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4 years ago

Solve 4x^4 - 37x^2 + 9 = 0 for ALL its solutions

1 answer:

4 0

Solve for x over the real numbers:4 x^4 - 37 x^2 + 9 = 0
Substitute y = x^2:4 y^2 - 37 y + 9 = 0
The left hand side factors into a product with two terms:(y - 9) (4 y - 1) = 0
Split into two equations:y - 9 = 0 or 4 y - 1 = 0
Add 9 to both sides:y = 9 or 4 y - 1 = 0
Substitute back for y = x^2:x^2 = 9 or 4 y - 1 = 0
Take the square root of both sides:x = 3 or x = -3 or 4 y - 1 = 0
Add 1 to both sides:x = 3 or x = -3 or 4 y = 1
Divide both sides by 4:x = 3 or x = -3 or y = 1/4
Substitute back for y = x^2:x = 3 or x = -3 or x^2 = 1/4
Take the square root of both sides:Answer(s): x = 3 or x = -3 or x = 1/2 or x = -1/2

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In a sample of 234 individuals over the age of 25, chosen at random from the state of Oregon, 48 did not have a high school dipl

Anna71 [15]

Answer:

The upper bound of a 95% confidence interval for the proportion of individuals over the age of 25 in Oregon who do not have a high school diploma is of 0.2568.

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 z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

95% confidence level

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

In a sample of 234 individuals over the age of 25, chosen at random from the state of Oregon, 48 did not have a high school diploma.

This means that $n = 234, \pi = \frac{48}{234} = 0.2051$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2051 + 1.96\sqrt{\frac{0.2051*0.7949}{234}} = 0.2568$

The upper bound of a 95% confidence interval for the proportion of individuals over the age of 25 in Oregon who do not have a high school diploma is of 0.2568.

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3 years ago

Given that -5 is a zero of the function f(x) = x^3 + x^2 - 14x + 30 find the remaining zeros

vampirchik [111]

Since the factors are (x+5)(x^2-4x+6)

the zeros would be 2+i√2 and 2−i√2

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3 years ago

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Marizza181 [45]

Answer:

y=80.05

Hope this helps

Step-by-step explanation:

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3 years ago