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3 years ago

I need some help with this rational equation. It's supposed to = -1, but for some strange reason I keep getting x^2 +2x = -1.

1 answer:

7 0

This one is so easy that your brain refuses to accept it.
It's looking for a harder answer, but can't find it !

You're totally correct, as far you went.    x² + 2x does = -1

Now add ' 1 ' to each side:   x² + 2x + 1 = 0

Can you factor that quadratic ?
Can you mash it through the quadratic formula ?

Actually, it's the simplest possible perfect square.

   x² + 2x + 1 = (x + 1)²

So the solutions of   x² + 2x + 1 = 0 are both   x = -1 .

Don't say anything.
I know it's embarrassing.

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From a July 2019 survey of 1186 randomly selected Americans ages 18-29, it was discovered that 248 of them vaped (used an e-ciga

jasenka [17]

Answer:

The 90% confidence interval is (0.1897, 0.2285).

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 interval $1-\alpha$ , 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:

From a July 2019 survey of 1186 randomly selected Americans ages 18-29, it was discovered that 248 of them vaped (used an e-cigarette) in the past week. This means that $n = 1186, \pi = \frac{248}{1186} = 0.2091$

Construct a 90% confidence interval to estimate the population proportion of Americans age 18-29 who vaped in the past week.

So $\alpha = 0.10$ , z is the value of Z that has a pvalue of $1 - \frac{0.10}{2} = 0.95$ , so $z = 1.645$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2091 - 1.645\sqrt{\frac{0.2091*0.7909}{1186}} = 0.1897$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2091 + 1.645\sqrt{\frac{0.2091*0.7909}= 0.2285$

The 90% confidence interval is (0.1897, 0.2285).

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3 years ago

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Answer:

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Step-by-step explanation:

This is because y = arcsin x can be re-written as sin y = x, We then differentiate sin y = x implicitly with respect to z to obtain

d(siny)/dz = dx/dz

(cosy)dy/dz = dx/dz

dy/dz = (1/cosy)dx/dz

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2 years ago

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Aleks04 [339]

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