All categories

1 year ago

Z=25/5 what is the next step in the equation solving sequence.

Mathematics

1 answer:

lbvjy [14]1 year ago

3 0

Answer:

Step-by-step explanation:

Z = 25/5

in simplest form........

25/5 = 5/1

so the answer is 5.

You might be interested in

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

The percent defective for parts produced by a manufacturing process is targeted at 4%. The process is monitored daily by taking

Anna [14]

Answer:

The 88% confidence interval for the proportion of defectives today is (0.053, 0.123)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 160, \pi = \frac{14}{160} = 0.088$

88% confidence level

So $\alpha = 0.12$ , z is the value of Z that has a pvalue of $1 - \frac{0.12}{2} = 0.94$ , so $Z = 1.555$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.088 - 1.555\sqrt{\frac{0.088*0.912}{160}} = 0.053$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.088 + 1.555\sqrt{\frac{0.088*0.912}{160}} = 0.123$

The 88% confidence interval for the proportion of defectives today is (0.053, 0.123)

6 0

2 years ago

Can someone help please

riadik2000 [5.3K]

Answer:

62 Sunday papers were sold

Step-by-step explanation:

Let x represent the number of Sunday papers sold. Then half that many, or x/2, is the number of Friday papers sold. The total revenue from the sales is the sum of products of quantity and price:

1.50 · x + 0.75 · (x/2) = 116.25

Multiplying by 2, this becomes ...

3.00x +0.75x = 232.50

3.75x = 232.50

Dividing by the coefficient of x gives ...

232.50/3.75 = x = 62

The number of Sunday newspapers sold is 62.

6 0

2 years ago

Consider two people where one person is 20% taller than the other but proportioned in exactly the same way. (That is, the tall

Masja [62]

Answer:

43.2in

Step-by-step explanation:

If the two people are equally proportional, then knowing the size of the waist of one of them, we gonna we be able to know the other's wais size, by the relation.

36in*(1*20%) = 36in*1.2 = 43.2in

7 0

2 years ago

Read 2 more answers

A business breaks even when the production costs are equal to the revenue. The expression 120+4x represents the cost of producin

nika2105 [10]

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

The expression 120+4x represents the cost of producing x items. The selling price is $5 for each item.

<u>The net income formula:</u>

y= (5 - 4)x - 120

(5-4)= contribution margin per unit sold (x)

120= fixed costs

<u>To calculate the break-even point in units, we need to use the following formula:</u>

Break-even point in units= fixed costs/ contribution margin per unit

Break-even point in units= 120 / 1

Break-even point in units= 120 units

Prove:

y= 1*120 - 120

y= 0

5 0

2 years ago