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3 years ago

Use the x-intercept method to find all real solutions of the equation. x^3-8x^2+9x+18=0

Mathematics

2 answers:

meriva3 years ago

8 0

Answer:

a. $x=-1,3,\:or\:6$

Step-by-step explanation:

The given equation is;

$x^3-8x^2+9x+18=0$

To solve by the x-intercept method we need to graph the corresponding function using a graphing calculator or software.

The corresponding function is

$f(x)=x^3-8x^2+9x+18$

The solution to $x^3-8x^2+9x+18=0$ is where the graph touches the x-axis.

We can see from the graph that; the x-intercepts are;

(-1,0),(3,0) and (6,0).

Therefore the real solutions are:

$x=-1,3,\:or\:6$

hichkok12 [17]3 years ago

8 0

Answer:

Use a graphing utility or a graphing calculator.

x = -1, 3, 6. (3 real solutions).

Step-by-step explanation:

The points of intersection on the x axis are the 3 solutions to the equation.

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In a sample of 70 stores of a certain company, 62 violated a scanner accuracy standard. It has been demonstrated that the condi

uysha [10]

Answer:

We need at least 243 stores.

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 $1 - \frac{\alpha}{2}$ .

The margin of error of the interval is:

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

For this problem, we have that:

$n = 70, p = \frac{62}{70} = 0.886$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

Determine the number of stores that must be sampled in order to estimate the true proportion to within 0.04 with 95% confidence using the large-sample method.

We need at least n stores.

n is found when M = 0.04. So

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

$0.04 = 1.96\sqrt{\frac{0.886*0.114}}{n}}$