1 point

Mathematics

1 answer:

galina1969 [7]3 years ago

3 0

Answer:

(B) 20

Step-by-step explanation:

Let small puppet be represented by-----------------s

Let large puppet be represented by-----------------l

Total number of puppets expression will be: s+l =25---------a

The expression for total costs will be : 1$ s + $2l=$30-------b

Equation a can be written as; s= 25-l ------------c

Use equation c in equation b as

$1( 25-l )+$ 2l = $30

25-l + 2l = 30

25+l =30

l= 30-25 =5

l, large puppets = 5

s, small puppets = 25-5 = 20

Answer choice A is incorrect because 25 is the total number of all puppets

Answer choice C and D are incorrect because the numbers are less that that of small puppets.

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The dwarves of the Grey Mountains wish to conduct a survey of their pick-axes in order to construct a 99% confidence interval ab

Dmitry_Shevchenko [17]

Answer:

The minimum sample size needed is 125.

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 is:

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

For this problem, we have that:

$\pi = 0.25$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

What minimum sample size would be necessary in order ensure a margin of error of 10 percentage points (or less) if they use the prior estimate that 25 percent of the pick-axes are in need of repair?

This minimum sample size is n.

n is found when $M = 0.1$