What is the scale factor of the dilation?

A survey is planned to estimate the proportion of voters who support a proposed gun control law. The estimate should be within a

laila [671]

Complete Question

A survey is planned to estimate the proportion of voters who support a proposed gun control law. The estimate should be within a margin of error of ±5% with 90% confidence, and we do not have any prior knowledge about the proportion who might support the law. How many people need to be included in the sample?

Round your answer up to the nearest integer.

sample size = _____

Answer:

The sample size is $n = 271$

Step-by-step explanation:

From the question we are told that

The margin of error is E = 5% = 0.05

Generally given that there was no prior knowledge about the proportion of who might support the law, we will assume the sample proportion to be

$\^ p = 0.5$

From the question we are told the confidence level is 90% , hence the level of significance is

$\alpha = (100 - 90 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the sample size is mathematically represented as

$n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p )$

=> $n = [\frac{1.645 }{0.05} ]^2 * 0.5 (1 - 0.5 )$

=> $n = 271$

5 0

2 years ago

2 The Skoblickis are building a new home. The scale

yanalaym [24]

The actual width of the room is 20 ft and the actual length of the room is 15 ft

Since on the scale, 2 in : 5 ft and the width of the room on the drawing is 8 in.

Let the actual width of the room is w.

The ratio of the drawing to actual width is 8 in : w

So, 2 in : 5 ft = 8 in : w

2 in/5 ft = 8 in/w

So, w = 8 in × 5 ft/2 in

w = 4 × 5 ft

w = 20 ft

Also, the length of the room on the drawing on the drawing is 6 in.

Let the actual length of the room is L.

The ratio of the drawing to actual length is 6 in : L

So, 2 in : 5 ft = 6 in : L

2 in/5 ft = 6 in/L

So, L = 6 in × 5 ft/2 in

L = 3 × 5 ft

L = 15 ft

So, the actual width of the room is 20 ft and the actual length of the room is 15 ft.

Learn more about scale drawing here:

brainly.com/question/25324744

4 0

2 years ago

Which of the following is(are) the solution(s) to |5x+2|=8

iren [92.7K]

Option A.

Hope it helps.

6 0

2 years ago

Read 2 more answers

Which of the following represents the cosine of 70 degrees

Westkost [7]

Using a calculator: cos 70 deg = 0.342. Note: it sounds as tho' you were given several answer options. Where are they?

6 0

3 years ago

If r = 4 and ^a8 = 100, what is the first term of the geometric sequence?

telo118 [61]

The first term of the geometric sequence is 0.0061

Step-by-step explanation:

The general form of geometric sequence is a, ar, ar²,ar³,.......

where,

a is the first term of the sequence.
r is the common ratio. Here, the common ratio r = 4.
The 8th term of the sequence is 100. Hence n = 8.

The formula to find the nth term of the geometric sequence is given by :

⇒ $n_{th} term = ar^{n-1}$

⇒ $8_{th}term = a\times4^{8-1}$

⇒ $100 = a \times 4^{7}$

⇒ $100 = a \times 16384$

⇒ $a = \frac{100}{16384}$

⇒ a = 0.0061

Therefore, the first term of the geometric sequence is 0.0061

6 0

2 years ago