<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B4%7D%20%20%2B%20%20%5Cfrac%7B1%7D%7B4%7D%20%20%2B%20x%20-%20%20%5Cfrac%7B3

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3 years ago

%7D%7B4%7D%20" id="TexFormula1" title=" \frac{1}{4} + \frac{1}{4} + x - \frac{3}{4} " alt=" \frac{1}{4} + \frac{1}{4} + x - \frac{3}{4} " align="absmiddle" class="latex-formula">

Mathematics

1 answer:

S_A_V [24]3 years ago

5 0

$\dfrac{1}{4}+\dfrac{1}{4}+x-\dfrac{3}{4}=\left(\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{3}{4}\right)+x=\dfrac{1+1-3}{4}+x=\dfrac{-1}{4}+x=x-\dfrac{1}{4}$

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Elderly drivers. In January 2011, The Marist Poll published a report stating that 66% of adults nationally think licensed driver

katrin [286]

Answer:

(a) Hence, the margin of error reported by The Marist Poll was correct.

(b) Based on a 95% confidence interval the poll does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65.

Step-by-step explanation:

We are given that the Marist Poll published a report stating that 66% of adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age.

It was also reported that interviews were conducted on 1,018 American adults, and that the margin of error was 3% using a 95% confidence level.

(a) <u>Margin of error formula is given by;</u>

Margin of Error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$

where, $\alpha$ = level of significance = 1 - 0.95 = 0.05 or 5%

Standard of error = $\sqrt{\frac{\hat p(1-\hat p)}{n} }$

Also, $\hat p$ = sample proportion of adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age = 66%

n = sample of American adults = 1.018

The critical value of z for level of significance of 2.5% is 1.96.

So, <em>Margin of Error </em>= $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$

= $1.96 \times \sqrt{\frac{0.66(1-0.66)}{1,018} }$ = 0.03 or 3%

Hence, the margin of error reported by The Marist Poll was correct.

(b) Now, the pivotal quantity for 95% confidence interval for the population proportion who think that licensed drivers should be required to retake their road test once they turn 65 is given by;

P.Q. = $\frac{\hat p-p}{ \sqrt{\frac{\hat p(1-\hat p)}{n} }}$ ~ N(0,1)

So, <u>95% confidence interval for p</u> = $\hat p \pm \text{Margin of error}$

= $0.66 \pm 0.03$

= [0.66 - 0.03 , 0.66 + 0.03]

= [0.63 , 0.69]

Hence, based on a 95% confidence interval the poll does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65 because the interval does not include the value of 70% or more.

7 0

3 years ago

What is the sequence of transformations that maps △ABC to △A′B′C′ ? Select from the drop-down menus to correctly identify each s

torisob [31]

<h3>Answer:</h3>

Any 1 of the following transformations will work. There are others that are also possible.

translation up 4 units, followed by rotation CCW by 90°.
rotation CCW by 90°, followed by translation left 4 units.
rotation CCW 90° about the center (-2, -2).

<h3>Step-by-step explanation:</h3>

The order of vertices ABC is clockwise, as is the order of vertices A'B'C'. Thus, if reflection is involved, there are two (or some other even number of) reflections.

The orientation of line CA is to the east. The orientation of line C'A' is to the north, so the figure has been rotated 90° CCW. In general, such rotation can be accomplished by a single transformation about a suitably chosen center. Here, we're told there is <em>a sequence of transformations</em> involved, so a single rotation is probably not of interest.

If we rotate the figure 90° CCW, we find it ends up 4 units east of the final position. So, one possible transformation is 90° CCW + translation left 4 units.

If we rotate the final figure 90° CW, we find it ends up 4 units north of the starting position. So, another possible transformation is translation up 4 units + rotation 90° CCW.

Of course, rotation 90° CCW in either case is the same as rotation 270° CW.

_____

We have described transformations that will work. What we don't know is what is in your drop-down menu lists. There are many other transformations that will also work, so guessing the one you have available is difficult.