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3 years ago

Which equation shows y = -1/2x + 4 is in standard form?

Mathematics

2 answers:

Scrat [10]3 years ago

4 0

For this case we have that by definition, the standard way to write the equation of a line, is given by:

$ax + by = c$

Where a, b and c are integers.

Given $y =-\frac{1}{2}x+ 4$

We can write it in the standard way:

$\frac{1}{2}x+ y = 4$

$a=\frac{1}{2}$ and by the previous definition, the numbers a, b and c must be integers.

Thus, we multiply the equation by 2, on both sides so as not to alter the equality.

$2*\frac{1}{2}x+ 2 * y= 2 * 4$

$x + 2y = 8$

Thus, the equation of $y =-\frac{1}{2}x+ 4$ , in its standard form is given by:

$x + 2y = 8$

Answer:

Option B

ohaa [14]3 years ago

3 0

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2 years ago

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

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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) Margin of error formula is given by;

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

= $1.96 \times \sqrt{\frac{0.66(1-0.66)}{1,018} }$ = 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, 95% confidence interval for p = $\hat p \pm \text{Margin of error}$

= $0.66 \pm 0.03$

= [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.

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3 years ago