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3 years ago

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Find a recurrence relation for the number of sequences of 1s, 3s, and 5s whose terms sum to n. (b) Repeat part (a) with the adde

d condition that no 5 can be followed by a 1. (c) Repeat part (a) with the condition of no subsequence of 135

1 answer:

Vladimir [108]3 years ago

3 0

Answer:

The solution has been given in the following attachment .

Step-by-step explanation:

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X^3 - x^2 + x / x^3 + 1 simplified

Ad libitum [116K]

I think it’s x+1x^3... not sure if this helps

8 0

3 years ago

5000 12% compounded quarterly compound interest table find earned after 5 years

kolezko [41]

<h3>Amount earned after 5 years is $ 9030.5561</h3>

<em><u>Solution:</u></em>

<em><u>The formula for compound interest, including principal sum, is:</u></em>

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

A = the future value of the investment including interest

P = the principal investment amount

r = the annual interest rate in decimal

n = the number of times that interest is compounded per unit t

t = the time the money is invested

From given,

p = 5000

t = 5 years

$r = 12 \% = \frac{12}{100} = 0.12$

<em><u>n = 4 ( since interest is compounded quarterly )</u></em>

<em><u>Substituting the values we get,</u></em>

$A = 5000(1+\frac{0.12}{4})^{4 \times 5}\\\\A = 5000(1+0.03)^{20}\\\\A = 5000 \times 1.03^{20}\\\\A = 5000 \times 1.806111\\\\A = 9030.5561$

Thus amount earned after 5 years is $ 9030.5561

7 0

3 years ago

864 multiple by two third ?

harkovskaia [24]

Here we will explain how to calculate two thirds of 864.

Two thirds of 864 is simply two thirds times 864, which can be written as follows:

Two/thirds x 864

Furthermore, you can convert "two" to "2" and "thirds" to "3" and then the equation and answer is:

2/3 x 864 = 576.00

Two thirds written as a fraction is 2/3. You can also write it as a decimal by simply dividing 2 by 3 which is 0.67.<span>If you multiply 0.67 with 864 you will see that you will end up with the same answer as above. </span>

<span>You may also find it useful to know that if you multiply 0.67 with 100 you get 66.67. Which means that our answer of 576.00 is 66.67 percent of 864. </span>

3 0

3 years ago

Suppose y varies directly as x, and y=14 when x=4. What is the value of y when x=9

Katena32 [7]

Given :-

y varies directly as x, and y=14 when x=4.

To Find :-

the value of y when x=9 .

Solution :-

<u>A</u><u>c</u><u>c</u><u>o</u><u>r</u><u>d</u><u>i</u><u>n</u><u>g</u><u> </u><u>t</u><u>o</u><u> </u><u>Q</u><u>u</u><u>e</u><u>s</u><u>t</u><u>i</u><u>o</u><u>n</u><u> </u><u>,</u>

y = kx ( k is constant )

<u>When</u><u> </u><u>y</u><u> </u><u>=</u><u> </u><u>1</u><u>4</u><u> </u><u>a</u><u>n</u><u>d</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>4</u><u> </u><u>,</u>

14 = k(4)
k = 14/4
k = 7/2

<u>W</u><u>h</u><u>e</u><u>n</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>9</u><u> </u><u>,</u>

y = 7/2*9
y = 63/2
y = 31.5

8 0

3 years ago

the width of a rectangle is the length minus 2 units. The area of the rectangle is48 units. What is the width, in units, of the

tatuchka [14]

Answer:

6

Step-by-step explanation:

put unknown as y

area of rectangle = width × long

y(y - 2)=48

y² -2y =48

u can use scientific calculator to find this

y²-2y-48=0

(y-8)(y+6)=0

y=8 y=-6

take the positive value and ignore the negative value

width=y-2 long=8

8-2=6

I hope this help you :)

6 0

3 years ago