3\sum_{n\ge1}h_nx^n+8x^4\sum_{n\ge0}h_nx^n
G(x)-h_0-h_1x-h_2x^2-h_3x^3=5x(G(x)-h_0-h_1x-h_2x^2)-6x^2(G(x)-h_0-h_1x)-4x^3(G(x)-h_0)+8x^4G(x)
G(x)-x-x^2-2x^3=5x(G(x)-x-x^2)-6x^2(G(x)-x)-4x^3G(x)+8x^4G(x)
(1-5x+6x^2+4x^3-8x^4)G(x)=x-4x^2+3x^3
G(x)=\dfrac{x-4x^2+3x^3}{1-5x+6x^2+4x^3-8x^4}
G(x)=\dfrac{17}{108}\dfrac1{1-2x}+\dfrac29\dfrac1{(1-2x)^2}-\dfrac1{12}\dfrac1{(1-2x)^3}-\dfrac8{27}\dfrac1{1+x}

From here you would write each term as a power series (easy enough, since they're all geometric or derived from a geometric series), combine the series into one, and the solution to the recurrence will be the coefficient of x^n, ideally matching the solution found in part (a).
3 0
2 years ago
Find a polynomial function of degree 3 such that f(10)=17 and the zeros of f are 0, 5 and 8
fomenos

Step-by-step explanation:

Since f(0) = f(5) = f(8) = 0, we have f(x) = Ax(x - 5)(x - 8), where A is a real constant.

We know that f(10) = 17.

=> A(10)(10 - 5)(10 - 8) = 17

=> A(10)(5)(2) = 17

=> 100A = 17, A = 0.17.

Hence the answer is f(x) = 0.17x(x - 5)(x - 8).

3 0
1 year ago
A company will make a cereal box with whole number dimensions and a volume of 100 cubic centimeters. if cardboard costs $0.05 pe
Evgen [1.6K]

Answer:

The best dimension to use to have the least cost to make 100 boxes is 5 x 5 x 4. It only costs $6.50 to make 100 boxes.

Step-by-step explanation:

8 0
2 years ago
Jamie made the tree diagram below to show the different choices he has for ordering a pizza for lunch. According to the tree dia
USPshnik [31]
Sizes = Small, Medium and Large, so they has 3 choices for size.

Crust = Thin or thick for each size, so they have 2 choices for crust.

Topping = Tomato or meatball for each one, so they have 2 choices for toppings.

The answer would be:

<span>Three choices for size, two choices for crust, and two choices for topping</span>

8 0
1 year ago
Read 3 more answers
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