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olganol [36]
3 years ago
13

A polling company is trying to estimate the percentage of adults that consider themselves happy. A confidence interval based on

a sample size of 180 has a larger than desired margin of error. The company wants to conduct another poll and obtain another confidence interval of the same level but reduce the error to one-third the size of the original sample. How many adults should they now interview
Mathematics
1 answer:
Digiron [165]3 years ago
6 0

Answer:

They should interview 1620 adults now.

Step-by-step explanation:

Margin of error of a confidence interval:

The margin of error of a confidence interval has the following format:

M = z\frac{\sigma}{\sqrt{n}}

In which z is related to the confidence level, \sigma is the standard deviation of the population and n is the size of the sample.

In this question:

z wont change, neither will \sigma

We want to increase n as such the margin of error is reduced to one third.

We have that the margin of error is inversely proportional to the square root of the size of the sample, which means that for the margin of error to be reduced to one third, the sample size has to be multiplied by 3^2 = 9. So

180*9 = 1620

They should interview 1620 adults now.

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2b + 9x +(2 + 5).  

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4 0
3 years ago
What is this property 14-8=2x+8-8<br> 6=2x
Molodets [167]

Answer:

Distributive?

Step-by-step explanation:

The way the problem is laid out confuses me but if it is the problem that you laid out, it should be Distributive.

8 0
3 years ago
What is the equation of the circle with center (-3,1) that passes through the point (-5, 3)?
Natali5045456 [20]

Answer:

Option B) (x + 3)^2 + (y – 1)^2 = 8 is the correct answer.

Step-by-step explanation:

The equation of a circle with center (h,k) and radius r is given by:

(x-h)^2 + (y-k)^2 = r^2

Given

Center = (h,k) = (-3,1)

=> h = -3

=> k = 1

The distance between the center of circle and the point through which the circle passes will be the radius.

The distance formula is given by:

r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2

Given

(x_1,y_1) = (-3,1)\\(x_2,y_2) = (-5,3)

Putting the values in the formula

r = \sqrt{(-5+3)^2+(3-1)^2}\\r = \sqrt{(-2)^2+(2)^2}\\r = \sqrt{4+4}\\r = \sqrt{8}

Putting the values of h,k and r in general form of equation

\{x-(-3)}^2\} +(y-1)^2 = (\sqrt{8})^2\\(x+3)^2+(y-1)^2 = 8

Hence,

Option B) (x + 3)^2 + (y – 1)^2 = 8 is the correct answer.

4 0
3 years ago
In an aquarium,2/5 of fish are surgeon. Of these ,3/4 are yellow tangs.what fraction of all fish in the aquarium are yellow tang
hoa [83]
8 are surgeon, 15 are yellow tangs
8 0
3 years ago
Q 1 PLEASE HELP ME FIGURE THIS OUT 2
dimulka [17.4K]

Answer: \frac{\pi }{3}

<u>Step-by-step explanation:</u>

cot is \frac{cos}{sin} on the Unit Circle. When is cos = \frac{1}{2} and sin = \frac{\sqrt{3}} {2}?  In other words, where is the coordinate (\frac{1}{2},\frac{\sqrt{3}} {2}) on the Unit Circle?

It occurs at 60° = \frac{\pi }{3} radians

**************************************************************************************

Answer: cot θ

<u>Step-by-step explanation:</u>

  sec (90 - θ) * cos θ

= \frac{1}{cos (90 -\theta)} * cos θ

= \frac{cos\theta}{cos(90 - \theta)}

= \frac{cos\theta}{cos90*cos\theta+sin90*sin\theta}

= \frac{cos\theta}{0*cos\theta+1*sin\theta}

= \frac{cos\theta}{sin\theta}

= cot θ

**************************************************************************************

Answer: BC = √5, AC = 2√5

<u>Step-by-step explanation:</u>

\frac{\pi} {3} = 60°, which means ΔABC is a 30°-60°-90° triangle so we can use the side length formulas: x - x√3 - 2x.

∠C is the 60°. It matches to side AB so: AB = x√3 = √15   ⇒   x = √5

∠A is the 30°. It matches to side BC so: BC = x = √5

∠B is the 90°. It matches to side AC so: AC = 2x = 2(√5)  = 2√5

**************************************************************************************

Answer: k = 4, RS = 12, QS = 28

<u>Step-by-step explanation:</u>

\frac{QR}{MN} = \frac{RS}{NO}= \frac{QS}{MO}

\frac{24}{6} = \frac{RS}{3}= \frac{QS}{7}

proportionality constant k can be found with \frac{QR}{MN} = \frac{24}{6} = 4

\frac{QR}{MN} = \frac{RS}{NO}

→ 4 = \frac{RS}{3}

→ 4(3) = RS

→ 12 = RS

\frac{QR}{MN} = \frac{QS}{MO}

→ 4 = \frac{QS}{7}

→ 4(7) = QS

→ 28 = QS


3 0
3 years ago
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