How can 1,6,2,-4 equal 24

Mathematics

1 answer:

krek1111 [17]4 years ago

7 0

Answer: 1,6,2,-4 are equal to 24 because they all equal 24

Step-by-step explanation: 24x1=24, 6x4=24 and so on

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In a survey of randomly selected 3,900 family-owned businesses with revenues exceeding $1 million a year, it was found that 1,91

Maurinko [17]

Answer:

a) The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.

b) Wider

Step-by-step explanation:

Question a:

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

In a survey of randomly selected 3,900 family-owned businesses with revenues exceeding $1 million a year, it was found that 1,911 of them had no strategic business plan.

This means that $n = 3900, \pi = \frac{1911}{3900} = 0.49$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a p-value of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 - 1.645\sqrt{\frac{0.49*0.51}{3900}} = 0.4768$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 + 1.645\sqrt{\frac{0.49*0.51}{3900}} = 0.5032$

The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.

Question b:

The margin of error is:

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

The higher the confidence level, the higher the value of z, thus the higher the margin of error and the interval is wider. Thus, a 99% confidence interval is wider than a 90% confidence interval.

3 0

3 years ago

Lim ln(tan x) as tends to pi/2 from the left

ioda

Let $x=\arctan y$ . Then $\tan x=y$ , and so as $x\to\dfrac\pi2^-$ , you have $y\to+\infty$ . The limit is then equivalent to

$\displaystyle\lim_{x\to\frac\pi2^-}\ln(\tan x)=\lim_{y\to\infty}\ln y=\infty$