Write an equivalent expression for 3(y-6)+4

My brother wants to estimate the proportion of Canadians who own their house.What sample size should be obtained if he wants the

AVprozaik [17]

Answer:

a) $n=\frac{0.675(1-0.675)}{(\frac{0.02}{1.64})^2}=1475.07$

And rounded up we have that n=1476

b) $n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.64})^2}=1681$

And rounded up we have that n=1681

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

If solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.9=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=\pm 1.64$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.02$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.675(1-0.675)}{(\frac{0.02}{1.64})^2}=1475.07$

And rounded up we have that n=1476

Part b

For this case since we don't have a prior estimate we can use $\hat p =0.5$

$n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.64})^2}=1681$

And rounded up we have that n=1681

8 0

3 years ago

Hello :) Please help me solve this Explain answer

USPshnik [31]

Answer:

$Scale\ Factor = \frac{1}{2}$

ABC dilated

Step-by-step explanation:

Given

Triangles ABC and DEF

Required

Determine the scale of dilation

First, we pick a side on ABC

$AB = 6$

Pick a corresponding side on DEF

$DE = 3$

The scale factor is then calculated as:

$Scale\ Factor = \frac{DE}{AB}$

$Scale\ Factor = \frac{1}{2}$

i.e. ABC was dilated by 1/2

5 0

3 years ago

For the circle, a 70° central angle cuts off an arc of 8 inches what is the circumference of the circle (there are 360° in a cir

Natalija [7]

There are 360° in a circle, now, this "sector" of the circle has an angle of 70°, so for 70°, there are 8in or circumference, or arc length

how much arc length or circumference in 360° then?

well $\bf \begin{array}{ccllll}
degrees&circumference\\
-----&--------\\
70&8\\
360&x
\end{array}\implies \cfrac{70}{360}=\cfrac{8}{x}$

solve for "x"

3 0

3 years ago

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Your friend is going to buy a used car. The one he is considering costs $4000 and will lose value at a rate of 13% per year. How

guapka [62]

13% of $4000 is $520
If the $4000 car loses value at a rate of 13% each year for 3 years
$520 x 3 = $1560
Subtract this amount from $4000
$4000 - $1560 = $2440

Answer: In 3 years, the used car will be worth $2440 in 3 years

6 0

2 years ago

What is the value of x in the diagram of Circle O below? *

Anestetic [448]

Answer:

60 degrees

Step-by-step explanation:

As we know that a circle is 360 degrees, and as line AB bisects the circle, then the resulting "semi-circle" is 180 degrees. As we know that angle AC is 120 degrees, it's simple subtraction, to find that 180-120 is 60. Therefore, the value of x must be 60 degrees.

Hope this explanation helped!

5 0

3 years ago

Read 2 more answers